update
This commit is contained in:
Morten Hjorth-Jensen
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0 -> 1 [labeldistance=2.5, labelangle=45, headlabel="True"] ;
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2 [label="worst concave points <= 0.135\ngini = 0.031\nsamples = 253\nvalue = [[249, 4]\n[4, 249]]", fillcolor="#e78946"] ;
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1 -> 2 ;
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3 [label="radius error <= 0.643\ngini = 0.008\nsamples = 242\nvalue = [[241, 1]\n[1, 241]]", fillcolor="#e5833c"] ;
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3 [label="area error <= 48.975\ngini = 0.008\nsamples = 242\nvalue = [[241, 1]\n[1, 241]]", fillcolor="#e5833c"] ;
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2 -> 3 ;
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4 [label="gini = 0.0\nsamples = 239\nvalue = [[239, 0]\n[0, 239]]", fillcolor="#e58139"] ;
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3 -> 4 ;
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5 [label="mean smoothness <= 0.094\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ;
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5 [label="symmetry error <= 0.025\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ;
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3 -> 5 ;
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6 [label="gini = 0.0\nsamples = 2\nvalue = [[2, 0]\n[0, 2]]", fillcolor="#e58139"] ;
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6 [label="gini = 0.0\nsamples = 1\nvalue = [[0, 1]\n[1, 0]]", fillcolor="#e58139"] ;
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7 [label="gini = 0.0\nsamples = 1\nvalue = [[0, 1]\n[1, 0]]", fillcolor="#e58139"] ;
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7 [label="gini = 0.0\nsamples = 2\nvalue = [[2, 0]\n[0, 2]]", fillcolor="#e58139"] ;
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5 -> 7 ;
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8 [label="mean texture <= 20.84\ngini = 0.397\nsamples = 11\nvalue = [[8, 3]\n[3, 8]]", fillcolor="#fae9dd"] ;
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2 -> 8 ;
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@@ -30,11 +30,11 @@ edge [fontname="helvetica"] ;
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11 -> 13 ;
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14 [label="worst texture <= 20.645\ngini = 0.202\nsamples = 167\nvalue = [[19, 148]\n[148, 19]]", fillcolor="#f0b68c"] ;
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0 -> 14 [labeldistance=2.5, labelangle=-45, headlabel="False"] ;
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15 [label="worst perimeter <= 116.8\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#f9e3d4"] ;
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15 [label="worst concavity <= 0.318\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#f9e3d4"] ;
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14 -> 15 ;
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16 [label="gini = 0.0\nsamples = 11\nvalue = [[11, 0]\n[0, 11]]", fillcolor="#e58139"] ;
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15 -> 16 ;
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17 [label="mean smoothness <= 0.084\ngini = 0.32\nsamples = 5\nvalue = [[1, 4]\n[4, 1]]", fillcolor="#f6d5bd"] ;
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17 [label="area error <= 23.16\ngini = 0.32\nsamples = 5\nvalue = [[1, 4]\n[4, 1]]", fillcolor="#f6d5bd"] ;
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18 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ;
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@@ -42,13 +42,13 @@ edge [fontname="helvetica"] ;
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20 [label="mean concave points <= 0.049\ngini = 0.088\nsamples = 151\nvalue = [[7, 144]\n[144, 7]]", fillcolor="#ea985d"] ;
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14 -> 20 ;
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21 [label="compactness error <= 0.016\ngini = 0.48\nsamples = 15\nvalue = [[6, 9]\n[9, 6]]", fillcolor="#ffffff"] ;
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21 [label="concave points error <= 0.01\ngini = 0.48\nsamples = 15\nvalue = [[6, 9]\n[9, 6]]", fillcolor="#ffffff"] ;
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22 [label="gini = 0.0\nsamples = 9\nvalue = [[0, 9]\n[9, 0]]", fillcolor="#e58139"] ;
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23 [label="gini = 0.0\nsamples = 6\nvalue = [[6, 0]\n[0, 6]]", fillcolor="#e58139"] ;
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21 -> 23 ;
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24 [label="worst smoothness <= 0.096\ngini = 0.015\nsamples = 136\nvalue = [[1, 135]\n[135, 1]]", fillcolor="#e6853f"] ;
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24 [label="mean smoothness <= 0.079\ngini = 0.015\nsamples = 136\nvalue = [[1, 135]\n[135, 1]]", fillcolor="#e6853f"] ;
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25 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ;
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@@ -0,0 +1,717 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Exercises week 43\n",
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"\n",
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"**October 18-25, 2024**\n",
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"\n",
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"Date: **Deadline is Friday October 25 at midnight**\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Overarching aims of the exercises this week\n",
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"\n",
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"The aim of the exercises this week is to train the neural network you implemented last week.\n",
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"\n",
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"To train neural networks, we use gradient descent, since there is no analytical expression for the optimal parameters. This means you will need to compute the gradient of the cost function wrt. the network parameters. And then you will need to implement some gradient method.\n",
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"\n",
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"You will begin by computing gradients for a network with one layer, then two layers, then any number of layers. Keeping track of the shapes and doing things step by step will be very important this week.\n",
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"\n",
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"We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the neural network correctly, and running small parts of the code at a time will be important for understanding the methods. If you have trouble running a notebook, you can run this notebook in google colab instead(https://colab.research.google.com/drive/1FfvbN0XlhV-lATRPyGRTtTBnJr3zNuHL#offline=true&sandboxMode=true), though we recommend that you set up VSCode and your python environment to run code like this locally.\n",
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"\n",
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"First, some setup code that you will need.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"import autograd.numpy as np # We need to use this numpy wrapper to make automatic differentiation work later\n",
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"from autograd import grad, elementwise_grad\n",
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"from sklearn import datasets\n",
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"import matplotlib.pyplot as plt\n",
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"from sklearn.metrics import accuracy_score\n",
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"\n",
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"\n",
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"# Defining some activation functions\n",
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"def ReLU(z):\n",
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" return np.where(z > 0, z, 0)\n",
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"\n",
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"\n",
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"# Derivative of the ReLU function\n",
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"def ReLU_der(z):\n",
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" return np.where(z > 0, 1, 0)\n",
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"\n",
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"\n",
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"def sigmoid(z):\n",
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" return 1 / (1 + np.exp(-z))\n",
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"\n",
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"\n",
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"def mse(predict, target):\n",
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" return np.mean((predict - target) ** 2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Exercise 1 - Understand the feed forward pass\n",
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"\n",
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"**a)** Complete last weeks' mandatory exercises if you haven't already.\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Exercise 2 - Gradient with one layer using autograd\n",
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"\n",
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"For the first few exercises, we will not use batched inputs. Only a single input vector is passed through the layer at a time.\n",
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"\n",
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"In this exercise you will compute the gradient of a single layer. You only need to change the code in the cells right below an exercise, the rest works out of the box. Feel free to make changes and see how stuff works though!\n"
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]
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},
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{
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"cell_type": "markdown",
|
||||
"metadata": {},
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||||
"source": [
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"**a)** If the weights and bias of a layer has shapes (10, 4) and (10), what will the shapes of the gradients of the cost function wrt. these weights and this bias be?\n"
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]
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},
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{
|
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"cell_type": "markdown",
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||||
"metadata": {},
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"source": [
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"**b)** Complete the feed_forward_one_layer function. It should use the sigmoid activation function. Also define the weigth and bias with the correct shapes.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 41,
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"metadata": {},
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"outputs": [],
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"source": [
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"def feed_forward_one_layer(W, b, x):\n",
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" z = ...\n",
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" a = ...\n",
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" return a\n",
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"\n",
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"\n",
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"def cost_one_layer(W, b, x, target):\n",
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" predict = feed_forward_one_layer(W, b, x)\n",
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" return mse(predict, target)\n",
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"\n",
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"\n",
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"x = np.random.rand(2)\n",
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"target = np.random.rand(3)\n",
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"\n",
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"W = ...\n",
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"b = ..."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**c)** Compute the gradient of the cost function wrt. the weigth and bias by running the cell below. You will not need to change anything, just make sure it runs by defining things correctly in the cell above. This code uses the autograd package which uses backprogagation to compute the gradient!\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"autograd_one_layer = grad(cost_one_layer, [0, 1])\n",
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"W_g, b_g = autograd_one_layer(W, b, x, target)\n",
|
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"print(W_g, b_g)"
|
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]
|
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},
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{
|
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"cell_type": "markdown",
|
||||
"metadata": {},
|
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"source": [
|
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"# Exercise 3 - Gradient with one layer writing backpropagation by hand\n",
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"\n",
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"Before you use the gradient you found using autograd, you will have to find the gradient \"manually\", to better understand how the backpropagation computation works. To do backpropagation \"manually\", you will need to write out expressions for many derivatives along the computation.\n"
|
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]
|
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},
|
||||
{
|
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"cell_type": "markdown",
|
||||
"metadata": {},
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"source": [
|
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"We want to find the gradient of the cost function wrt. the weight and bias. This is quite hard to do directly, so we instead use the chain rule to combine multiple derivatives which are easier to compute.\n",
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"\n",
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"$$\n",
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"\\frac{dC}{dW} = \\frac{dC}{da}\\frac{da}{dz}\\frac{dz}{dW}\n",
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"$$\n",
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"\n",
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"$$\n",
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"\\frac{dC}{db} = \\frac{dC}{da}\\frac{da}{dz}\\frac{dz}{db}\n",
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"$$\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"**a)** Which intermediary results can be reused between the two expressions?\n"
|
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]
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},
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{
|
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"cell_type": "markdown",
|
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"metadata": {},
|
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"source": [
|
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"**b)** What is the derivative of the cost wrt. the final activation? You can use the autograd calculation to make sure you get the correct result. Remember that we compute the mean in mse.\n"
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]
|
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},
|
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{
|
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"cell_type": "code",
|
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"execution_count": null,
|
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"metadata": {},
|
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"outputs": [],
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"source": [
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"z = W @ x + b\n",
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"a = sigmoid(z)\n",
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"\n",
|
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"predict = a\n",
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"\n",
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"\n",
|
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"def mse_der(predict, target):\n",
|
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" return ...\n",
|
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"\n",
|
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"\n",
|
||||
"print(mse_der(predict, target))\n",
|
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"\n",
|
||||
"cost_autograd = grad(mse, 0)\n",
|
||||
"print(cost_autograd(predict, target))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**c)** What is the expression for the derivative of the sigmoid activation function? You can use the autograd calculation to make sure you get the correct result.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
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"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def sigmoid_der(z):\n",
|
||||
" return ...\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"print(sigmoid_der(z))\n",
|
||||
"\n",
|
||||
"sigmoid_autograd = elementwise_grad(sigmoid, 0)\n",
|
||||
"print(sigmoid_autograd(z))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**d)** Using the two derivatives you just computed, compute this intermetidary gradient you will use later:\n",
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"\n",
|
||||
"$$\n",
|
||||
"\\frac{dC}{dz} = \\frac{dC}{da}\\frac{da}{dz}\n",
|
||||
"$$\n"
|
||||
]
|
||||
},
|
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{
|
||||
"cell_type": "code",
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"execution_count": 54,
|
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"metadata": {},
|
||||
"outputs": [],
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"source": [
|
||||
"dC_da = ...\n",
|
||||
"dC_dz = ..."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
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||||
"source": [
|
||||
"**e)** What is the derivative of the intermediary z wrt. the weight and bias? What should the shapes be? The one for the weights is a little tricky, it can be easier to play around in the next exercise first. You can also try computing it with autograd to get a hint.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**f)** Now combine the expressions you have worked with so far to compute the gradients! Note that you always need to do a feed forward pass while saving the zs and as before you do backpropagation, as they are used in the derivative expressions\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
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"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
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||||
"source": [
|
||||
"dC_da = ...\n",
|
||||
"dC_dz = ...\n",
|
||||
"dC_dW = ...\n",
|
||||
"dC_db = ...\n",
|
||||
"\n",
|
||||
"print(dC_dW, dC_db)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"You should get the same results as with autograd.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"W_g, b_g = autograd_one_layer(W, b, x, target)\n",
|
||||
"print(W_g, b_g)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Exercise 4 - Gradient with two layers writing backpropagation by hand\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Now that you have implemented backpropagation for one layer, you have found most of the expressions you will need for more layers. Let's move up to two layers.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 59,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"x = np.random.rand(2)\n",
|
||||
"target = np.random.rand(4)\n",
|
||||
"\n",
|
||||
"W1 = np.random.rand(3, 2)\n",
|
||||
"b1 = np.random.rand(3)\n",
|
||||
"\n",
|
||||
"W2 = np.random.rand(4, 3)\n",
|
||||
"b2 = np.random.rand(4)\n",
|
||||
"\n",
|
||||
"layers = [(W1, b1), (W2, b2)]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 60,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"z1 = W1 @ x + b1\n",
|
||||
"a1 = sigmoid(z1)\n",
|
||||
"z2 = W2 @ a1 + b2\n",
|
||||
"a2 = sigmoid(z2)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We begin by computing the gradients of the last layer, as the gradients must be propagated backwards from the end.\n",
|
||||
"\n",
|
||||
"**a)** Compute the gradients of the last layer, just like you did the single layer in the previous exercise.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 61,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"dC_da2 = ...\n",
|
||||
"dC_dz2 = ...\n",
|
||||
"dC_dW2 = ...\n",
|
||||
"dC_db2 = ..."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"To find the derivative of the cost wrt. the activation of the first layer, we need a new expression, the one furthest to the right in the following.\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\frac{dC}{da_1} = \\frac{dC}{dz_2}\\frac{dz_2}{da_1}\n",
|
||||
"$$\n",
|
||||
"\n",
|
||||
"**b)** What is the derivative of the second layer intermetiate wrt. the first layer activation? (First recall how you compute $z_2$)\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\frac{dz_2}{da_1}\n",
|
||||
"$$\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**c)** Use this expression, together with expressions which are equivelent to ones for the last layer to compute all the derivatives of the first layer.\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\frac{dC}{dW_1} = \\frac{dC}{da_1}\\frac{da_1}{dz_1}\\frac{dz_1}{dW_1}\n",
|
||||
"$$\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\frac{dC}{db_1} = \\frac{dC}{da_1}\\frac{da_1}{dz_1}\\frac{dz_1}{db_1}\n",
|
||||
"$$\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 63,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"dC_da1 = ...\n",
|
||||
"dC_dz1 = ...\n",
|
||||
"dC_dW1 = ...\n",
|
||||
"dC_db1 = ..."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"print(dC_dW1, dC_db1)\n",
|
||||
"print(dC_dW2, dC_db2)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**d)** Make sure you got the same gradient as the following code which uses autograd to do backpropagation.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 67,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def feed_forward_two_layers(layers, x):\n",
|
||||
" W1, b1 = layers[0]\n",
|
||||
" z1 = W1 @ x + b1\n",
|
||||
" a1 = sigmoid(z1)\n",
|
||||
"\n",
|
||||
" W2, b2 = layers[1]\n",
|
||||
" z2 = W2 @ a1 + b2\n",
|
||||
" a2 = sigmoid(z2)\n",
|
||||
"\n",
|
||||
" return a2"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def cost_two_layers(layers, x, target):\n",
|
||||
" predict = feed_forward_two_layers(layers, x)\n",
|
||||
" return mse(predict, target)\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"grad_two_layers = grad(cost_two_layers, 0)\n",
|
||||
"grad_two_layers(layers, x, target)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**e)** How would you use the gradient from this layer to compute the gradient of an even earlier layer? Would the expressions be any different?\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Exercise 5 - Gradient with any number of layers writing backpropagation by hand\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Well done on getting this far! Now it's time to compute the gradient with any number of layers.\n",
|
||||
"\n",
|
||||
"First, some code from the general neural network code from last week. Note that we are still sending in one input vector at a time. We will change it to use batched inputs later.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def create_layers(network_input_size, layer_output_sizes):\n",
|
||||
" layers = []\n",
|
||||
"\n",
|
||||
" i_size = network_input_size\n",
|
||||
" for layer_output_size in layer_output_sizes:\n",
|
||||
" W = np.random.randn(layer_output_size, i_size)\n",
|
||||
" b = np.random.randn(layer_output_size)\n",
|
||||
" layers.append((W, b))\n",
|
||||
"\n",
|
||||
" i_size = layer_output_size\n",
|
||||
" return layers\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def feed_forward(input, layers, activation_funcs):\n",
|
||||
" a = input\n",
|
||||
" for (W, b), activation_func in zip(layers, activation_funcs):\n",
|
||||
" z = W @ a + b\n",
|
||||
" a = activation_func(z)\n",
|
||||
" return a\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def cost(layers, input, activation_funcs, target):\n",
|
||||
" predict = feed_forward(input, layers, activation_funcs)\n",
|
||||
" return mse(predict, target)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"You might have already have noticed a very important detail in backpropagation: You need the values from the forward pass to compute all the gradients! The feed forward method above is great for efficiency and for using autograd, as it only cares about computing the final output, but now we need to also save the results along the way.\n",
|
||||
"\n",
|
||||
"Here is a function which does that for you.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def feed_forward_saver(input, layers, activation_funcs):\n",
|
||||
" layer_inputs = []\n",
|
||||
" zs = []\n",
|
||||
" a = input\n",
|
||||
" for (W, b), activation_func in zip(layers, activation_funcs):\n",
|
||||
" layer_inputs.append(a)\n",
|
||||
" z = W @ a + b\n",
|
||||
" a = activation_func(z)\n",
|
||||
"\n",
|
||||
" zs.append(z)\n",
|
||||
"\n",
|
||||
" return layer_inputs, zs, a"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**a)** Now, complete the backpropagation function so that it returns the gradient of the cost function wrt. all the weigths and biases. Use the autograd calculation below to make sure you get the correct answer.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def backpropagation(\n",
|
||||
" input, layers, activation_funcs, target, activation_ders, cost_der=mse_der\n",
|
||||
"):\n",
|
||||
" layer_inputs, zs, predict = feed_forward_saver(input, layers, activation_funcs)\n",
|
||||
"\n",
|
||||
" layer_grads = [() for layer in layers]\n",
|
||||
"\n",
|
||||
" # We loop over the layers, from the last to the first\n",
|
||||
" for i in reversed(range(len(layers))):\n",
|
||||
" layer_input, z, activation_der = layer_inputs[i], zs[i], activation_ders[i]\n",
|
||||
"\n",
|
||||
" if i == len(layers) - 1:\n",
|
||||
" # For last layer we use cost derivative as dC_da(L) can be computed directly\n",
|
||||
" dC_da = ...\n",
|
||||
" else:\n",
|
||||
" # For other layers we build on previous z derivative, as dC_da(i) = dC_dz(i+1) * dz(i+1)_da(i)\n",
|
||||
" (W, b) = layers[i + 1]\n",
|
||||
" dC_da = ...\n",
|
||||
"\n",
|
||||
" dC_dz = ...\n",
|
||||
" dC_dW = ...\n",
|
||||
" dC_db = ...\n",
|
||||
"\n",
|
||||
" layer_grads[i] = (dC_dW, dC_db)\n",
|
||||
"\n",
|
||||
" return layer_grads"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"network_input_size = 2\n",
|
||||
"layer_output_sizes = [3, 4]\n",
|
||||
"activation_funcs = [sigmoid, ReLU]\n",
|
||||
"activation_ders = [sigmoid_der, ReLU_der]\n",
|
||||
"\n",
|
||||
"layers = create_layers(network_input_size, layer_output_sizes)\n",
|
||||
"\n",
|
||||
"x = np.random.rand(network_input_size)\n",
|
||||
"target = np.random.rand(4)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"layer_grads = backpropagation(x, layers, activation_funcs, target, activation_ders)\n",
|
||||
"print(layer_grads)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"cost_grad = grad(cost, 0)\n",
|
||||
"cost_grad(layers, x, [sigmoid, ReLU], target)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Exercise 6 - Batched inputs\n",
|
||||
"\n",
|
||||
"Make new versions of all the functions in exercise 5 which now take batched inputs instead. See last weeks exercise 5 for details on how to batch inputs to neural networks. You will also need to update the backpropogation function.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Exercise 7 - Training\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**a)** Complete exercise 6 and 7 from last week, but use your own backpropogation implementation to compute the gradient.\n",
|
||||
"\n",
|
||||
"**b)** Use stochastic gradient descent with momentum when you train your network.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Exercise 8 (Optional) - Object orientation\n",
|
||||
"\n",
|
||||
"Passing in the layers, activations functions, activation derivatives and cost derivatives into the functions each time leads to code which is easy to understand in isoloation, but messier when used in a larger context with data splitting, data scaling, gradient methods and so forth. Creating an object which stores these values can lead to code which is much easier to use.\n",
|
||||
"\n",
|
||||
"**a)** Write a neural network class. You are free to implement it how you see fit, though we strongly recommend to not save any input or output values as class attributes, nor let the neural network class handle gradient methods internally. Gradient methods should be handled outside, by performing general operations on the layer_grads list using functions or classes separate to the neural network.\n",
|
||||
"\n",
|
||||
"We provide here a skeleton structure which should get you started.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"class NeuralNetwork:\n",
|
||||
" def __init__(\n",
|
||||
" self,\n",
|
||||
" network_input_size,\n",
|
||||
" layer_output_sizes,\n",
|
||||
" activation_funcs,\n",
|
||||
" activation_ders,\n",
|
||||
" cost_fun,\n",
|
||||
" cost_der,\n",
|
||||
" ):\n",
|
||||
" pass\n",
|
||||
"\n",
|
||||
" def predict(self, inputs):\n",
|
||||
" # Simple feed forward pass\n",
|
||||
" pass\n",
|
||||
"\n",
|
||||
" def cost(self, inputs, targets):\n",
|
||||
" pass\n",
|
||||
"\n",
|
||||
" def _feed_forward_saver(self, inputs):\n",
|
||||
" pass\n",
|
||||
"\n",
|
||||
" def compute_gradient(self, inputs, targets):\n",
|
||||
" pass\n",
|
||||
"\n",
|
||||
" def update_weights(self, layer_grads):\n",
|
||||
" pass\n",
|
||||
"\n",
|
||||
" # These last two methods are not needed in the project, but they can be nice to have! The first one has a layers parameter so that you can use autograd on it\n",
|
||||
" def autograd_compliant_predict(self, layers, inputs):\n",
|
||||
" pass\n",
|
||||
"\n",
|
||||
" def autograd_gradient(self, inputs, targets):\n",
|
||||
" pass"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": ".venv",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.12.7"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 2
|
||||
}
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -850,7 +855,9 @@ classification.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(426, 30)
|
||||
(143, 30)
|
||||
Test set accuracy with Logistic Regression: 0.94
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Test set accuracy with Logistic Regression: 0.94
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):
|
||||
@@ -990,9 +997,6 @@ applications. This will be discussed later this semester (<a class="reference ex
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(426, 30)
|
||||
(143, 30)
|
||||
[1. 0.86666667 1. 0.85714286 1. 0.85714286
|
||||
1. 0.92857143 0.92857143 1. ]
|
||||
Test set accuracy with Logistic Regression: 0.94
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):
|
||||
@@ -1085,9 +1089,14 @@ Please also refer to the documentation for alternative solver options:
|
||||
n_iter_i = _check_optimize_result(
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/additionweek42_50_2.png" src="_images/additionweek42_50_2.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[1. 0.86666667 1. 0.85714286 1. 0.85714286
|
||||
1. 0.92857143 0.92857143 1. ]
|
||||
Test set accuracy with Logistic Regression: 0.94
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/additionweek42_50_3.png" src="_images/additionweek42_50_3.png" />
|
||||
<img alt="_images/additionweek42_50_4.png" src="_images/additionweek42_50_4.png" />
|
||||
<img alt="_images/additionweek42_50_5.png" src="_images/additionweek42_50_5.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1076,11 +1081,11 @@ example of the functionality of <strong>Scikit-Learn</strong>.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The intercept alpha:
|
||||
[2.0412828]
|
||||
[1.97438607]
|
||||
Coefficient beta :
|
||||
[[4.99449129]]
|
||||
Mean squared error: 0.27
|
||||
Variance score: 0.89
|
||||
[[5.01837528]]
|
||||
Mean squared error: 0.24
|
||||
Variance score: 0.91
|
||||
Mean squared log error: 0.01
|
||||
Mean absolute error: 0.41
|
||||
</pre></div>
|
||||
@@ -1182,7 +1187,7 @@ a linear <span class="math notranslate nohighlight">\(x\)</span>-dependence we s
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<img alt="_images/chapter1_33_0.png" src="_images/chapter1_33_0.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.004999999999999989
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.005000000000000009
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1393,7 +1398,7 @@ the <em>Hadamard product</em>, meaning element-wise multiplication.</p>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Old accuracy on training data: 0.1440501043841336
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1727,7 +1732,7 @@ Lambda = 10.0
|
||||
Accuracy score on test set: 0.19166666666666668
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1736,7 +1741,7 @@ Lambda = 1e-05
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1745,7 +1750,7 @@ Lambda = 0.0001
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1754,7 +1759,7 @@ Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1763,7 +1768,7 @@ Lambda = 0.01
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1772,7 +1777,7 @@ Lambda = 0.1
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1781,7 +1786,7 @@ Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1790,11 +1795,11 @@ Lambda = 10.0
|
||||
Accuracy score on test set: 0.09166666666666666
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1803,11 +1808,11 @@ Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1816,156 +1821,37 @@ Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94023/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||||
<span class="ne">KeyboardInterrupt</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||||
<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">8</span><span class="p">],</span> <span class="n">line</span> <span class="mi">11</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">lmbd</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">lmbd_vals</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">dnn</span> <span class="o">=</span> <span class="n">NeuralNetwork</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train_onehot</span><span class="p">,</span> <span class="n">eta</span><span class="o">=</span><span class="n">eta</span><span class="p">,</span> <span class="n">lmbd</span><span class="o">=</span><span class="n">lmbd</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="n">epochs</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">10</span> <span class="n">n_hidden_neurons</span><span class="o">=</span><span class="n">n_hidden_neurons</span><span class="p">,</span> <span class="n">n_categories</span><span class="o">=</span><span class="n">n_categories</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">11</span> <span class="n">dnn</span><span class="o">.</span><span class="n">train</span><span class="p">()</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">13</span> <span class="n">DNN_numpy</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dnn</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">15</span> <span class="n">test_predict</span> <span class="o">=</span> <span class="n">dnn</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">Cell In[6], line 99,</span> in <span class="ni">NeuralNetwork.train</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">96</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data_full</span><span class="p">[</span><span class="n">chosen_datapoints</span><span class="p">]</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">98</span> <span class="bp">self</span><span class="o">.</span><span class="n">feed_forward</span><span class="p">()</span>
|
||||
<span class="ne">---> </span><span class="mi">99</span> <span class="bp">self</span><span class="o">.</span><span class="n">backpropagation</span><span class="p">()</span>
|
||||
|
||||
<span class="nn">Cell In[6], line 64,</span> in <span class="ni">NeuralNetwork.backpropagation</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">61</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_weights_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a_h</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">error_output</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">62</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_bias_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">error_output</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">64</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_weights_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">X_data</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">error_hidden</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">65</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_bias_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">error_hidden</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">67</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">lmbd</span> <span class="o">></span> <span class="mf">0.0</span><span class="p">:</span>
|
||||
|
||||
<span class="ne">KeyboardInterrupt</span>:
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2011,22 +1897,6 @@ Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87222/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter10_59_1.png" src="_images/chapter10_59_1.png" />
|
||||
<img alt="_images/chapter10_59_2.png" src="_images/chapter10_59_2.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="scikit-learn-implementation">
|
||||
@@ -2062,329 +1932,6 @@ performance overall.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.18333333333333332
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.18611111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.13055555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.24444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.23333333333333334
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.12777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.1527777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9111111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.8305555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8944444444444445
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.975
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9722222222222222
|
||||
|
||||
Learning rate = 0.01
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9527777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9027777777777778
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8583333333333333
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9055555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8666666666666667
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.17777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.08333333333333333
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.17222222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.11666666666666667
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.1388888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.11388888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="id1">
|
||||
@@ -2428,10 +1975,6 @@ Accuracy score on test set: 0.09444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<img alt="_images/chapter10_63_0.png" src="_images/chapter10_63_0.png" />
|
||||
<img alt="_images/chapter10_63_1.png" src="_images/chapter10_63_1.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="building-neural-networks-in-tensorflow-and-keras">
|
||||
@@ -2470,14 +2013,6 @@ and/or if you use <strong>anaconda</strong>, just write (or install from the gra
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span> <span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">12</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
|
||||
<span class="n">conda</span> <span class="n">create</span> <span class="o">-</span><span class="n">n</span> <span class="n">tf</span> <span class="n">tensorflow</span>
|
||||
<span class="o">^</span>
|
||||
<span class="ne">SyntaxError</span>: invalid syntax
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>To install the current release of GPU TensorFlow</p>
|
||||
<div class="cell docutils container">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1325,10 +1330,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.1982973034395375
|
||||
3.328462040651484
|
||||
[[ 1.08036056 3.23565337]
|
||||
[ 3.23565337 10.80845707]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.06291984474217532
|
||||
4.095077148135215
|
||||
[[0.8942779 2.56719397]
|
||||
[2.56719397 8.13485566]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1365,10 +1370,10 @@ a more brute force way. Here we scale the mean values for each column of the des
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08154221680664263
|
||||
2.12282958127703
|
||||
[[1. 0.6177137]
|
||||
[0.6177137 1. ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07603598322691016
|
||||
1.4323043635926456
|
||||
[[1. 0.58435095]
|
||||
[0.58435095 1. ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1398,30 +1403,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 0.14690374 -1.08896995]
|
||||
[-0.14465374 -0.8889085 ]
|
||||
[-0.01877081 0.85085928]
|
||||
[-0.20536579 -1.03613164]
|
||||
[ 0.28162714 0.25445 ]
|
||||
[-0.25588843 -2.27916593]
|
||||
[-0.11479519 -0.41788797]
|
||||
[ 0.19483625 1.37363888]
|
||||
[-0.03282533 0.94863824]
|
||||
[ 0.14893216 2.28347758]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-1.2105986 -2.92044261]
|
||||
[-0.59585933 -2.0072114 ]
|
||||
[-0.7336627 -1.27166993]
|
||||
[ 0.50493371 0.54649725]
|
||||
[-0.76911228 -2.66017222]
|
||||
[ 0.70843895 3.92226956]
|
||||
[ 0.61516316 2.7399476 ]
|
||||
[ 0.3114655 -0.76958689]
|
||||
[ 1.49817031 3.74791021]
|
||||
[-0.32893873 -1.32754157]]
|
||||
0 1
|
||||
0 0.146904 -1.088970
|
||||
1 -0.144654 -0.888908
|
||||
2 -0.018771 0.850859
|
||||
3 -0.205366 -1.036132
|
||||
4 0.281627 0.254450
|
||||
5 -0.255888 -2.279166
|
||||
6 -0.114795 -0.417888
|
||||
7 0.194836 1.373639
|
||||
8 -0.032825 0.948638
|
||||
9 0.148932 2.283478
|
||||
0 -1.210599 -2.920443
|
||||
1 -0.595859 -2.007211
|
||||
2 -0.733663 -1.271670
|
||||
3 0.504934 0.546497
|
||||
4 -0.769112 -2.660172
|
||||
5 0.708439 3.922270
|
||||
6 0.615163 2.739948
|
||||
7 0.311466 -0.769587
|
||||
8 1.498170 3.747910
|
||||
9 -0.328939 -1.327542
|
||||
0 1
|
||||
0 1.000000 0.631471
|
||||
1 0.631471 1.000000
|
||||
0 1.000000 0.915842
|
||||
1 0.915842 1.000000
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1478,37 +1483,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
|
||||
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.0 0.072263 0.073863 0.075238 0.072577 0.069597 0.068931 0.065674
|
||||
2 0.0 0.073863 0.076665 0.078474 0.076248 0.073525 0.072653 0.069507
|
||||
3 0.0 0.075238 0.078474 0.083331 0.081232 0.078589 0.079443 0.076163
|
||||
4 0.0 0.072577 0.076248 0.081232 0.079487 0.077139 0.077899 0.074866
|
||||
5 0.0 0.069597 0.073525 0.078589 0.077139 0.075058 0.075761 0.072967
|
||||
6 0.0 0.068931 0.072653 0.079443 0.077899 0.075761 0.077837 0.074911
|
||||
7 0.0 0.065674 0.069507 0.076163 0.074866 0.072967 0.074911 0.072226
|
||||
8 0.0 0.062481 0.066354 0.072859 0.071774 0.070087 0.071919 0.069457
|
||||
9 0.0 0.059398 0.063264 0.069606 0.068701 0.067204 0.068939 0.066680
|
||||
10 0.0 0.061779 0.065469 0.073182 0.072011 0.070273 0.073144 0.070581
|
||||
11 0.0 0.058670 0.062345 0.069785 0.068797 0.067249 0.069948 0.067597
|
||||
12 0.0 0.055715 0.059348 0.066520 0.065690 0.064311 0.066854 0.064699
|
||||
13 0.0 0.052918 0.056491 0.063401 0.062709 0.061482 0.063883 0.061907
|
||||
14 0.0 0.050281 0.053781 0.060435 0.059864 0.058774 0.061045 0.059233
|
||||
1 0.0 0.083046 0.078912 0.083582 0.082947 0.081772 0.074931 0.074984
|
||||
2 0.0 0.078912 0.078913 0.075718 0.076758 0.077825 0.065957 0.066785
|
||||
3 0.0 0.083582 0.075718 0.089055 0.086655 0.083266 0.082876 0.082018
|
||||
4 0.0 0.082947 0.076758 0.086655 0.085096 0.082753 0.079657 0.079265
|
||||
5 0.0 0.081772 0.077825 0.083266 0.082753 0.081750 0.075343 0.075494
|
||||
6 0.0 0.074931 0.065957 0.082876 0.079657 0.075343 0.079164 0.077785
|
||||
7 0.0 0.074984 0.066785 0.082018 0.079265 0.075494 0.077785 0.076698
|
||||
8 0.0 0.074979 0.067759 0.080910 0.078709 0.075600 0.076076 0.075321
|
||||
9 0.0 0.074820 0.068872 0.079393 0.077861 0.075576 0.073869 0.073497
|
||||
10 0.0 0.066329 0.057411 0.075255 0.071789 0.067261 0.073246 0.071643
|
||||
11 0.0 0.066412 0.057907 0.074831 0.071648 0.067437 0.072501 0.071093
|
||||
12 0.0 0.066546 0.058532 0.074371 0.071511 0.067667 0.071672 0.070480
|
||||
13 0.0 0.066707 0.059294 0.073827 0.071341 0.067930 0.070701 0.069750
|
||||
14 0.0 0.066858 0.060197 0.073125 0.071081 0.068193 0.069506 0.068828
|
||||
|
||||
8 9 10 11 12 13 14
|
||||
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.062481 0.059398 0.061779 0.058670 0.055715 0.052918 0.050281
|
||||
2 0.066354 0.063264 0.065469 0.062345 0.059348 0.056491 0.053781
|
||||
3 0.072859 0.069606 0.073182 0.069785 0.066520 0.063401 0.060435
|
||||
4 0.071774 0.068701 0.072011 0.068797 0.065690 0.062709 0.059864
|
||||
5 0.070087 0.067204 0.070273 0.067249 0.064311 0.061482 0.058774
|
||||
6 0.071919 0.068939 0.073144 0.069948 0.066854 0.063883 0.061045
|
||||
7 0.069457 0.066680 0.070581 0.067597 0.064699 0.061907 0.059233
|
||||
8 0.066896 0.064314 0.067935 0.065156 0.062446 0.059827 0.057312
|
||||
9 0.064314 0.061915 0.065282 0.062695 0.060163 0.057711 0.055349
|
||||
10 0.067935 0.065282 0.069784 0.066877 0.064054 0.061333 0.058726
|
||||
11 0.065156 0.062695 0.066877 0.064176 0.061545 0.059003 0.056561
|
||||
12 0.062446 0.060163 0.064054 0.061545 0.059093 0.056718 0.054432
|
||||
13 0.059827 0.057711 0.061333 0.059003 0.056718 0.054500 0.052360
|
||||
14 0.057312 0.055349 0.058726 0.056561 0.054432 0.052360 0.050357
|
||||
1 0.074979 0.074820 0.066329 0.066412 0.066546 0.066707 0.066858
|
||||
2 0.067759 0.068872 0.057411 0.057907 0.058532 0.059294 0.060197
|
||||
3 0.080910 0.079393 0.075255 0.074831 0.074371 0.073827 0.073125
|
||||
4 0.078709 0.077861 0.071789 0.071648 0.071511 0.071341 0.071081
|
||||
5 0.075600 0.075576 0.067261 0.067437 0.067667 0.067930 0.068193
|
||||
6 0.076076 0.073869 0.073246 0.072501 0.071672 0.070701 0.069506
|
||||
7 0.075321 0.073497 0.071643 0.071093 0.070480 0.069750 0.068828
|
||||
8 0.074328 0.072954 0.069693 0.069359 0.068986 0.068528 0.067920
|
||||
9 0.072954 0.072121 0.067239 0.067143 0.067040 0.066893 0.066650
|
||||
10 0.069693 0.067239 0.068729 0.067831 0.066827 0.065661 0.064254
|
||||
11 0.069359 0.067143 0.067831 0.067072 0.066218 0.065217 0.063990
|
||||
12 0.068986 0.067040 0.066827 0.066218 0.065529 0.064708 0.063682
|
||||
13 0.068528 0.066893 0.065661 0.065217 0.064708 0.064088 0.063287
|
||||
14 0.067920 0.066650 0.064254 0.063990 0.063682 0.063287 0.062745
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -879,10 +884,10 @@ number <span class="math notranslate nohighlight">\(i\)</span> is left out. Usin
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.132756 sec
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.147161 sec
|
||||
Jackknife Statistics :
|
||||
original bias std. error
|
||||
99.9573 99.9473 0.149003
|
||||
100.113 100.103 0.15078
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1101,7 +1106,7 @@ theorem.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
|
||||
original bias std. error
|
||||
100.299 15.0473 100.299 0.149379
|
||||
99.966 14.8724 99.9645 0.146212
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1313,7 +1318,9 @@ Error: 0.10398646080125035
|
||||
Bias^2: 0.1007711427354898
|
||||
Var: 0.0032153180657605116
|
||||
0.10398646080125035 >= 0.1007711427354898 + 0.0032153180657605116 = 0.10398646080125032
|
||||
Polynomial degree: 3
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 3
|
||||
Error: 0.06547790180152355
|
||||
Bias^2: 0.06208238634231949
|
||||
Var: 0.0033955154592040936
|
||||
@@ -1338,14 +1345,14 @@ Error: 0.02760977349102253
|
||||
Bias^2: 0.022999498260366312
|
||||
Var: 0.004610275230656212
|
||||
0.02760977349102253 >= 0.022999498260366312 + 0.004610275230656212 = 0.027609773491022525
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 8
|
||||
Polynomial degree: 8
|
||||
Error: 0.017355848195593347
|
||||
Bias^2: 0.010331721306655127
|
||||
Var: 0.007024126888938232
|
||||
0.017355848195593347 >= 0.010331721306655127 + 0.007024126888938232 = 0.01735584819559336
|
||||
Polynomial degree: 9
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 9
|
||||
Error: 0.02660572763718093
|
||||
Bias^2: 0.010018312644137363
|
||||
Var: 0.016587414993043573
|
||||
@@ -1355,7 +1362,9 @@ Error: 0.021592704588025025
|
||||
Bias^2: 0.010516485576645508
|
||||
Var: 0.011076219011379514
|
||||
0.021592704588025025 >= 0.010516485576645508 + 0.011076219011379514 = 0.021592704588025022
|
||||
Polynomial degree: 11
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 11
|
||||
Error: 0.07160048164233104
|
||||
Bias^2: 0.014436800088904942
|
||||
Var: 0.05716368155342608
|
||||
@@ -1365,16 +1374,14 @@ Error: 0.11547777218872497
|
||||
Bias^2: 0.01628578269596628
|
||||
Var: 0.09919198949275869
|
||||
0.11547777218872497 >= 0.01628578269596628 + 0.09919198949275869 = 0.11547777218872497
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 13
|
||||
Polynomial degree: 13
|
||||
Error: 0.22842468702219465
|
||||
Bias^2: 0.01975416527185249
|
||||
Var: 0.20867052175034223
|
||||
0.22842468702219465 >= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter3_66_3.png" src="_images/chapter3_66_3.png" />
|
||||
<img alt="_images/chapter3_66_4.png" src="_images/chapter3_66_4.png" />
|
||||
</div>
|
||||
</div>
|
||||
<p>The bias-variance tradeoff summarizes the fundamental tension in
|
||||
@@ -1689,9 +1696,9 @@ Mean squared error on training data: 0.00060704
|
||||
Mean squared error on test data: 3262.26814548
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87367/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87367/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(testerror), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1925,7 +1932,7 @@ cross-validation (LOOCV).</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87367/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2814,7 +2821,7 @@ linear system as an equation would reduce this down to
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87367/4162706317.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/4162706317.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2958,7 +2965,7 @@ with the form utilized in linear regression, viz.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87367/3777801602.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/3777801602.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2998,7 +3005,7 @@ cost function is given by</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87367/438060758.py:10: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/438060758.py:10: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3033,7 +3040,7 @@ cost function is given by</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87367/3544313922.py:9: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/3544313922.py:9: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3086,43 +3093,43 @@ constant as opposed to ridge and OLS. We get a sparse solution with
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0%| | 0/10 [00:00<?, ?it/s]
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||||
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|
||||
</pre></div>
|
||||
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|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_coordinate_descent.py:628: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 3.924e+00, tolerance: 1.797e+00
|
||||
model = cd_fast.enet_coordinate_descent(
|
||||
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 20%|████████████████████ | 2/10 [00:01<00:07, 1.07it/s]
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||||
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|
||||
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|
||||
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|
||||
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||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 30%|█████████████████████████████████▌ | 3/10 [00:02<00:05, 1.33it/s]
|
||||
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|
||||
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|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 40%|████████████████████████████████████████ | 4/10 [00:03<00:04, 1.22it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 40%|████████████████████████████████████████████▊ | 4/10 [00:03<00:04, 1.41it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 50%|██████████████████████████████████████████████████ | 5/10 [00:04<00:03, 1.27it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 50%|████████████████████████████████████████████████████████ | 5/10 [00:03<00:03, 1.51it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 60%|████████████████████████████████████████████████████████████ | 6/10 [00:04<00:03, 1.28it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 60%|███████████████████████████████████████████████████████████████████▏ | 6/10 [00:04<00:02, 1.54it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 70%|██████████████████████████████████████████████████████████████████████ | 7/10 [00:05<00:02, 1.30it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 70%|██████████████████████████████████████████████████████████████████████████████▍ | 7/10 [00:04<00:01, 1.56it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 80%|████████████████████████████████████████████████████████████████████████████████ | 8/10 [00:06<00:01, 1.29it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 80%|█████████████████████████████████████████████████████████████████████████████████████████▌ | 8/10 [00:05<00:01, 1.48it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 90%|██████████████████████████████████████████████████████████████████████████████████████████ | 9/10 [00:07<00:00, 1.30it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 90%|████████████████████████████████████████████████████████████████████████████████████████████████████▊ | 9/10 [00:06<00:00, 1.43it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:07<00:00, 1.33it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06<00:00, 1.52it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:07<00:00, 1.27it/s]
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06<00:00, 1.45it/s]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -807,9 +812,9 @@ predicting the target features of query instances is as follows:</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2nd degree coefficients:
|
||||
zero power: 0.7112242518460867
|
||||
first power: 0.15008902218011533
|
||||
second power: -0.00042767357088773335
|
||||
zero power: 2.1974520015546233
|
||||
first power: -0.07706200276162956
|
||||
second power: -0.00041883582579717597
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter6_1_1.png" src="_images/chapter6_1_1.png" />
|
||||
@@ -1672,7 +1677,9 @@ attributes at each step while growing the tree.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(426, 30)
|
||||
(143, 30)
|
||||
Test set accuracy with Logistic Regression: 0.94
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Test set accuracy with Logistic Regression: 0.94
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Test set accuracy with SVM: 0.63
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -761,10 +766,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.1621766238509487
|
||||
3.735490390687699
|
||||
[[0.74336924 2.19036055]
|
||||
[2.19036055 7.50414881]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.1255057631975562
|
||||
3.579533981545493
|
||||
[[0.80708107 2.37821193]
|
||||
[2.37821193 8.11221557]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -804,10 +809,10 @@ a more brute force way. Here we scale the mean values for each column of the des
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07865450504129884
|
||||
1.6463440100796987
|
||||
[[1. 0.63797452]
|
||||
[0.63797452 1. ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07588754093232836
|
||||
1.3745699019323765
|
||||
[[1. 0.60314576]
|
||||
[0.60314576 1. ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -836,30 +841,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.00615047 -0.51495078]
|
||||
[-1.23076025 -3.95226818]
|
||||
[ 0.14038959 1.1457534 ]
|
||||
[ 0.7408594 2.69734853]
|
||||
[ 0.19517373 1.18571046]
|
||||
[-0.04178558 -0.58598227]
|
||||
[ 0.45796224 0.7947491 ]
|
||||
[ 0.3351443 0.35268457]
|
||||
[ 0.04648472 0.35436034]
|
||||
[-0.63731768 -1.47740516]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-1.4664985 -5.74309684]
|
||||
[ 0.4437291 1.90952533]
|
||||
[ 1.55472805 4.78691713]
|
||||
[-1.49928561 -4.52502695]
|
||||
[ 1.17766528 3.5035492 ]
|
||||
[-1.53311882 -4.84616248]
|
||||
[ 0.58757487 2.2352456 ]
|
||||
[-1.60585931 -5.88080569]
|
||||
[ 1.30905952 3.50820404]
|
||||
[ 1.03200542 5.05165065]]
|
||||
0 1
|
||||
0 -0.006150 -0.514951
|
||||
1 -1.230760 -3.952268
|
||||
2 0.140390 1.145753
|
||||
3 0.740859 2.697349
|
||||
4 0.195174 1.185710
|
||||
5 -0.041786 -0.585982
|
||||
6 0.457962 0.794749
|
||||
7 0.335144 0.352685
|
||||
8 0.046485 0.354360
|
||||
9 -0.637318 -1.477405
|
||||
0 -1.466499 -5.743097
|
||||
1 0.443729 1.909525
|
||||
2 1.554728 4.786917
|
||||
3 -1.499286 -4.525027
|
||||
4 1.177665 3.503549
|
||||
5 -1.533119 -4.846162
|
||||
6 0.587575 2.235246
|
||||
7 -1.605859 -5.880806
|
||||
8 1.309060 3.508204
|
||||
9 1.032005 5.051651
|
||||
0 1
|
||||
0 1.000000 0.954148
|
||||
1 0.954148 1.000000
|
||||
0 1.000000 0.986472
|
||||
1 0.986472 1.000000
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -916,40 +921,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
|
||||
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.0 0.078267 0.080363 0.077060 0.080735 0.084346 0.068278 0.071704
|
||||
2 0.0 0.080363 0.084687 0.077184 0.081702 0.086410 0.067314 0.071070
|
||||
3 0.0 0.077060 0.077184 0.081107 0.083982 0.086548 0.074851 0.078039
|
||||
4 0.0 0.080735 0.081702 0.083982 0.087340 0.090475 0.076894 0.080380
|
||||
5 0.0 0.084346 0.086410 0.086548 0.090475 0.094304 0.078548 0.082355
|
||||
6 0.0 0.068278 0.067314 0.074851 0.076894 0.078548 0.071058 0.073683
|
||||
7 0.0 0.071704 0.071070 0.078039 0.080380 0.082355 0.073683 0.076547
|
||||
8 0.0 0.075284 0.075083 0.081283 0.083968 0.086326 0.076306 0.079429
|
||||
9 0.0 0.079000 0.079369 0.084535 0.087621 0.090437 0.078867 0.082274
|
||||
10 0.0 0.059805 0.058347 0.067435 0.068873 0.069916 0.065387 0.067507
|
||||
11 0.0 0.062733 0.061411 0.070367 0.072006 0.073253 0.067940 0.070248
|
||||
12 0.0 0.065842 0.064698 0.073442 0.075310 0.076791 0.070595 0.073109
|
||||
13 0.0 0.069136 0.068226 0.076654 0.078782 0.080535 0.073340 0.076079
|
||||
14 0.0 0.072615 0.072013 0.079987 0.082412 0.084486 0.076154 0.079138
|
||||
1 0.0 0.083504 0.075256 0.078921 0.075567 0.072065 0.068904 0.066579
|
||||
2 0.0 0.075256 0.068613 0.070518 0.067902 0.065165 0.061508 0.059695
|
||||
3 0.0 0.078921 0.070518 0.080620 0.076840 0.072951 0.073809 0.071199
|
||||
4 0.0 0.075567 0.067902 0.076840 0.073512 0.070072 0.070294 0.068019
|
||||
5 0.0 0.072065 0.065165 0.072951 0.070072 0.067082 0.066709 0.064764
|
||||
6 0.0 0.068904 0.061508 0.073809 0.070294 0.066709 0.069698 0.067255
|
||||
7 0.0 0.066579 0.059695 0.071199 0.068019 0.064764 0.067255 0.065071
|
||||
8 0.0 0.064363 0.057976 0.068705 0.065848 0.062910 0.064922 0.062985
|
||||
9 0.0 0.062226 0.056324 0.066296 0.063752 0.061123 0.062673 0.060974
|
||||
10 0.0 0.059775 0.053480 0.066103 0.063023 0.059897 0.063806 0.061651
|
||||
11 0.0 0.057936 0.052040 0.064062 0.061249 0.058385 0.061895 0.059951
|
||||
12 0.0 0.056217 0.050702 0.062151 0.059593 0.056978 0.060108 0.058364
|
||||
13 0.0 0.054609 0.049456 0.060358 0.058043 0.055668 0.058432 0.056880
|
||||
14 0.0 0.053099 0.048295 0.058671 0.056590 0.054443 0.056857 0.055488
|
||||
|
||||
8 9 10 11 12 13 14
|
||||
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.075284 0.079000 0.059805 0.062733 0.065842 0.069136 0.072615
|
||||
2 0.075083 0.079369 0.058347 0.061411 0.064698 0.068226 0.072013
|
||||
3 0.081283 0.084535 0.067435 0.070367 0.073442 0.076654 0.079987
|
||||
4 0.083968 0.087621 0.068873 0.072006 0.075310 0.078782 0.082412
|
||||
5 0.086326 0.090437 0.069916 0.073253 0.076791 0.080535 0.084486
|
||||
6 0.076306 0.078867 0.065387 0.067940 0.070595 0.073340 0.076154
|
||||
7 0.079429 0.082274 0.067507 0.070248 0.073109 0.076079 0.079138
|
||||
8 0.082598 0.085762 0.069592 0.072533 0.075613 0.078825 0.082151
|
||||
9 0.085762 0.089288 0.071587 0.074738 0.078051 0.081523 0.085141
|
||||
10 0.069592 0.071587 0.061178 0.063336 0.065565 0.067851 0.070172
|
||||
11 0.072533 0.074738 0.063336 0.065655 0.068057 0.070529 0.073050
|
||||
12 0.075613 0.078051 0.065565 0.068057 0.070647 0.073320 0.076057
|
||||
13 0.078825 0.081523 0.067851 0.070529 0.073320 0.076212 0.079184
|
||||
14 0.082151 0.085141 0.070172 0.073050 0.076057 0.079184 0.082414
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
|
||||
1 0.064363 0.062226 0.059775 0.057936 0.056217 0.054609 0.053099
|
||||
2 0.057976 0.056324 0.053480 0.052040 0.050702 0.049456 0.048295
|
||||
3 0.068705 0.066296 0.066103 0.064062 0.062151 0.060358 0.058671
|
||||
4 0.065848 0.063752 0.063023 0.061249 0.059593 0.058043 0.056590
|
||||
5 0.062910 0.061123 0.059897 0.058385 0.056978 0.055668 0.054443
|
||||
6 0.064922 0.062673 0.063806 0.061895 0.060108 0.058432 0.056857
|
||||
7 0.062985 0.060974 0.061651 0.059951 0.058364 0.056880 0.055488
|
||||
8 0.061136 0.059355 0.059595 0.058098 0.056703 0.055402 0.054185
|
||||
9 0.059355 0.057796 0.057619 0.056315 0.055105 0.053981 0.052934
|
||||
10 0.059595 0.057619 0.059363 0.057675 0.056097 0.054621 0.053236
|
||||
11 0.058098 0.056315 0.057675 0.056161 0.054750 0.053432 0.052199
|
||||
12 0.056703 0.055105 0.056097 0.054750 0.053497 0.052330 0.051241
|
||||
13 0.055402 0.053981 0.054621 0.053432 0.052330 0.051307 0.050356
|
||||
14 0.054185 0.052934 0.053236 0.052199 0.051241 0.050356 0.049538
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1138,10 +1140,10 @@ We can write our own code or simply use either the functionaly of <strong>numpy<
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
|
||||
0 3.847343 1.919895
|
||||
1 1.919895 1.934339
|
||||
[[3.8473429 1.91989533]
|
||||
[1.91989533 1.934339 ]]
|
||||
0 3.969573 1.988769
|
||||
1 1.988769 2.007390
|
||||
[[3.96957289 1.98876882]
|
||||
[1.98876882 2.00738983]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1168,8 +1170,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Centered covariance using own code
|
||||
[[3.8473429 1.91989533]
|
||||
[1.91989533 1.934339 ]]
|
||||
[[3.96957289 1.98876882]
|
||||
[1.98876882 2.00738983]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
|
||||
@@ -1229,16 +1231,16 @@ questions.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Covariance matrix
|
||||
5.035810431523915
|
||||
0.7458714725617228
|
||||
5.206079615468402
|
||||
0.7708831044105582
|
||||
First eigenvector
|
||||
[0.8502729 0.52634209]
|
||||
[0.84923841 0.52800959]
|
||||
Second eigenvector
|
||||
[-0.52634209 0.8502729 ]
|
||||
[-0.52800959 0.84923841]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
|
||||
[-0.8502729 -0.52634209]
|
||||
[-0.84923841 -0.52800959]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -341,6 +341,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -814,15 +819,15 @@ regression.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.2561719 ]
|
||||
[2.65632442]]
|
||||
Eigenvalues of Hessian Matrix:[0.33282365 4.37023448]
|
||||
[[4.15515965]
|
||||
[2.99763835]]
|
||||
Eigenvalues of Hessian Matrix:[0.3156062 4.19886862]
|
||||
theta from own gd
|
||||
[[4.2561719 ]
|
||||
[2.65632442]]
|
||||
[[4.15515965]
|
||||
[2.99763835]]
|
||||
theta from own sdg
|
||||
[[4.25767462]
|
||||
[2.65759127]]
|
||||
[[4.18290649]
|
||||
[2.96486591]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_5_1.png" src="_images/exercisesweek41_5_1.png" />
|
||||
@@ -944,12 +949,12 @@ first example shows results with ordinary leats squares.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.96801916]
|
||||
[2.95289375]]
|
||||
Eigenvalues of Hessian Matrix:[0.27223854 4.51713064]
|
||||
[[3.98635543]
|
||||
[2.9642492 ]]
|
||||
Eigenvalues of Hessian Matrix:[0.31545424 4.4234122 ]
|
||||
theta from own gd
|
||||
[[3.96801916]
|
||||
[2.95289375]]
|
||||
[[3.98635543]
|
||||
[2.9642492 ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_16_1.png" src="_images/exercisesweek41_16_1.png" />
|
||||
@@ -1020,73 +1025,73 @@ theta from own gd
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.]
|
||||
[3.]]
|
||||
Eigenvalues of Hessian Matrix:[0.29155617 4.71527295]
|
||||
0 [-13.19526866] [-16.48597324]
|
||||
1 [-0.06810332] [0.05402091]
|
||||
2 [-0.06389233] [0.05068067]
|
||||
3 [-0.05994172] [0.04754697]
|
||||
4 [-0.05623539] [0.04460703]
|
||||
5 [-0.05275823] [0.04184888]
|
||||
6 [-0.04949606] [0.03926126]
|
||||
7 [-0.04643561] [0.03683365]
|
||||
8 [-0.04356439] [0.03455614]
|
||||
9 [-0.0408707] [0.03241945]
|
||||
10 [-0.03834357] [0.03041488]
|
||||
11 [-0.0359727] [0.02853426]
|
||||
12 [-0.03374843] [0.02676992]
|
||||
13 [-0.03166168] [0.02511468]
|
||||
14 [-0.02970397] [0.02356178]
|
||||
15 [-0.0278673] [0.0221049]
|
||||
16 [-0.0261442] [0.0207381]
|
||||
17 [-0.02452765] [0.01945582]
|
||||
18 [-0.02301105] [0.01825282]
|
||||
19 [-0.02158822] [0.01712421]
|
||||
20 [-0.02025337] [0.01606538]
|
||||
21 [-0.01900106] [0.01507202]
|
||||
22 [-0.01782618] [0.01414008]
|
||||
23 [-0.01672395] [0.01326577]
|
||||
24 [-0.01568987] [0.01244551]
|
||||
25 [-0.01471973] [0.01167598]
|
||||
26 [-0.01380957] [0.01095403]
|
||||
27 [-0.01295569] [0.01027671]
|
||||
28 [-0.01215461] [0.00964128]
|
||||
29 [-0.01140307] [0.00904514]
|
||||
Eigenvalues of Hessian Matrix:[0.35350927 4.2330123 ]
|
||||
0 [-10.02028415] [-11.38281882]
|
||||
1 [-0.12978318] [0.11144292]
|
||||
2 [-0.11894467] [0.10213605]
|
||||
3 [-0.10901131] [0.09360642]
|
||||
4 [-0.0999075] [0.08578912]
|
||||
5 [-0.09156398] [0.07862466]
|
||||
6 [-0.08391725] [0.07205852]
|
||||
7 [-0.07690911] [0.06604073]
|
||||
8 [-0.07048624] [0.06052551]
|
||||
9 [-0.06459976] [0.05547088]
|
||||
10 [-0.05920488] [0.05083837]
|
||||
11 [-0.05426053] [0.04659273]
|
||||
12 [-0.0497291] [0.04270166]
|
||||
13 [-0.0455761] [0.03913554]
|
||||
14 [-0.04176993] [0.03586723]
|
||||
15 [-0.03828162] [0.03287187]
|
||||
16 [-0.03508463] [0.03012666]
|
||||
17 [-0.03215463] [0.02761071]
|
||||
18 [-0.02946931] [0.02530487]
|
||||
19 [-0.02700826] [0.0231916]
|
||||
20 [-0.02475273] [0.02125481]
|
||||
21 [-0.02268557] [0.01947977]
|
||||
22 [-0.02079104] [0.01785297]
|
||||
23 [-0.01905473] [0.01636202]
|
||||
24 [-0.01746342] [0.01499559]
|
||||
25 [-0.01600501] [0.01374327]
|
||||
26 [-0.01466839] [0.01259554]
|
||||
27 [-0.0134434] [0.01154365]
|
||||
28 [-0.01232071] [0.01057961]
|
||||
29 [-0.01129178] [0.00969608]
|
||||
theta from own gd
|
||||
[[3.96330728]
|
||||
[3.02910539]]
|
||||
0 [-0.01069799] [0.00848586]
|
||||
1 [-0.01003651] [0.00796116]
|
||||
2 [-0.00921748] [0.00731149]
|
||||
3 [-0.00840184] [0.0066645]
|
||||
4 [-0.00763764] [0.00605833]
|
||||
5 [-0.00693613] [0.00550187]
|
||||
6 [-0.0062968] [0.00499474]
|
||||
7 [-0.00571565] [0.00453377]
|
||||
8 [-0.0051879] [0.00411514]
|
||||
9 [-0.00470879] [0.00373511]
|
||||
10 [-0.0042739] [0.00339014]
|
||||
11 [-0.00387917] [0.00307704]
|
||||
12 [-0.00352089] [0.00279284]
|
||||
13 [-0.00319571] [0.0025349]
|
||||
14 [-0.00290055] [0.00230078]
|
||||
15 [-0.00263266] [0.00208828]
|
||||
16 [-0.00238951] [0.0018954]
|
||||
17 [-0.00216881] [0.00172034]
|
||||
18 [-0.0019685] [0.00156145]
|
||||
19 [-0.00178669] [0.00141724]
|
||||
20 [-0.00162167] [0.00128634]
|
||||
21 [-0.0014719] [0.00116754]
|
||||
22 [-0.00133595] [0.0010597]
|
||||
23 [-0.00121256] [0.00096183]
|
||||
24 [-0.00110057] [0.000873]
|
||||
25 [-0.00099892] [0.00079237]
|
||||
26 [-0.00090666] [0.00071918]
|
||||
27 [-0.00082292] [0.00065276]
|
||||
28 [-0.00074692] [0.00059247]
|
||||
29 [-0.00067793] [0.00053775]
|
||||
[[3.9707256]
|
||||
[3.0251375]]
|
||||
0 [-0.01034877] [0.00888634]
|
||||
1 [-0.00948452] [0.00814422]
|
||||
2 [-0.00843317] [0.00724144]
|
||||
3 [-0.00741349] [0.00636586]
|
||||
4 [-0.00648847] [0.00557155]
|
||||
5 [-0.00566909] [0.00486797]
|
||||
6 [-0.00494984] [0.00425036]
|
||||
7 [-0.00432069] [0.00371011]
|
||||
8 [-0.00377111] [0.0032382]
|
||||
9 [-0.00329131] [0.0028262]
|
||||
10 [-0.0028725] [0.00246657]
|
||||
11 [-0.00250697] [0.0021527]
|
||||
12 [-0.00218794] [0.00187876]
|
||||
13 [-0.00190952] [0.00163967]
|
||||
14 [-0.00166652] [0.00143102]
|
||||
15 [-0.00145445] [0.00124891]
|
||||
16 [-0.00126936] [0.00108998]
|
||||
17 [-0.00110783] [0.00095127]
|
||||
18 [-0.00096685] [0.00083022]
|
||||
19 [-0.00084381] [0.00072457]
|
||||
20 [-0.00073643] [0.00063236]
|
||||
21 [-0.00064272] [0.00055189]
|
||||
22 [-0.00056093] [0.00048166]
|
||||
23 [-0.00048955] [0.00042037]
|
||||
24 [-0.00042725] [0.00036687]
|
||||
25 [-0.00037288] [0.00032019]
|
||||
26 [-0.00032543] [0.00027944]
|
||||
27 [-0.00028402] [0.00024388]
|
||||
28 [-0.00024787] [0.00021284]
|
||||
29 [-0.00021633] [0.00018576]
|
||||
theta from own gd wth momentum
|
||||
[[3.99788953]
|
||||
[3.00167406]]
|
||||
[[3.99946593]
|
||||
[3.0004586 ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1139,17 +1144,17 @@ theta from own gd wth momentum
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.86138568]
|
||||
[3.1477805 ]]
|
||||
Eigenvalues of Hessian Matrix:[0.36889994 4.06507762]
|
||||
0 [-10.57231587] [-11.4303589]
|
||||
1 [-1.09374315e-15] [-4.626889e-15]
|
||||
2 [-3.72965547e-17] [-7.31971976e-17]
|
||||
3 [-3.72965547e-17] [-7.31971976e-17]
|
||||
4 [-3.72965547e-17] [-7.31971976e-17]
|
||||
[[4.16849001]
|
||||
[3.03642937]]
|
||||
Eigenvalues of Hessian Matrix:[0.3039241 4.51493779]
|
||||
0 [-12.93402104] [-15.39497785]
|
||||
1 [9.11944131e-15] [7.63687445e-15]
|
||||
2 [2.11636264e-16] [3.19670115e-16]
|
||||
3 [2.11636264e-16] [3.19670115e-16]
|
||||
4 [2.11636264e-16] [3.19670115e-16]
|
||||
beta from own Newton code
|
||||
[[3.86138568]
|
||||
[3.1477805 ]]
|
||||
[[4.16849001]
|
||||
[3.03642937]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1238,18 +1243,20 @@ beta from own Newton code
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.94897376]
|
||||
[2.96037553]]
|
||||
Eigenvalues of Hessian Matrix:[0.32588151 4.12462963]
|
||||
theta from own gd
|
||||
[[3.94897376]
|
||||
[2.96037553]]
|
||||
[[4.37133465]
|
||||
[2.74809387]]
|
||||
Eigenvalues of Hessian Matrix:[0.32760411 4.2384333 ]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_22_1.png" src="_images/exercisesweek41_22_1.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
|
||||
[[4.37133465]
|
||||
[2.74809387]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_22_2.png" src="_images/exercisesweek41_22_2.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
|
||||
[[3.95568161]
|
||||
[2.9638104 ]]
|
||||
[[4.31985268]
|
||||
[2.72067593]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1331,15 +1338,15 @@ theta from own gd
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.1880258 ]
|
||||
[2.90273253]]
|
||||
Eigenvalues of Hessian Matrix:[0.32354671 4.36490166]
|
||||
[[4.34039341]
|
||||
[2.74045887]]
|
||||
Eigenvalues of Hessian Matrix:[0.31262618 4.15129596]
|
||||
theta from own gd
|
||||
[[4.18757012]
|
||||
[2.9031162 ]]
|
||||
[[4.340226 ]
|
||||
[2.74060714]]
|
||||
theta from own sdg with momentum
|
||||
[[4.11556912]
|
||||
[2.89211256]]
|
||||
[[4.30982672]
|
||||
[2.69332574]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1414,9 +1421,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own AdaGrad
|
||||
[[2.0004377 ]
|
||||
[2.99782503]
|
||||
[4.0020899 ]]
|
||||
[[2.0009282 ]
|
||||
[2.99447213]
|
||||
[4.00526145]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1498,9 +1505,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own RMSprop
|
||||
[[1.99457257]
|
||||
[2.99607686]
|
||||
[3.99588057]]
|
||||
[[1.99998409]
|
||||
[2.99993515]
|
||||
[4.00003694]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1586,9 +1593,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own ADAM
|
||||
[[2.00003022]
|
||||
[2.99976375]
|
||||
[4.00024415]]
|
||||
[[2.00011851]
|
||||
[2.99937234]
|
||||
[4.00068042]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1661,7 +1668,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
|
||||
return asarray(x, dtype=self.dtype)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x11fa3db20>]
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x125606520>]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_39_2.png" src="_images/exercisesweek41_39_2.png" />
|
||||
@@ -1696,7 +1703,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><matplotlib.collections.PathCollection at 0x10746eeb0>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><matplotlib.collections.PathCollection at 0x1253cc610>
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_41_1.png" src="_images/exercisesweek41_41_1.png" />
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
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|
||||
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|
||||
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|
||||
Exercises week 43
|
||||
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|
||||
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|
||||
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|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@@ -339,6 +339,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
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|
||||
Exercises week 43
|
||||
</a>
|
||||
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|
||||
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|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -340,6 +340,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -663,8 +668,8 @@ matrices and vectors.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-0.16146139 -0.24200844 -0.43506123 -0.19800999 -0.44832989 -1.49768808
|
||||
0.43836612 -1.45052717 -0.76587916 0.22929165]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-0.08059005 0.26043697 0.54190252 -0.8321864 1.74960664 0.28855565
|
||||
1.03029311 -0.54136139 0.94583038 0.99378218]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -885,26 +890,26 @@ as (recall that we user lowercase letters for vectors and uppercase letters for
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.93164299 0.26835242 0.93001752 0.24829629 0.34832197 0.77112374
|
||||
0.42590512 0.36694417 0.51860019 0.03241936]
|
||||
[0.051782 0.7721643 0.87478387 0.96734276 0.59958693 0.96084123
|
||||
0.84869686 0.4488194 0.76561858 0.07510785]
|
||||
[0.26590299 0.6561141 0.87736602 0.5088893 0.08090942 0.77313451
|
||||
0.7024611 0.95132723 0.72184754 0.60480445]
|
||||
[0.01562424 0.15670465 0.82204612 0.8859754 0.42439452 0.82934918
|
||||
0.55678525 0.72754455 0.65765268 0.65295017]
|
||||
[0.55148543 0.11596287 0.12675974 0.63520537 0.81012733 0.50505108
|
||||
0.65976951 0.62246687 0.77878621 0.48944878]
|
||||
[0.31068981 0.26956051 0.24188439 0.28098147 0.31739522 0.47130422
|
||||
0.34488863 0.39503373 0.71143744 0.95882586]
|
||||
[0.91507022 0.58570955 0.28341932 0.03647182 0.51045268 0.31216736
|
||||
0.94607554 0.37468967 0.17285183 0.29134342]
|
||||
[0.13728124 0.92004534 0.81825652 0.82133401 0.54874017 0.45538713
|
||||
0.85189083 0.09919725 0.39730902 0.46053947]
|
||||
[0.49503632 0.30593976 0.18180717 0.31186409 0.7337962 0.78380113
|
||||
0.56237849 0.92761972 0.25034533 0.39919362]
|
||||
[0.37705573 0.05706322 0.70277293 0.90232941 0.83915415 0.62571719
|
||||
0.85724692 0.9308197 0.91496317 0.52038652]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.77235007 0.27529208 0.31199504 0.17293829 0.82162246 0.13378194
|
||||
0.90679215 0.39664124 0.3121824 0.13861839]
|
||||
[0.69473608 0.72612916 0.4570065 0.41275555 0.76067335 0.56239325
|
||||
0.33900003 0.83105136 0.14230327 0.04713857]
|
||||
[0.62377027 0.12392385 0.7500676 0.67969567 0.15971479 0.97072608
|
||||
0.00183119 0.95291169 0.59353543 0.03550103]
|
||||
[0.99152919 0.13537597 0.88366546 0.73118203 0.82120582 0.53939154
|
||||
0.01958776 0.59647764 0.17941609 0.34647125]
|
||||
[0.43263402 0.2754374 0.59137018 0.52019078 0.71121535 0.60648493
|
||||
0.94665557 0.66298436 0.22615136 0.29639686]
|
||||
[0.84424529 0.59603845 0.9219476 0.44909201 0.67715931 0.18908167
|
||||
0.76516101 0.38007856 0.83478186 0.75271427]
|
||||
[0.53862422 0.11323706 0.15316333 0.34540564 0.81994631 0.52292446
|
||||
0.26760957 0.02430273 0.03576146 0.67801091]
|
||||
[0.52928925 0.14990609 0.86292532 0.43014974 0.83844809 0.04560463
|
||||
0.84163178 0.80868063 0.8371938 0.39611129]
|
||||
[0.12607006 0.5113303 0.63901709 0.99976659 0.34756595 0.28622513
|
||||
0.89290901 0.84314251 0.31916189 0.29920799]
|
||||
[0.23476091 0.40074419 0.21933245 0.48906993 0.19899282 0.06752501
|
||||
0.85079729 0.64275853 0.33164051 0.08304321]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -964,13 +969,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.051916914594944144
|
||||
4.063621005600529
|
||||
-0.19857342950283463
|
||||
[[ 0.98101481 3.10179509 3.46796873]
|
||||
[ 3.10179509 10.80421021 10.86493273]
|
||||
[ 3.46796873 10.86493273 18.60084189]]
|
||||
[27.06474536 0.07037089 3.25095067]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.04071979724729911
|
||||
4.064820972167253
|
||||
-0.3254718508870977
|
||||
[[0.88727586 2.57584621 2.19767225]
|
||||
[2.57584621 8.44132765 6.34964801]
|
||||
[2.19767225 6.34964801 9.99322469]]
|
||||
[16.34233281 0.08212093 2.89737445]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
Binary file not shown.
@@ -56,7 +56,7 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
<link rel="index" title="Index" href="genindex.html" />
|
||||
<link rel="search" title="Search" href="search.html" />
|
||||
<link rel="next" title="Project 2 on Machine Learning, deadline November 4 (Midnight)" href="project2.html" />
|
||||
<link rel="prev" title="Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations" href="week43.html" />
|
||||
<link rel="prev" title="Exercises week 43" href="exercisesweek43.html" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||
<meta name="docsearch:language" content="None">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
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|
||||
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|
||||
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|
||||
Exercises week 43
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
@@ -1089,11 +1094,11 @@ of code developers and contributors keeps increasing.</p>
|
||||
|
||||
<!-- Previous / next buttons -->
|
||||
<div class='prev-next-area'>
|
||||
<a class='left-prev' id="prev-link" href="week43.html" title="previous page">
|
||||
<a class='left-prev' id="prev-link" href="exercisesweek43.html" title="previous page">
|
||||
<i class="fas fa-angle-left"></i>
|
||||
<div class="prev-next-info">
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<p class="prev-next-subtitle">previous</p>
|
||||
<p class="prev-next-title">Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations</p>
|
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<p class="prev-next-title">Exercises week 43</p>
|
||||
</div>
|
||||
</a>
|
||||
<a class='right-next' id="next-link" href="project2.html" title="next page">
|
||||
|
||||
@@ -342,6 +342,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
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|
||||
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|
||||
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|
||||
Exercises week 43
|
||||
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||||
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|
||||
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|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
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|
||||
|
||||
@@ -341,6 +341,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
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|
||||
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|
||||
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|
||||
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||||
Exercises week 43
|
||||
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||||
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|
||||
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||||
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||||
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|
||||
|
||||
@@ -345,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
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|
||||
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|
||||
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||||
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||||
Exercises week 43
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||||
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||||
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|
||||
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||||
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@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
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|
||||
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||||
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||||
Exercises week 43
|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
@@ -1035,27 +1040,27 @@ uncorrelated.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>3.1284100258440377
|
||||
[[ 0.02325785 0.69496248 0.57120988 0.52829142 0.60357007 0.10202674
|
||||
0.60672354 0.17840283 0.22718624 0.32447198]
|
||||
[ 0.69496248 20.76601702 17.06819354 15.78575679 18.03514117 3.04863792
|
||||
18.12936913 5.33081484 6.78850066 9.69547403]
|
||||
[ 0.57120988 17.06819354 14.02884485 12.97477277 14.82360724 2.5057642
|
||||
14.90105594 4.38155181 5.57966619 7.96899218]
|
||||
[ 0.52829142 15.78575679 12.97477277 11.99989951 13.70981984 2.31749096
|
||||
13.78144936 4.05233928 5.16043208 7.37023353]
|
||||
[ 0.60357007 18.03514117 14.82360724 13.70981984 15.66339452 2.6477208
|
||||
15.74523085 4.62977556 5.89576555 8.42045168]
|
||||
[ 0.10202674 3.04863792 2.5057642 2.31749096 2.6477208 0.44756744
|
||||
2.66155431 0.78261152 0.9966129 1.42338272]
|
||||
[ 0.60672354 18.12936913 14.90105594 13.78144936 15.74523085 2.66155431
|
||||
15.82749474 4.65396469 5.92656908 8.4644459 ]
|
||||
[ 0.17840283 5.33081484 4.38155181 4.05233928 4.62977556 0.78261152
|
||||
4.65396469 1.36846593 1.7426664 2.48891141]
|
||||
[ 0.22718624 6.78850066 5.57966619 5.16043208 5.89576555 0.9966129
|
||||
5.92656908 1.7426664 2.21919019 3.16949234]
|
||||
[ 0.32447198 9.69547403 7.96899218 7.37023353 8.42045168 1.42338272
|
||||
8.4644459 2.48891141 3.16949234 4.5267331 ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>1.792442235218746
|
||||
[[ 2.10296919 4.21086655 4.66575943 7.88378851 6.35849734 4.4257124
|
||||
3.96306539 0.81366409 3.49568351 5.17399603]
|
||||
[ 4.21086655 8.43160097 9.34245275 15.78605212 12.73189536 8.86179614
|
||||
7.93541793 1.62923495 6.9995589 10.36011695]
|
||||
[ 4.66575943 9.34245275 10.35170232 17.49139298 14.10730076 9.81912119
|
||||
8.79266789 1.80523848 7.75570956 11.4793031 ]
|
||||
[ 7.88378851 15.78605212 17.49139298 29.55541212 23.83727177 16.59148438
|
||||
14.85707419 3.05033266 13.10491353 19.39671325]
|
||||
[ 6.35849734 12.73189536 14.10730076 23.83727177 19.22543063 13.38149915
|
||||
11.98264851 2.46017915 10.56948162 15.64399519]
|
||||
[ 4.4257124 8.86179614 9.81912119 16.59148438 13.38149915 9.31394064
|
||||
8.34029698 1.71236139 7.35668876 10.88870842]
|
||||
[ 3.96306539 7.93541793 8.79266789 14.85707419 11.98264851 8.34029698
|
||||
7.46843429 1.5333577 6.58764871 9.75044457]
|
||||
[ 0.81366409 1.62923495 1.80523848 3.05033266 2.46017915 1.71236139
|
||||
1.5333577 0.31481643 1.35252202 2.00188134]
|
||||
[ 3.49568351 6.9995589 7.75570956 13.10491353 10.56948162 7.35668876
|
||||
6.58764871 1.35252202 5.81073808 8.60053139]
|
||||
[ 5.17399603 10.36011695 11.4793031 19.39671325 15.64399519 10.88870842
|
||||
9.75044457 2.00188134 8.60053139 12.72973232]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1323,15 +1328,15 @@ more practically oriented methods like the blocking technique.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.029114513319594925
|
||||
4.012687664954397
|
||||
-0.13206207781887236
|
||||
0.8800906083513416 8.622777986360822 8.409131380658218
|
||||
2.5686930390258937 2.11634286035477 5.981554571728081
|
||||
[[0.88009061 2.56869304 2.11634286]
|
||||
[2.56869304 8.62277799 5.98155457]
|
||||
[2.11634286 5.98155457 8.40913138]]
|
||||
[15.26310762 0.08312573 2.56576662]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.03309100631504689
|
||||
4.053690173865474
|
||||
0.19676409012950763
|
||||
0.9238126238237127 9.751549347323406 13.02381502730822
|
||||
2.8153623169095896 2.4608605587175947 7.2634338084990535
|
||||
[[ 0.92381262 2.81536232 2.46086056]
|
||||
[ 2.81536232 9.75154935 7.26343381]
|
||||
[ 2.46086056 7.26343381 13.02381503]]
|
||||
[19.56094738 0.08771271 4.05051691]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1661,7 +1666,7 @@ assumption for approximating <span class="math notranslate nohighlight">\(\sigma
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.015101938515449663 0.9784055938098051
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.01754817104095514 0.9184060613261256
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/statistics_188_1.png" src="_images/statistics_188_1.png" />
|
||||
|
||||
@@ -341,6 +341,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -341,6 +341,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1723,8 +1728,8 @@ developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly he
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-0.65354422 0.31335664 0.77994763 -0.26292935 -0.01705695 -2.16552497
|
||||
-1.06272254 -0.20520318 -1.70367841 -0.29687889]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-0.44898476 0.65543958 -0.19009894 -1.54003127 0.54908576 1.22268225
|
||||
0.85101172 -0.07094607 0.31613828 2.01311197]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1949,26 +1954,26 @@ lowercase letters for vectors and uppercase letters for matrices)</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.6564482 0.70711514 0.85049285 0.39741875 0.3000498 0.81984817
|
||||
0.08300526 0.16674251 0.85142265 0.15424679]
|
||||
[0.18013978 0.97321835 0.83785062 0.4313428 0.7889793 0.22625657
|
||||
0.54214936 0.00995699 0.81329201 0.11991488]
|
||||
[0.10520393 0.5823186 0.92301743 0.56913182 0.64344541 0.3466389
|
||||
0.20656353 0.16072855 0.08068207 0.13625288]
|
||||
[0.83693088 0.18251883 0.47900239 0.66340579 0.98244726 0.68291639
|
||||
0.53361935 0.2938162 0.74412221 0.32232922]
|
||||
[0.31743443 0.47830372 0.63116786 0.86885547 0.20263701 0.96029461
|
||||
0.50744967 0.68012971 0.16181877 0.4742433 ]
|
||||
[0.22426265 0.20640822 0.83408369 0.20353821 0.84269323 0.76183628
|
||||
0.957171 0.8509859 0.57000682 0.39184027]
|
||||
[0.03692749 0.36845893 0.17101958 0.31888254 0.67849271 0.60837213
|
||||
0.69164986 0.18146425 0.57604071 0.88445111]
|
||||
[0.10371767 0.87228174 0.52154966 0.04596002 0.52212442 0.73390423
|
||||
0.05999828 0.61076053 0.12394921 0.20365164]
|
||||
[0.90210098 0.59206051 0.09303501 0.51019911 0.00733216 0.04041644
|
||||
0.3615115 0.02784163 0.46893501 0.68008931]
|
||||
[0.80147746 0.00959357 0.80835002 0.63542565 0.20005403 0.21894241
|
||||
0.96907179 0.84745525 0.43713984 0.60568686]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.07297544 0.1366929 0.25398681 0.35559575 0.59290535 0.27121997
|
||||
0.13195623 0.10766611 0.92510128 0.09590878]
|
||||
[0.49781325 0.85327004 0.44122101 0.54419365 0.27783579 0.75720786
|
||||
0.59926703 0.31297469 0.46106755 0.95745534]
|
||||
[0.92393165 0.11004595 0.47187607 0.67191313 0.66545999 0.05772472
|
||||
0.82838817 0.45380039 0.95432881 0.5961356 ]
|
||||
[0.31723049 0.28868604 0.85458026 0.47874964 0.98191653 0.82894855
|
||||
0.78875722 0.15102593 0.82009906 0.65700779]
|
||||
[0.65533829 0.16452848 0.99858871 0.98654578 0.29760523 0.49945378
|
||||
0.01910339 0.58642686 0.67898825 0.25439747]
|
||||
[0.36573968 0.77838912 0.28065817 0.93388517 0.91321225 0.73880347
|
||||
0.48253511 0.51439255 0.72062943 0.69400286]
|
||||
[0.43445446 0.39467981 0.97900469 0.85944866 0.73824262 0.88071254
|
||||
0.11731667 0.9080271 0.71921281 0.90150448]
|
||||
[0.33085218 0.56245497 0.21046538 0.11038556 0.85669407 0.10200001
|
||||
0.47302573 0.00922097 0.36991768 0.65854722]
|
||||
[0.89515649 0.78939263 0.25828869 0.86260982 0.74693983 0.04328411
|
||||
0.01427038 0.14780956 0.07962663 0.39707815]
|
||||
[0.18461559 0.69297058 0.68332496 0.79758524 0.22346703 0.48744228
|
||||
0.50987248 0.04777426 0.15961465 0.20041381]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2023,13 +2028,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.007557567939261264
|
||||
3.9057119872872414
|
||||
0.43208935911369845
|
||||
[[0.8631855 2.56690562 2.08698097]
|
||||
[2.56690562 8.47187403 6.28078417]
|
||||
[2.08698097 6.28078417 9.31159615]]
|
||||
[15.90162133 0.07253999 2.67249437]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.09941804358942685
|
||||
4.135553999655979
|
||||
0.06128276434886384
|
||||
[[ 0.81985155 2.4736645 2.12220773]
|
||||
[ 2.4736645 8.54371074 6.81973052]
|
||||
[ 2.12220773 6.81973052 10.51290787]]
|
||||
[17.05928882 0.09257332 2.72460802]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2254,7 +2259,7 @@ Name: Aragorn, dtype: object
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||||
<span class="ne">AttributeError</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||||
<span class="nn">/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87525/1326197715.py</span> in <span class="ni">?</span><span class="nt">()</span>
|
||||
<span class="nn">/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94272/1326197715.py</span> in <span class="ni">?</span><span class="nt">()</span>
|
||||
<span class="ne">----> </span><span class="mi">6</span> <span class="n">new_hobbit</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'First Name'</span><span class="p">:</span> <span class="p">[</span><span class="s2">"Peregrin"</span><span class="p">],</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">7</span> <span class="s1">'Last Name'</span><span class="p">:</span> <span class="p">[</span><span class="s2">"Took"</span><span class="p">],</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="s1">'Place of birth'</span><span class="p">:</span> <span class="p">[</span><span class="s2">"Shire"</span><span class="p">],</span>
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1691,7 +1696,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9960490331171794
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9951746722640107
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1708,7 +1713,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.008128643056242772
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.011011355570628998
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1723,23 +1728,23 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.0414517 0.01527618 0.00673693 0.03003494 0.03248618 0.00283324
|
||||
0.03532164 0.07082844 0.05655534 0.00080345 0.00157346 0.004578
|
||||
0.0581406 0.01563358 0.06919343 0.00761546 0.00914784 0.05549907
|
||||
0.01149386 0.0110602 0.0271259 0.05232855 0.03351257 0.05334469
|
||||
0.0089987 0.01442817 0.00573681 0.00930457 0.00443629 0.06034627
|
||||
0.03612962 0.00485232 0.03143856 0.01643952 0.02448011 0.04006242
|
||||
0.01018465 0.02483712 0.02375066 0.05793564 0.01317824 0.02079774
|
||||
0.09129027 0.02990404 0.03601781 0.03065856 0.00210569 0.02038063
|
||||
0.01455301 0.00303686 0.0016202 0.05321642 0.00512149 0.01263474
|
||||
0.0260728 0.04836325 0.00520752 0.00059681 0.00067567 0.02206393
|
||||
0.03484946 0.08516604 0.00777619 0.0021452 0.03843478 0.00952138
|
||||
0.07036197 0.0482407 0.01746176 0.00458083 0.01525387 0.01671659
|
||||
0.03032534 0.02015755 0.02109876 0.01873823 0.01950331 0.02336409
|
||||
0.02234283 0.06037137 0.01105813 0.06082594 0.00288198 0.01532072
|
||||
0.00473744 0.03710736 0.0211042 0.00896253 0.02036067 0.07259548
|
||||
0.01074493 0.02028151 0.00893649 0.01709886 0.00821525 0.01655001
|
||||
0.05105586 0.01908329 0.06069047 0.00213716]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.04642309 0.0279278 0.0228686 0.0650014 0.01290661 0.01519201
|
||||
0.0016396 0.05684345 0.06249397 0.00778835 0.00518242 0.02159357
|
||||
0.00421124 0.01267244 0.02280587 0.00184147 0.07626658 0.02041607
|
||||
0.03238421 0.02937931 0.04215521 0.03179975 0.00508636 0.04983222
|
||||
0.0705828 0.00555576 0.02882718 0.00046916 0.00861192 0.04145287
|
||||
0.02255993 0.00567103 0.02731257 0.02307403 0.02643023 0.03374269
|
||||
0.02728257 0.00045414 0.01269348 0.01433606 0.0031986 0.00813523
|
||||
0.01677512 0.02132304 0.02971554 0.02671209 0.03110579 0.00701382
|
||||
0.0281646 0.01167316 0.00049905 0.01368052 0.01667926 0.00935737
|
||||
0.02496143 0.08648837 0.01394224 0.04394742 0.00582904 0.06185995
|
||||
0.03162926 0.05276967 0.01028953 0.05735741 0.01571214 0.02287532
|
||||
0.01947663 0.00861563 0.00414684 0.00858857 0.0036035 0.00523549
|
||||
0.01608796 0.03520118 0.02959231 0.00068056 0.02717123 0.02989838
|
||||
0.01203668 0.02622061 0.0109944 0.09258408 0.03607387 0.01775486
|
||||
0.08931681 0.00514007 0.03450725 0.03465317 0.01712306 0.00757359
|
||||
0.02069038 0.02243626 0.01508864 0.03202289 0.06776056 0.01054406
|
||||
0.0169931 0.01784495 0.00962196 0.03370657]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1808,15 +1813,15 @@ but now splitting the data into a training set and a test set.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.93967766 0.96157921 2.62927207 1.64642277 -0.14580867]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.99804178 -0.16533342 5.68321093 -0.84401704 0.35781308]
|
||||
Training R2
|
||||
0.9957680433056965
|
||||
0.9960664320362111
|
||||
Training MSE
|
||||
0.009277782622954527
|
||||
0.008377169630073601
|
||||
Test R2
|
||||
0.9959177108554428
|
||||
0.9944299733827195
|
||||
Test MSE
|
||||
0.01153294477941533
|
||||
0.01282028141098116
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1679,7 +1684,7 @@ theorem.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
|
||||
original bias std. error
|
||||
99.9716 15.1579 99.9734 0.151892
|
||||
100.052 15.0095 100.051 0.150055
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1904,7 +1909,9 @@ Error: 0.10398646080125035
|
||||
Bias^2: 0.1007711427354898
|
||||
Var: 0.0032153180657605116
|
||||
0.10398646080125035 >= 0.1007711427354898 + 0.0032153180657605116 = 0.10398646080125032
|
||||
Polynomial degree: 3
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 3
|
||||
Error: 0.06547790180152355
|
||||
Bias^2: 0.06208238634231949
|
||||
Var: 0.0033955154592040936
|
||||
@@ -1914,14 +1921,14 @@ Error: 0.06844519414009445
|
||||
Bias^2: 0.06453579006728324
|
||||
Var: 0.003909404072811226
|
||||
0.06844519414009445 >= 0.06453579006728324 + 0.003909404072811226 = 0.06844519414009446
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 5
|
||||
Polynomial degree: 5
|
||||
Error: 0.05227921801205686
|
||||
Bias^2: 0.0481872773043029
|
||||
Var: 0.004091940707753939
|
||||
0.05227921801205686 >= 0.0481872773043029 + 0.004091940707753939 = 0.052279218012056844
|
||||
Polynomial degree: 6
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 6
|
||||
Error: 0.037813671417389005
|
||||
Bias^2: 0.033657685071527665
|
||||
Var: 0.00415598634586135
|
||||
@@ -1931,7 +1938,9 @@ Error: 0.02760977349102253
|
||||
Bias^2: 0.022999498260366312
|
||||
Var: 0.004610275230656212
|
||||
0.02760977349102253 >= 0.022999498260366312 + 0.004610275230656212 = 0.027609773491022525
|
||||
Polynomial degree: 8
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 8
|
||||
Error: 0.017355848195593347
|
||||
Bias^2: 0.010331721306655127
|
||||
Var: 0.007024126888938232
|
||||
@@ -1951,21 +1960,21 @@ Error: 0.07160048164233104
|
||||
Bias^2: 0.014436800088904942
|
||||
Var: 0.05716368155342608
|
||||
0.07160048164233104 >= 0.014436800088904942 + 0.05716368155342608 = 0.07160048164233102
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 12
|
||||
Polynomial degree: 12
|
||||
Error: 0.11547777218872497
|
||||
Bias^2: 0.01628578269596628
|
||||
Var: 0.09919198949275869
|
||||
0.11547777218872497 >= 0.01628578269596628 + 0.09919198949275869 = 0.11547777218872497
|
||||
Polynomial degree: 13
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 13
|
||||
Error: 0.22842468702219465
|
||||
Bias^2: 0.01975416527185249
|
||||
Var: 0.20867052175034223
|
||||
0.22842468702219465 >= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week37_139_3.png" src="_images/week37_139_3.png" />
|
||||
<img alt="_images/week37_139_5.png" src="_images/week37_139_5.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2302,12 +2311,12 @@ Mean squared error on test data: 129963.83146596
|
||||
Degree of polynomial: 3
|
||||
Mean squared error on training data: 9054.61775176
|
||||
Mean squared error on test data: 10572.87627342
|
||||
Degree of polynomial: 4
|
||||
Mean squared error on training data: 302.15313054
|
||||
Mean squared error on test data: 433.26292364
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 5
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 4
|
||||
Mean squared error on training data: 302.15313054
|
||||
Mean squared error on test data: 433.26292364
|
||||
Degree of polynomial: 5
|
||||
Mean squared error on training data: 3.64316192
|
||||
Mean squared error on test data: 7.23528337
|
||||
Degree of polynomial: 6
|
||||
@@ -2316,12 +2325,12 @@ Mean squared error on test data: 10.50427787
|
||||
Degree of polynomial: 7
|
||||
Mean squared error on training data: 0.47313680
|
||||
Mean squared error on test data: 1.53738247
|
||||
Degree of polynomial: 8
|
||||
Mean squared error on training data: 0.04926746
|
||||
Mean squared error on test data: 0.14629156
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 9
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 8
|
||||
Mean squared error on training data: 0.04926746
|
||||
Mean squared error on test data: 0.14629156
|
||||
Degree of polynomial: 9
|
||||
Mean squared error on training data: 0.02546675
|
||||
Mean squared error on test data: 0.11202337
|
||||
Degree of polynomial: 10
|
||||
@@ -2330,12 +2339,12 @@ Mean squared error on test data: 0.22467274
|
||||
Degree of polynomial: 11
|
||||
Mean squared error on training data: 0.01594452
|
||||
Mean squared error on test data: 1.07641937
|
||||
Degree of polynomial: 12
|
||||
Mean squared error on training data: 0.00805074
|
||||
Mean squared error on test data: 0.04295757
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 13
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 12
|
||||
Mean squared error on training data: 0.00805074
|
||||
Mean squared error on test data: 0.04295757
|
||||
Degree of polynomial: 13
|
||||
Mean squared error on training data: 0.00781918
|
||||
Mean squared error on test data: 0.56965674
|
||||
Degree of polynomial: 14
|
||||
@@ -2344,12 +2353,12 @@ Mean squared error on test data: 0.28443039
|
||||
Degree of polynomial: 15
|
||||
Mean squared error on training data: 0.00420072
|
||||
Mean squared error on test data: 568.47051432
|
||||
Degree of polynomial: 16
|
||||
Mean squared error on training data: 0.00325450
|
||||
Mean squared error on test data: 48.97630233
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 17
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 16
|
||||
Mean squared error on training data: 0.00325450
|
||||
Mean squared error on test data: 48.97630233
|
||||
Degree of polynomial: 17
|
||||
Mean squared error on training data: 0.00242954
|
||||
Mean squared error on test data: 2.52780600
|
||||
Degree of polynomial: 18
|
||||
@@ -2358,12 +2367,12 @@ Mean squared error on test data: 429.25695398
|
||||
Degree of polynomial: 19
|
||||
Mean squared error on training data: 0.00154853
|
||||
Mean squared error on test data: 239.97065359
|
||||
Degree of polynomial: 20
|
||||
Mean squared error on training data: 0.00140846
|
||||
Mean squared error on test data: 1350.24493666
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 21
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 20
|
||||
Mean squared error on training data: 0.00140846
|
||||
Mean squared error on test data: 1350.24493666
|
||||
Degree of polynomial: 21
|
||||
Mean squared error on training data: 0.00119688
|
||||
Mean squared error on test data: 1840.50530832
|
||||
Degree of polynomial: 22
|
||||
@@ -2372,12 +2381,12 @@ Mean squared error on test data: 1184.60929685
|
||||
Degree of polynomial: 23
|
||||
Mean squared error on training data: 0.00089193
|
||||
Mean squared error on test data: 3892.17483760
|
||||
Degree of polynomial: 24
|
||||
Mean squared error on training data: 0.00083355
|
||||
Mean squared error on test data: 1332.46736215
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 25
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 24
|
||||
Mean squared error on training data: 0.00083355
|
||||
Mean squared error on test data: 1332.46736215
|
||||
Degree of polynomial: 25
|
||||
Mean squared error on training data: 0.00079904
|
||||
Mean squared error on test data: 7577.76690383
|
||||
Degree of polynomial: 26
|
||||
@@ -2386,19 +2395,19 @@ Mean squared error on test data: 1079.36895644
|
||||
Degree of polynomial: 27
|
||||
Mean squared error on training data: 0.00068091
|
||||
Mean squared error on test data: 3207.25343155
|
||||
Degree of polynomial: 28
|
||||
Mean squared error on training data: 0.00063362
|
||||
Mean squared error on test data: 674.79633065
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 29
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 28
|
||||
Mean squared error on training data: 0.00063362
|
||||
Mean squared error on test data: 674.79633065
|
||||
Degree of polynomial: 29
|
||||
Mean squared error on training data: 0.00063866
|
||||
Mean squared error on test data: 3099.60342978
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87545/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94293/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87545/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94293/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(testerror), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2483,7 +2492,7 @@ Mean squared error on test data: 3099.60342978
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87545/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94293/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1822,7 +1827,7 @@ which equals</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x130ca6a60>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x1220ecf70>
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_82_1.png" src="_images/week39_82_1.png" />
|
||||
@@ -1880,7 +1885,7 @@ which equals</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x13134a100>]
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x122eac100>]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_90_1.png" src="_images/week39_90_1.png" />
|
||||
@@ -2174,11 +2179,11 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Hessian Matrix:[0.33357783 4.08691139]
|
||||
[[3.94040981]
|
||||
[2.96332346]]
|
||||
[[3.94040981]
|
||||
[2.96332346]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Hessian Matrix:[0.2823954 4.41825413]
|
||||
[[3.80708727]
|
||||
[3.19057517]]
|
||||
[[3.80708727]
|
||||
[3.19057517]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_153_1.png" src="_images/week39_153_1.png" />
|
||||
@@ -2209,9 +2214,9 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.33718234]
|
||||
[2.67555087]]
|
||||
[4.32262934] [2.68074588]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[3.93061247]
|
||||
[3.05485826]]
|
||||
[3.94361404] [3.09345236]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2311,11 +2316,11 @@ minimum of this function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Hessian Matrix:[0.29716773 4.6565507 ]
|
||||
[[3.75592582]
|
||||
[3.18603548]]
|
||||
[[3.75409398]
|
||||
[3.18750351]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Hessian Matrix:[0.28261591 4.24106633]
|
||||
[[4.11425439]
|
||||
[2.70819495]]
|
||||
[[4.11313433]
|
||||
[2.70917646]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_166_1.png" src="_images/week39_166_1.png" />
|
||||
@@ -2429,7 +2434,7 @@ minimum of this function.</p>
|
||||
>29 f([0.00115631]) = 0.00000
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87566/394505933.py:33: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94310/394505933.py:33: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
|
||||
print('>%d f(%s) = %.5f' % (i, solution, solution_eval))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2540,7 +2545,7 @@ minimum of this function.</p>
|
||||
>29 f([6.17748881e-07]) = 0.00000
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87566/476849792.py:39: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94310/476849792.py:39: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
|
||||
print('>%d f(%s) = %.5f' % (i, solution, solution_eval))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3605,13 +3610,11 @@ Eigenvalues of Hessian Matrix:[0.31248425 4.44418124]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[3.94499279]
|
||||
[[3.94499279]
|
||||
[3.03306538]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_263_3.png" src="_images/week39_263_3.png" />
|
||||
<img alt="_images/week39_263_2.png" src="_images/week39_263_2.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -3900,14 +3903,18 @@ beta from own Newton code
|
||||
[[4.0586484]
|
||||
[3.0718316]]
|
||||
Eigenvalues of Hessian Matrix:[0.29860173 3.8931686 ]
|
||||
theta from own gd
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
|
||||
[[4.0586484]
|
||||
[3.0718316]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_269_1.png" src="_images/week39_269_1.png" />
|
||||
<img alt="_images/week39_269_2.png" src="_images/week39_269_2.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
|
||||
[[4.02496085]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.02496085]
|
||||
[3.12081773]]
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3996,9 +4003,7 @@ Eigenvalues of Hessian Matrix:[0.27470622 4.24106503]
|
||||
theta from own gd
|
||||
[[3.95906059]
|
||||
[3.02296298]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg with momentum
|
||||
theta from own sdg with momentum
|
||||
[[3.95611042]
|
||||
[2.99475306]]
|
||||
</pre></div>
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1324,17 +1329,17 @@ We summarize some of these here for the methods we hvae studied in project one,
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Parameters for OLS using gradient descent
|
||||
[[3.99232771]
|
||||
[2.9722424 ]
|
||||
[5.02157768]]
|
||||
[[3.79341574]
|
||||
[3.45532899]
|
||||
[4.79869224]]
|
||||
Parameters for Ridge using gradient descent
|
||||
[[3.48717555]
|
||||
[4.38506982]
|
||||
[4.33519245]]
|
||||
[[3.66467908]
|
||||
[3.67744448]
|
||||
[4.69668411]]
|
||||
Parameters for Lasso using gradient descent
|
||||
[[3.82677051]
|
||||
[3.44384079]
|
||||
[4.7949388 ]]
|
||||
[[3.8936154 ]
|
||||
[3.05785843]
|
||||
[5.01267038]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1386,11 +1391,11 @@ Parameters for Lasso using gradient descent
|
||||
[[4.]
|
||||
[3.]
|
||||
[5.]]
|
||||
0 [-22.8745559] [-27.28341218]
|
||||
1 [9.27968813e-14] [1.11928633e-13]
|
||||
2 [-7.10542736e-17] [-9.75573622e-17]
|
||||
3 [-7.10542736e-17] [-9.75573622e-17]
|
||||
4 [-7.10542736e-17] [-9.75573622e-17]
|
||||
0 [-28.98027789] [-37.42420721]
|
||||
1 [1.31983313e-14] [3.4924028e-14]
|
||||
2 [7.99360578e-16] [9.55743376e-16]
|
||||
3 [-1.42108547e-16] [-2.57209333e-16]
|
||||
4 [-1.59872116e-16] [6.89684207e-17]
|
||||
beta from own Newton code
|
||||
[[4.]
|
||||
[3.]
|
||||
@@ -1732,15 +1737,15 @@ function.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.60753606]
|
||||
[3.27788872]]
|
||||
Eigenvalues of Hessian Matrix:[0.25915746 4.55929651]
|
||||
[[3.8125468]
|
||||
[3.3410149]]
|
||||
Eigenvalues of Hessian Matrix:[0.30966921 4.24520733]
|
||||
theta from own gd
|
||||
[[3.60753606]
|
||||
[3.27788872]]
|
||||
[[3.8125468]
|
||||
[3.3410149]]
|
||||
theta from own sdg
|
||||
[[3.62299126]
|
||||
[3.28377068]]
|
||||
[[3.76103892]
|
||||
[3.31388878]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_34_1.png" src="_images/week40_34_1.png" />
|
||||
@@ -2454,12 +2459,12 @@ first example shows results with ordinary leats squares.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.23770713]
|
||||
[2.82891669]]
|
||||
Eigenvalues of Hessian Matrix:[0.26781531 4.61565184]
|
||||
[[4.14040757]
|
||||
[2.84482599]]
|
||||
Eigenvalues of Hessian Matrix:[0.29095968 3.92422684]
|
||||
theta from own gd
|
||||
[[4.23770713]
|
||||
[2.82891669]]
|
||||
[[4.14040757]
|
||||
[2.84482599]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_100_1.png" src="_images/week40_100_1.png" />
|
||||
@@ -2530,73 +2535,73 @@ theta from own gd
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.]
|
||||
[3.]]
|
||||
Eigenvalues of Hessian Matrix:[0.34031551 4.01826645]
|
||||
0 [-16.43418708] [-17.66734487]
|
||||
1 [-0.20743662] [0.18810873]
|
||||
2 [-0.18986837] [0.1721774]
|
||||
3 [-0.17378802] [0.15759533]
|
||||
4 [-0.15906954] [0.14424825]
|
||||
5 [-0.14559761] [0.13203156]
|
||||
6 [-0.13326664] [0.12084953]
|
||||
7 [-0.12198] [0.11061452]
|
||||
8 [-0.11164926] [0.10124634]
|
||||
9 [-0.10219344] [0.09267158]
|
||||
10 [-0.09353846] [0.08482302]
|
||||
11 [-0.08561649] [0.07763918]
|
||||
12 [-0.07836545] [0.07106376]
|
||||
13 [-0.07172852] [0.06504522]
|
||||
14 [-0.06565368] [0.0595364]
|
||||
15 [-0.06009333] [0.05449413]
|
||||
16 [-0.05500389] [0.04987891]
|
||||
17 [-0.0503455] [0.04565456]
|
||||
18 [-0.04608163] [0.04178798]
|
||||
19 [-0.04217888] [0.03824887]
|
||||
20 [-0.03860666] [0.03500949]
|
||||
21 [-0.03533698] [0.03204446]
|
||||
22 [-0.03234422] [0.02933055]
|
||||
23 [-0.02960492] [0.02684648]
|
||||
24 [-0.02709761] [0.0245728]
|
||||
25 [-0.02480266] [0.02249167]
|
||||
26 [-0.02270207] [0.02058681]
|
||||
27 [-0.02077938] [0.01884327]
|
||||
28 [-0.01901953] [0.01724739]
|
||||
29 [-0.01740873] [0.01578667]
|
||||
Eigenvalues of Hessian Matrix:[0.28379561 4.4050219 ]
|
||||
0 [-10.19786399] [-11.56308108]
|
||||
1 [-0.23478113] [0.19832989]
|
||||
2 [-0.21965525] [0.1855524]
|
||||
3 [-0.20550386] [0.1735981]
|
||||
4 [-0.19226417] [0.16241396]
|
||||
5 [-0.17987746] [0.15195036]
|
||||
6 [-0.16828877] [0.14216089]
|
||||
7 [-0.15744669] [0.13300211]
|
||||
8 [-0.14730311] [0.12443338]
|
||||
9 [-0.13781304] [0.1164167]
|
||||
10 [-0.12893437] [0.1089165]
|
||||
11 [-0.12062771] [0.10189951]
|
||||
12 [-0.11285621] [0.09533458]
|
||||
13 [-0.1055854] [0.08919261]
|
||||
14 [-0.09878301] [0.08344633]
|
||||
15 [-0.09241887] [0.07807026]
|
||||
16 [-0.08646474] [0.07304055]
|
||||
17 [-0.08089421] [0.06833488]
|
||||
18 [-0.07568256] [0.06393237]
|
||||
19 [-0.07080668] [0.0598135]
|
||||
20 [-0.06624492] [0.05595998]
|
||||
21 [-0.06197706] [0.05235474]
|
||||
22 [-0.05798416] [0.04898176]
|
||||
23 [-0.0542485] [0.04582608]
|
||||
24 [-0.05075352] [0.04287372]
|
||||
25 [-0.0474837] [0.04011156]
|
||||
26 [-0.04442454] [0.03752735]
|
||||
27 [-0.04156247] [0.03510963]
|
||||
28 [-0.03888479] [0.03284768]
|
||||
29 [-0.03637961] [0.03073145]
|
||||
theta from own gd
|
||||
[[3.95317772]
|
||||
[3.04245961]]
|
||||
0 [-0.01593435] [0.01444966]
|
||||
1 [-0.01458483] [0.01322589]
|
||||
2 [-0.01294476] [0.01173863]
|
||||
3 [-0.01135642] [0.01029828]
|
||||
4 [-0.00991812] [0.008994]
|
||||
5 [-0.00864664] [0.00784099]
|
||||
6 [-0.00753289] [0.00683102]
|
||||
7 [-0.00656079] [0.00594949]
|
||||
8 [-0.00571352] [0.00518116]
|
||||
9 [-0.00497544] [0.00451186]
|
||||
10 [-0.00433264] [0.00392895]
|
||||
11 [-0.00377286] [0.00342132]
|
||||
12 [-0.00328539] [0.00297928]
|
||||
13 [-0.00286091] [0.00259434]
|
||||
14 [-0.00249126] [0.00225914]
|
||||
15 [-0.00216938] [0.00196725]
|
||||
16 [-0.00188909] [0.00171307]
|
||||
17 [-0.00164501] [0.00149173]
|
||||
18 [-0.00143246] [0.00129899]
|
||||
19 [-0.00124738] [0.00113116]
|
||||
20 [-0.00108622] [0.00098501]
|
||||
21 [-0.00094587] [0.00085774]
|
||||
22 [-0.00082366] [0.00074692]
|
||||
23 [-0.00071724] [0.00065041]
|
||||
24 [-0.00062457] [0.00056637]
|
||||
25 [-0.00054387] [0.0004932]
|
||||
26 [-0.0004736] [0.00042947]
|
||||
27 [-0.00041241] [0.00037398]
|
||||
28 [-0.00035912] [0.00032566]
|
||||
29 [-0.00031272] [0.00028359]
|
||||
[[3.88006918]
|
||||
[3.10131081]]
|
||||
0 [-0.03403584] [0.02875156]
|
||||
1 [-0.03184307] [0.02689923]
|
||||
2 [-0.02913373] [0.02461054]
|
||||
3 [-0.02644397] [0.02233838]
|
||||
4 [-0.02393338] [0.02021757]
|
||||
5 [-0.02163828] [0.01827881]
|
||||
6 [-0.0195557] [0.01651955]
|
||||
7 [-0.01767104] [0.0149275]
|
||||
8 [-0.01596717] [0.01348817]
|
||||
9 [-0.01442732] [0.01218739]
|
||||
10 [-0.01303588] [0.01101198]
|
||||
11 [-0.0117786] [0.0099499]
|
||||
12 [-0.01064258] [0.00899025]
|
||||
13 [-0.00961612] [0.00812316]
|
||||
14 [-0.00868866] [0.00733969]
|
||||
15 [-0.00785065] [0.00663179]
|
||||
16 [-0.00709346] [0.00599216]
|
||||
17 [-0.00640931] [0.00541422]
|
||||
18 [-0.00579114] [0.00489203]
|
||||
19 [-0.00523259] [0.0044202]
|
||||
20 [-0.00472792] [0.00399388]
|
||||
21 [-0.00427191] [0.00360867]
|
||||
22 [-0.00385989] [0.00326062]
|
||||
23 [-0.00348761] [0.00294614]
|
||||
24 [-0.00315124] [0.00266199]
|
||||
25 [-0.0028473] [0.00240524]
|
||||
26 [-0.00257269] [0.00217326]
|
||||
27 [-0.00232455] [0.00196365]
|
||||
28 [-0.00210035] [0.00177426]
|
||||
29 [-0.00189778] [0.00160314]
|
||||
theta from own gd wth momentum
|
||||
[[3.99919981]
|
||||
[3.00072563]]
|
||||
[[3.99395784]
|
||||
[3.00510408]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2685,20 +2690,18 @@ theta from own gd wth momentum
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.13706862]
|
||||
[2.74803743]]
|
||||
Eigenvalues of Hessian Matrix:[0.2974512 4.33165194]
|
||||
[[3.97904015]
|
||||
[3.11938084]]
|
||||
Eigenvalues of Hessian Matrix:[0.29437712 4.50172351]
|
||||
theta from own gd
|
||||
[[3.97904015]
|
||||
[3.11938084]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
|
||||
[[4.13706862]
|
||||
[2.74803743]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_104_2.png" src="_images/week40_104_2.png" />
|
||||
<img alt="_images/week40_104_1.png" src="_images/week40_104_1.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
|
||||
[[4.09649893]
|
||||
[2.76751116]]
|
||||
[[3.97069113]
|
||||
[3.13904707]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2780,17 +2783,17 @@ Eigenvalues of Hessian Matrix:[0.2974512 4.33165194]
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.16147054]
|
||||
[2.8496945 ]]
|
||||
Eigenvalues of Hessian Matrix:[0.31764285 4.29777705]
|
||||
[[4.20902858]
|
||||
[2.82421714]]
|
||||
Eigenvalues of Hessian Matrix:[0.29463222 4.67204559]
|
||||
theta from own gd
|
||||
[[4.20862308]
|
||||
[2.82454109]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
|
||||
[[4.16119967]
|
||||
[2.84992628]]
|
||||
theta from own sdg with momentum
|
||||
[[4.18864495]
|
||||
[2.78810857]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg with momentum
|
||||
[[4.13343872]
|
||||
[2.81165023]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2859,9 +2862,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own AdaGrad
|
||||
[[2.00028632]
|
||||
[2.99833653]
|
||||
[4.00168427]]
|
||||
[[1.90103664]
|
||||
[3.54492296]
|
||||
[3.47989639]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2937,9 +2940,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own RMSprop
|
||||
[[2.00002192]
|
||||
[2.9999923 ]
|
||||
[4.00001976]]
|
||||
[[1.99858474]
|
||||
[3.00521037]
|
||||
[3.99718155]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -3019,9 +3022,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own ADAM
|
||||
[[2.00000262]
|
||||
[2.99995454]
|
||||
[4.00004164]]
|
||||
[[2.00002505]
|
||||
[2.99981314]
|
||||
[4.00017937]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -3142,7 +3145,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
|
||||
return asarray(x, dtype=self.dtype)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x11baaec10>]
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x117269df0>]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_120_2.png" src="_images/week40_120_2.png" />
|
||||
@@ -3177,7 +3180,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><matplotlib.collections.PathCollection at 0x11ba4a5b0>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><matplotlib.collections.PathCollection at 0x117195940>
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_122_1.png" src="_images/week40_122_1.png" />
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -3386,7 +3391,7 @@ the <em>Hadamard product</em>, meaning element-wise multiplication.</p>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Old accuracy on training data: 0.1440501043841336
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94334/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3722,7 +3727,7 @@ Lambda = 10.0
|
||||
Accuracy score on test set: 0.19166666666666668
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94334/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3731,7 +3736,7 @@ Lambda = 1e-05
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94334/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3740,7 +3745,7 @@ Lambda = 0.0001
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94334/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3749,7 +3754,7 @@ Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94334/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3758,7 +3763,7 @@ Lambda = 0.01
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94334/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3767,7 +3772,7 @@ Lambda = 0.1
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94334/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3776,191 +3781,33 @@ Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94334/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09166666666666666
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||||
<span class="ne">KeyboardInterrupt</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||||
<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">10</span><span class="p">],</span> <span class="n">line</span> <span class="mi">11</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">lmbd</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">lmbd_vals</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">dnn</span> <span class="o">=</span> <span class="n">NeuralNetwork</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train_onehot</span><span class="p">,</span> <span class="n">eta</span><span class="o">=</span><span class="n">eta</span><span class="p">,</span> <span class="n">lmbd</span><span class="o">=</span><span class="n">lmbd</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="n">epochs</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">10</span> <span class="n">n_hidden_neurons</span><span class="o">=</span><span class="n">n_hidden_neurons</span><span class="p">,</span> <span class="n">n_categories</span><span class="o">=</span><span class="n">n_categories</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">11</span> <span class="n">dnn</span><span class="o">.</span><span class="n">train</span><span class="p">()</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">13</span> <span class="n">DNN_numpy</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dnn</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">15</span> <span class="n">test_predict</span> <span class="o">=</span> <span class="n">dnn</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">Cell In[8], line 99,</span> in <span class="ni">NeuralNetwork.train</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">96</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data_full</span><span class="p">[</span><span class="n">chosen_datapoints</span><span class="p">]</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">98</span> <span class="bp">self</span><span class="o">.</span><span class="n">feed_forward</span><span class="p">()</span>
|
||||
<span class="ne">---> </span><span class="mi">99</span> <span class="bp">self</span><span class="o">.</span><span class="n">backpropagation</span><span class="p">()</span>
|
||||
|
||||
<span class="nn">Cell In[8], line 59,</span> in <span class="ni">NeuralNetwork.backpropagation</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">57</span> <span class="k">def</span> <span class="nf">backpropagation</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">58</span> <span class="n">error_output</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">probabilities</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data</span>
|
||||
<span class="ne">---> </span><span class="mi">59</span> <span class="n">error_hidden</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">error_output</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_weights</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">a_h</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">a_h</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">61</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_weights_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a_h</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">error_output</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">62</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_bias_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">error_output</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||||
|
||||
<span class="ne">KeyboardInterrupt</span>:
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -4006,22 +3853,6 @@ Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87597/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week42_258_1.png" src="_images/week42_258_1.png" />
|
||||
<img alt="_images/week42_258_2.png" src="_images/week42_258_2.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="scikit-learn-implementation">
|
||||
@@ -4057,327 +3888,6 @@ performance overall.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.18333333333333332
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.18611111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.13055555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.24444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.23333333333333334
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.12777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.1527777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9111111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.8305555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8944444444444445
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.975
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9722222222222222
|
||||
|
||||
Learning rate = 0.01
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9527777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9027777777777778
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8583333333333333
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9055555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8666666666666667
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.17777777777777778
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.08333333333333333
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.17222222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.11666666666666667
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.1388888888888889
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.11388888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="id1">
|
||||
@@ -4421,10 +3931,6 @@ Accuracy score on test set: 0.09444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<img alt="_images/week42_262_0.png" src="_images/week42_262_0.png" />
|
||||
<img alt="_images/week42_262_1.png" src="_images/week42_262_1.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="building-neural-networks-in-tensorflow-and-keras">
|
||||
@@ -4463,14 +3969,6 @@ how simple solving a machine learning problem can be.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span> <span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">14</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
|
||||
<span class="n">pip3</span> <span class="n">install</span> <span class="n">tensorflow</span>
|
||||
<span class="o">^</span>
|
||||
<span class="ne">SyntaxError</span>: invalid syntax
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>and/or if you use <strong>anaconda</strong>, just write (or install from the graphical user interface)
|
||||
(current release of CPU-only TensorFlow)</p>
|
||||
|
||||
@@ -55,7 +55,7 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||||
<link rel="index" title="Index" href="genindex.html" />
|
||||
<link rel="search" title="Search" href="search.html" />
|
||||
<link rel="next" title="Project 1 on Machine Learning, deadline October 7 (midnight), 2024" href="project1.html" />
|
||||
<link rel="next" title="Exercises week 43" href="exercisesweek43.html" />
|
||||
<link rel="prev" title="Exercises Week 42: Logistic Regression and Optimization, reminders from week 38 and week 40" href="additionweek42.html" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||
<meta name="docsearch:language" content="None">
|
||||
@@ -343,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek43.html">
|
||||
Exercises week 43
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -2346,7 +2351,7 @@ the <em>Hadamard product</em>, meaning element-wise multiplication.</p>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Old accuracy on training data: 0.1440501043841336
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_93488/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2677,30 +2682,250 @@ Lambda = 1.0
|
||||
Accuracy score on test set: 0.7694444444444445
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||||
<span class="ne">KeyboardInterrupt</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||||
<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">8</span><span class="p">],</span> <span class="n">line</span> <span class="mi">11</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">lmbd</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">lmbd_vals</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">dnn</span> <span class="o">=</span> <span class="n">NeuralNetwork</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train_onehot</span><span class="p">,</span> <span class="n">eta</span><span class="o">=</span><span class="n">eta</span><span class="p">,</span> <span class="n">lmbd</span><span class="o">=</span><span class="n">lmbd</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="n">epochs</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">10</span> <span class="n">n_hidden_neurons</span><span class="o">=</span><span class="n">n_hidden_neurons</span><span class="p">,</span> <span class="n">n_categories</span><span class="o">=</span><span class="n">n_categories</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">11</span> <span class="n">dnn</span><span class="o">.</span><span class="n">train</span><span class="p">()</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">13</span> <span class="n">DNN_numpy</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dnn</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">15</span> <span class="n">test_predict</span> <span class="o">=</span> <span class="n">dnn</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">Cell In[6], line 98,</span> in <span class="ni">NeuralNetwork.train</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">95</span> <span class="bp">self</span><span class="o">.</span><span class="n">X_data</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">X_data_full</span><span class="p">[</span><span class="n">chosen_datapoints</span><span class="p">]</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">96</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data_full</span><span class="p">[</span><span class="n">chosen_datapoints</span><span class="p">]</span>
|
||||
<span class="ne">---> </span><span class="mi">98</span> <span class="bp">self</span><span class="o">.</span><span class="n">feed_forward</span><span class="p">()</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">99</span> <span class="bp">self</span><span class="o">.</span><span class="n">backpropagation</span><span class="p">()</span>
|
||||
|
||||
<span class="nn">Cell In[6], line 38,</span> in <span class="ni">NeuralNetwork.feed_forward</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">36</span> <span class="k">def</span> <span class="nf">feed_forward</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">37</span> <span class="c1"># feed-forward for training</span>
|
||||
<span class="ne">---> </span><span class="mi">38</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">X_data</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_weights</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_bias</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">39</span> <span class="bp">self</span><span class="o">.</span><span class="n">a_h</span> <span class="o">=</span> <span class="n">sigmoid</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z_h</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">41</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_o</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a_h</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_weights</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_bias</span>
|
||||
|
||||
<span class="ne">KeyboardInterrupt</span>:
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.19166666666666668
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09166666666666666
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2746,6 +2971,22 @@ Accuracy score on test set: 0.7694444444444445
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94373/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week43_96_1.png" src="_images/week43_96_1.png" />
|
||||
<img alt="_images/week43_96_2.png" src="_images/week43_96_2.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="scikit-learn-implementation">
|
||||
@@ -2781,6 +3022,328 @@ performance overall.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.18333333333333332
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.18611111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.13055555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.24444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.23333333333333334
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.12777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.1527777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9111111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.8305555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8944444444444445
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.975
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9722222222222222
|
||||
|
||||
Learning rate = 0.01
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9527777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9027777777777778
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8583333333333333
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9055555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
|
||||
Learning rate = 0.1
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8666666666666667
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.17777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.08333333333333333
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.17222222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.11666666666666667
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.1388888888888889
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.11388888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="id1">
|
||||
@@ -2824,6 +3387,10 @@ performance overall.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<img alt="_images/week43_100_0.png" src="_images/week43_100_0.png" />
|
||||
<img alt="_images/week43_100_1.png" src="_images/week43_100_1.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="building-neural-networks-in-tensorflow-and-keras">
|
||||
@@ -2862,6 +3429,14 @@ how simple solving a machine learning problem can be.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span> <span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">12</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
|
||||
<span class="n">pip3</span> <span class="n">install</span> <span class="n">tensorflow</span>
|
||||
<span class="o">^</span>
|
||||
<span class="ne">SyntaxError</span>: invalid syntax
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>and/or if you use <strong>anaconda</strong>, just write (or install from the graphical user interface)
|
||||
(current release of CPU-only TensorFlow)</p>
|
||||
@@ -6600,10 +7175,10 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)
|
||||
<p class="prev-next-title">Exercises Week 42: Logistic Regression and Optimization, reminders from week 38 and week 40</p>
|
||||
</div>
|
||||
</a>
|
||||
<a class='right-next' id="next-link" href="project1.html" title="next page">
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<a class='right-next' id="next-link" href="exercisesweek43.html" title="next page">
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||||
<div class="prev-next-info">
|
||||
<p class="prev-next-subtitle">next</p>
|
||||
<p class="prev-next-title">Project 1 on Machine Learning, deadline October 7 (midnight), 2024</p>
|
||||
<p class="prev-next-title">Exercises week 43</p>
|
||||
</div>
|
||||
<i class="fas fa-angle-right"></i>
|
||||
</a>
|
||||
|
||||
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