347 lines
110 KiB
Plaintext
347 lines
110 KiB
Plaintext
{
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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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"# Predicting the phase transition of the two dimensional Ising model using neural networks\n",
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"\n",
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"We will in this notebook repeat the process of predicting the phase transition of the two dimensional Ising model as we did with logistic regression, but now we will employ a _feed-forwad neural network_."
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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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"## Predicting the phase of the two-dimensional Ising model using a feed-forward neural network\n",
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"\n",
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"We now predict the phase transition using Scikit-learn's implementation of a _multilayer perceptron neural network_. This is one of the simpler versions of a neural network.\n",
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"\n",
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"A neural network consists of layers of _neurons_ or perceptrons. A neuron can take a continuous value where as a perceptron will be either \"on\" or \"off\". Scikit-learn's `MLPClassifier` is called a multilayer perceptron model, but it uses neurons. A neuron accepts a vector of inputs $x$ and produces a scalar output $a_i$. A layer of neurons take in the a matrix $X$ and produces an activation vector $a$ consisting of each $a_i$ from each neuron in that layer.\n",
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"\n",
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"\\begin{align}\n",
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" z^{(l)} = a^{(l - 1)}w^{(l)} + b^{(l)},\n",
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"\\end{align}\n",
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"\n",
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"where $w^{(l)}$ is that layers _weights_ and $b^{(l)}$ is that layers _biases_. The activation $a^{(l)}$ is now computed by\n",
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"\n",
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"\\begin{align}\n",
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" a^{(l)} = f(z^{(l)}),\n",
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"\\end{align}\n",
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"\n",
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"where $f(z)$ is an _activation function_. The first activation is given by $a^{(0)} = X$, where $X$ is the input data.\n",
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"\n",
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"It is common to use the cross-entropy as the cost function for a categorical neural network. This is the same the one used in logistic regression."
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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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"### Training a neural network\n",
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"\n",
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"The training of a neural network is a tricky affair as each neuron in each layer must be updated to minimize a cost function. The minimization process resembles that of other classifiers and regressors in that we use an optimization algorithm, e.g., stochastic gradient descent, to compute the change in the weights and biases in order to find a minimum of the cost function. The tricky part comes in computing the gradients of the weights and biases in the neural network. Due to an ingenious technique called _backpropagation_ this can be done within reasonable time. The algorithm is listed below.\n",
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"\n",
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"1. Do a feedforward pass, i.e., compute all activations $a^{(l)}$ as listed above.\n",
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"2. Calculate the error of the weights and biases using\n",
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"\\begin{align}\n",
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" \\delta_{j}^{(l)} = \\frac{\\partial C}{\\partial a_{j}^{(l)}} \\frac{\\mathrm{d}f(z_j^{(l)})}{\\mathrm{d}z}.\n",
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"\\end{align}\n",
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"3. Propagate the error backwards (hence backpropagation) using\n",
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"\\begin{align}\n",
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" \\delta_{j}^{(l)} = \\left(\n",
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" \\sum_{k}\\delta_k^{(l + 1)}\\omega_{kj}^{(l + 1)}\n",
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" \\right)\\frac{\\mathrm{d}f(z_j^{(l)}}{\\mathrm{d}z}.\n",
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"\\end{align}\n",
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"4. Compute the change in the gradients of the weights and biases.\n",
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"\\begin{align}\n",
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" \\omega^{(l)} &\\to \\omega^{(l)} - \\frac{\\eta}{m}\\sum_{k}\\delta^{(l)}_ka_k^{(l - 1)}, \\\\\n",
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" b^{(l)} &\\to b^{(l)} - \\frac{\\eta}{m}\\sum_{k}\\delta^{(l)}_k,\n",
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"\\end{align}\n",
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" where $\\eta$ is the learning rate and $m$ is the number of elements (batch size in the case of stochastic gradient descent)."
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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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"We will do a large search over a two-dimensional parameter grid for varying hidden layer sizes and learning rate."
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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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"## DIY Neural net from Keras\n",
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"\n",
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"\n",
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"An easier approach is to use libraries such as Tensorflow or Keras (which by default uses Tensorflow as a backend) to specify how the neural net should be. The libraries then build a neural net based on your specifications and lets you fit and predict on your very own construct. As a bonus, Tensorflow builds a graph from the executing code thus figuring out the most optimal way of executing the code and which parts of the code that can be done in parallel.\n",
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"\n",
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"A perk of building a neural net this way is that we have a lot of freedom in how we build our neural net. For instance, we can set individual activation functions for each layer, decide the optimization technique to use, the cost function to minimize, which metric to evaluate our model on etc."
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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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"We now build a neural net from Keras with three hidden layers. The input and the hidden layer uses the activation function\n",
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"\n",
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"\\begin{align}\n",
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" f(z_j) = \\tanh(z_j),\n",
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"\\end{align}\n",
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"\n",
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"whereas the output layer uses the _softmax_ activation function.\n",
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"\n",
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"\\begin{align}\n",
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" g(z_j) = \\frac{e^{z_j}}{\\sum_{i = 1}^{n} e^{z_i}}.\n",
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"\\end{align}\n",
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"\n",
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"We avoid using the tangent hyperbolicus for the output layer as $f(z_j) \\in [-1, 1]$ as opposed to the softmax function with $g(z_j) \\in [0, 1]$. The latter more fits the categorical classification. Another perk of using the softmax activation function is that it better weighs all the classes in a multiclassification setting much as the partition function. We use stochastic gradient descent as our optimizer and the cross-entropy (shown in the notebook on logistic regression) as our cost function."
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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": 32,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"clf = km.Sequential()\n",
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"\n",
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"clf.add(\n",
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" kl.Dense(50, activation=\"tanh\", input_dim=X_train.shape[1])\n",
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")\n",
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"clf.add(\n",
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" kl.Dense(100, activation=\"tanh\")\n",
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")\n",
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"clf.add(\n",
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" kl.Dense(200, activation=\"tanh\")\n",
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")\n",
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"\n",
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"clf.add(\n",
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" kl.Dense(2, activation=\"softmax\")\n",
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")\n",
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"clf.compile(\n",
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" loss=\"binary_crossentropy\",\n",
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" optimizer=ko.SGD(\n",
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" lr=0.01\n",
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" ),\n",
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" metrics=[\"accuracy\"]\n",
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")"
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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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"We have to convert our integer labels to categorical values in a format that Keras accepts."
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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": 33,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"y_train_k = to_categorical(y_train[:, np.newaxis])\n",
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"y_test_k = to_categorical(y_test[:, np.newaxis])\n",
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"y_critical_k = to_categorical(labels[critical][:, np.newaxis])"
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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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"We now fit our model for $10$ epochs and validate on the test data."
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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": 34,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Train on 65000 samples, validate on 65000 samples\n",
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"Epoch 1/10\n",
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"65000/65000 [==============================] - 6s 88us/step - loss: 0.6629 - acc: 0.6971 - val_loss: 0.5873 - val_acc: 0.8317\n",
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"Epoch 2/10\n",
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"65000/65000 [==============================] - 5s 72us/step - loss: 0.4253 - acc: 0.9397 - val_loss: 0.2529 - val_acc: 0.9956\n",
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"Epoch 3/10\n",
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"65000/65000 [==============================] - 5s 76us/step - loss: 0.1287 - acc: 0.9950 - val_loss: 0.0639 - val_acc: 0.9989\n",
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"Epoch 4/10\n",
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"65000/65000 [==============================] - 3s 44us/step - loss: 0.0419 - acc: 0.9992 - val_loss: 0.0300 - val_acc: 0.9990\n",
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"Epoch 5/10\n",
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"65000/65000 [==============================] - 3s 46us/step - loss: 0.0222 - acc: 0.9994 - val_loss: 0.0189 - val_acc: 0.9991\n",
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"Epoch 6/10\n",
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"65000/65000 [==============================] - 3s 43us/step - loss: 0.0146 - acc: 0.9994 - val_loss: 0.0137 - val_acc: 0.9991\n",
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"Epoch 7/10\n",
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"65000/65000 [==============================] - 3s 48us/step - loss: 0.0106 - acc: 0.9994 - val_loss: 0.0107 - val_acc: 0.9992\n",
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"Epoch 8/10\n",
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"65000/65000 [==============================] - 4s 56us/step - loss: 0.0083 - acc: 0.9995 - val_loss: 0.0087 - val_acc: 0.9992\n",
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"Epoch 9/10\n",
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"65000/65000 [==============================] - 4s 59us/step - loss: 0.0068 - acc: 0.9995 - val_loss: 0.0074 - val_acc: 0.9992\n",
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"Epoch 10/10\n",
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"65000/65000 [==============================] - 3s 53us/step - loss: 0.0057 - acc: 0.9996 - val_loss: 0.0064 - val_acc: 0.9992\n"
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]
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}
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],
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"source": [
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"history = clf.fit(\n",
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" X_train, y_train_k,\n",
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" validation_data=(X_test, y_test_k),\n",
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" epochs=10,\n",
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" batch_size=200,\n",
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" verbose=True\n",
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")"
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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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"We now evaluate the model."
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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": 35,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"65000/65000 [==============================] - 2s 34us/step\n",
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"65000/65000 [==============================] - 4s 54us/step\n",
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"30000/30000 [==============================] - 3s 103us/step\n",
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"Accuracy on train data: 0.999538461978619\n",
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"Accuracy on test data: 0.9992307699643649\n",
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"Accuracy on critical data: 0.9312000012397766\n"
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]
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}
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],
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"source": [
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"train_accuracy = clf.evaluate(X_train, y_train_k, batch_size=200)[1]\n",
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"test_accuracy = clf.evaluate(X_test, y_test_k, batch_size=200)[1]\n",
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"critical_accuracy = clf.evaluate(data[critical], y_critical_k, batch_size=200)[1]\n",
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"\n",
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"print (\"Accuracy on train data: {0}\".format(train_accuracy))\n",
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"print (\"Accuracy on test data: {0}\".format(test_accuracy))\n",
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"print (\"Accuracy on critical data: {0}\".format(critical_accuracy))"
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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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"Then we plot the ROC curve for three datasets."
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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": 36,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Keras AUC (Train): 0.9999965210789427\n",
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"Keras AUC (Test): 0.9999774128074636\n",
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"Keras AUC (Critical): 0.9849365475\n"
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]
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},
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{
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"data": {
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"image/png": 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hgUJ8fDyeeeYZ3HfffZg/fz5uvPFGDBkyBEVFRVi7di1yc3Nxxx13YN68ec3WZLPZ8Mgj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EUIoerB3+0BwFlFeZVOJucodlDXOuuRMSHqHd2J0U8AAAAAnBBCNRTXUwA6uPSTudqyLlklxZXy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\npW0AAAAASUVORK5CYII=\n",
|
|
"text/plain": [
|
|
"<matplotlib.figure.Figure at 0x12e47acc0>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(20, 14))\n",
|
|
"\n",
|
|
"for (_X, _y), label in zip(\n",
|
|
" [\n",
|
|
" (X_train, y_train_k),\n",
|
|
" (X_test, y_test_k),\n",
|
|
" (data[critical], y_critical_k)\n",
|
|
" ],\n",
|
|
" [\"Train\", \"Test\", \"Critical\"]\n",
|
|
"):\n",
|
|
" proba = clf.predict(_X)\n",
|
|
" fpr, tpr, _ = skm.roc_curve(_y[:, 1], proba[:, 1])\n",
|
|
" roc_auc = skm.auc(fpr, tpr)\n",
|
|
"\n",
|
|
" print (\"Keras AUC ({0}): {1}\".format(label, roc_auc))\n",
|
|
"\n",
|
|
" plt.plot(fpr, tpr, label=\"{0} (AUC = {1})\".format(label, roc_auc), linewidth=4.0)\n",
|
|
"\n",
|
|
"plt.plot([0, 1], [0, 1], \"--\", label=\"Guessing (AUC = 0.5)\", linewidth=4.0)\n",
|
|
"\n",
|
|
"plt.title(r\"The ROC curve for Keras\", fontsize=18)\n",
|
|
"plt.xlabel(r\"False positive rate\", fontsize=18)\n",
|
|
"plt.ylabel(r\"True positive rate\", fontsize=18)\n",
|
|
"plt.axis([-0.01, 1.01, -0.01, 1.01])\n",
|
|
"plt.xticks(fontsize=18)\n",
|
|
"plt.yticks(fontsize=18)\n",
|
|
"plt.legend(loc=\"best\", fontsize=18)\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"We see that we get much the same performance as for the `MLPClassifier` from Scikit-learn."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Conclusion\n",
|
|
"\n",
|
|
"We have successfully used a neural net using Keras and predicted the phase transition of the two-dimensional Ising model. As opposed to the logistic regression we get a much better performance on all datasets. More importantly we successfully predict reasonable values on the critical dataset which is extrapolated from the training and testing data."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"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": "3.6.5"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|