diff --git a/doc/pub/week47/html/._week47-bs001.html b/doc/pub/week47/html/._week47-bs001.html index 94a90cfc0..0f89e86a7 100644 --- a/doc/pub/week47/html/._week47-bs001.html +++ b/doc/pub/week47/html/._week47-bs001.html @@ -354,7 +354,10 @@ MathJax.Hub.Config({

Overview of week 47

_Reading recommendations:

diff --git a/doc/pub/week47/html/week47-reveal.html b/doc/pub/week47/html/week47-reveal.html index cced7c324..9165055c1 100644 --- a/doc/pub/week47/html/week47-reveal.html +++ b/doc/pub/week47/html/week47-reveal.html @@ -198,7 +198,12 @@ MathJax.Hub.Config({

Overview of week 47

diff --git a/doc/pub/week47/html/week47-solarized.html b/doc/pub/week47/html/week47-solarized.html index 12bcb3ae4..9eb67ec1a 100644 --- a/doc/pub/week47/html/week47-solarized.html +++ b/doc/pub/week47/html/week47-solarized.html @@ -301,7 +301,10 @@ MathJax.Hub.Config({

Overview of week 47

_Reading recommendations:

diff --git a/doc/pub/week47/html/week47.html b/doc/pub/week47/html/week47.html index c3c15e801..c3825d7b3 100644 --- a/doc/pub/week47/html/week47.html +++ b/doc/pub/week47/html/week47.html @@ -378,7 +378,10 @@ MathJax.Hub.Config({

Overview of week 47

_Reading recommendations:

diff --git a/doc/pub/week47/ipynb/ipynb-week47-src.tar.gz b/doc/pub/week47/ipynb/ipynb-week47-src.tar.gz index 95a2ef164..aa313d1a6 100644 Binary files a/doc/pub/week47/ipynb/ipynb-week47-src.tar.gz and b/doc/pub/week47/ipynb/ipynb-week47-src.tar.gz differ diff --git a/doc/pub/week47/ipynb/week47.ipynb b/doc/pub/week47/ipynb/week47.ipynb index ee404a167..7c4d4696e 100644 --- a/doc/pub/week47/ipynb/week47.ipynb +++ b/doc/pub/week47/ipynb/week47.ipynb @@ -2,8 +2,10 @@ "cells": [ { "cell_type": "markdown", - "id": "1708e9eb", - "metadata": {}, + "id": "688b8dde", + "metadata": { + "editable": true + }, "source": [ "\n", @@ -12,8 +14,10 @@ }, { "cell_type": "markdown", - "id": "aeceb3ed", - "metadata": {}, + "id": "dc557614", + "metadata": { + "editable": true + }, "source": [ "# Week 47: Support Vector Machines and Summary of Course\n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", @@ -25,12 +29,16 @@ }, { "cell_type": "markdown", - "id": "349d5566", - "metadata": {}, + "id": "9bdd5993", + "metadata": { + "editable": true + }, "source": [ "## Overview of week 47\n", "\n", - "* **Thursday**: Support Vector Machines, classification and regression. \n", + "* **Thursday**: Support Vector Machines, classification and regression.\n", + "\n", + " * [Video of Lecture](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureNovember25.mp4?vrtx=view-as-webpage)\n", "\n", "* **Friday**: Support Vector Machines and Summary of Course\n", "\n", @@ -46,8 +54,10 @@ }, { "cell_type": "markdown", - "id": "276c8d08", - "metadata": {}, + "id": "027a728b", + "metadata": { + "editable": true + }, "source": [ "## Support Vector Machines, overarching aims\n", "\n", @@ -78,8 +88,10 @@ }, { "cell_type": "markdown", - "id": "9b98a19a", - "metadata": {}, + "id": "6629bef8", + "metadata": { + "editable": true + }, "source": [ "## Hyperplanes and all that\n", "\n", @@ -98,31 +110,12 @@ { "cell_type": "code", "execution_count": 1, - "id": "d12c9e26", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "LinearSVC: [0.28475098] [[1.05364854 1.09903804]]\n", - "SVC: [0.31896852] [[1.1203284 1.02625193]]\n", - "SGDClassifier(alpha=0.00200): [0.117] [[0.77714169 0.72981762]]\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "id": "8e8b6d0b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "%matplotlib inline\n", "\n", @@ -196,8 +189,10 @@ }, { "cell_type": "markdown", - "id": "b0002a66", - "metadata": {}, + "id": "cdbeaba1", + "metadata": { + "editable": true + }, "source": [ "## What is a hyperplane?\n", "\n", @@ -214,8 +209,10 @@ }, { "cell_type": "markdown", - "id": "8f68e125", - "metadata": {}, + "id": "253ea27e", + "metadata": { + "editable": true + }, "source": [ "$$\n", "b+w_1x_1+w_2x_2=0,\n", @@ -224,8 +221,10 @@ }, { "cell_type": "markdown", - "id": "c4ff70be", - "metadata": {}, + "id": "a2ed8187", + "metadata": { + "editable": true + }, "source": [ "where $b$ is the intercept and $w_1$ and $w_2$ define the elements of a vector orthogonal to the line \n", "$b+w_1x_1+w_2x_2=0$. \n", @@ -235,8 +234,10 @@ }, { "cell_type": "markdown", - "id": "245ca618", - "metadata": {}, + "id": "240c6202", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}^T\\boldsymbol{w}+b=0.\n", @@ -245,16 +246,20 @@ }, { "cell_type": "markdown", - "id": "9cbde939", - "metadata": {}, + "id": "5ae76eec", + "metadata": { + "editable": true + }, "source": [ "For figures, see [handwritten notes](https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021) for Thursday November 25." ] }, { "cell_type": "markdown", - "id": "2053f3da", - "metadata": {}, + "id": "a60469d7", + "metadata": { + "editable": true + }, "source": [ "## A $p$-dimensional space of features\n", "\n", @@ -264,8 +269,10 @@ }, { "cell_type": "markdown", - "id": "edc8cd0b", - "metadata": {}, + "id": "8f2a4945", + "metadata": { + "editable": true + }, "source": [ "$$\n", "b+wx_1+w_2x_2+\\dots +w_px_p=0.\n", @@ -274,8 +281,10 @@ }, { "cell_type": "markdown", - "id": "72f2ceeb", - "metadata": {}, + "id": "b624e2ea", + "metadata": { + "editable": true + }, "source": [ "If we define a \n", "matrix $\\boldsymbol{X}=\\left[\\boldsymbol{x}_1,\\boldsymbol{x}_2,\\dots, \\boldsymbol{x}_p\\right]$\n", @@ -284,8 +293,10 @@ }, { "cell_type": "markdown", - "id": "5b6e0a88", - "metadata": {}, + "id": "b05c4115", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_i = \\begin{bmatrix} x_{i1} \\\\ x_{i2} \\\\ \\dots \\\\ \\dots \\\\ x_{ip} \\end{bmatrix}.\n", @@ -294,16 +305,20 @@ }, { "cell_type": "markdown", - "id": "73e2d917", - "metadata": {}, + "id": "079b9a56", + "metadata": { + "editable": true + }, "source": [ "If the above condition is not met for a given vector $\\boldsymbol{x}_i$ we have" ] }, { "cell_type": "markdown", - "id": "6de10722", - "metadata": {}, + "id": "34ec2eba", + "metadata": { + "editable": true + }, "source": [ "$$\n", "b+w_1x_{i1}+w_2x_{i2}+\\dots +w_px_{ip} >0,\n", @@ -312,8 +327,10 @@ }, { "cell_type": "markdown", - "id": "d55fa0e3", - "metadata": {}, + "id": "765234de", + "metadata": { + "editable": true + }, "source": [ "if our output $y_i=1$.\n", "In this case we say that $\\boldsymbol{x}_i$ lies on one of the sides of the hyperplane and if" @@ -321,8 +338,10 @@ }, { "cell_type": "markdown", - "id": "567365ad", - "metadata": {}, + "id": "ec821bc3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "b+w_1x_{i1}+w_2x_{i2}+\\dots +w_px_{ip} < 0,\n", @@ -331,8 +350,10 @@ }, { "cell_type": "markdown", - "id": "033c5353", - "metadata": {}, + "id": "f7e13157", + "metadata": { + "editable": true + }, "source": [ "for the class of observations $y_i=-1$, \n", "then $\\boldsymbol{x}_i$ lies on the other side. \n", @@ -342,8 +363,10 @@ }, { "cell_type": "markdown", - "id": "dfa1a17c", - "metadata": {}, + "id": "f3b0b0ab", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i\\left(b+w_1x_{i1}+w_2x_{i2}+\\dots +w_px_{ip}\\right) > 0.\n", @@ -352,16 +375,20 @@ }, { "cell_type": "markdown", - "id": "d9b56fb1", - "metadata": {}, + "id": "309e659d", + "metadata": { + "editable": true + }, "source": [ "When we try to separate hyperplanes, if it exists, we can use it to construct a natural classifier: a test observation is assigned a given class depending on which side of the hyperplane it is located." ] }, { "cell_type": "markdown", - "id": "461d38f0", - "metadata": {}, + "id": "57835c0d", + "metadata": { + "editable": true + }, "source": [ "## The two-dimensional case\n", "\n", @@ -387,8 +414,10 @@ }, { "cell_type": "markdown", - "id": "325dabde", - "metadata": {}, + "id": "ea3df06a", + "metadata": { + "editable": true + }, "source": [ "## Getting into the details\n", "\n", @@ -397,8 +426,10 @@ }, { "cell_type": "markdown", - "id": "16861109", - "metadata": {}, + "id": "63a04897", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(x) = \\boldsymbol{w}^T\\boldsymbol{x}+b = 0,\n", @@ -407,8 +438,10 @@ }, { "cell_type": "markdown", - "id": "f2ddedc9", - "metadata": {}, + "id": "79b373ad", + "metadata": { + "editable": true + }, "source": [ "as the function that determines the line $L$ that separates two classes (our two features), see the figures in the [handwritten notes](https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021) for Thursday November 25.\n", ". \n", @@ -420,8 +453,10 @@ }, { "cell_type": "markdown", - "id": "4306bffb", - "metadata": {}, + "id": "8bc275b3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\delta = \\frac{1}{\\vert\\vert \\boldsymbol{w}\\vert\\vert}(\\boldsymbol{w}^T\\boldsymbol{x}+b).\n", @@ -430,8 +465,10 @@ }, { "cell_type": "markdown", - "id": "9a1f970e", - "metadata": {}, + "id": "508d8760", + "metadata": { + "editable": true + }, "source": [ "## First attempt at a minimization approach\n", "\n", @@ -442,8 +479,10 @@ }, { "cell_type": "markdown", - "id": "686298c8", - "metadata": {}, + "id": "25793ffc", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{w},b) = -\\sum_{i\\in M} y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b).\n", @@ -452,16 +491,20 @@ }, { "cell_type": "markdown", - "id": "c00fa0cb", - "metadata": {}, + "id": "3c44fe1f", + "metadata": { + "editable": true + }, "source": [ "We could now for example define all values $y_i =1$ as misclassified in case we have $\\boldsymbol{w}^T\\boldsymbol{x}_i+b < 0$ and the opposite if we have $y_i=-1$. Taking the derivatives gives us" ] }, { "cell_type": "markdown", - "id": "a45a44e2", - "metadata": {}, + "id": "b801b7ef", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial C}{\\partial b} = -\\sum_{i\\in M} y_i,\n", @@ -470,16 +513,20 @@ }, { "cell_type": "markdown", - "id": "cb71bc88", - "metadata": {}, + "id": "79152f7e", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "0fb319c6", - "metadata": {}, + "id": "0d8b820a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial C}{\\partial \\boldsymbol{w}} = -\\sum_{i\\in M} y_ix_i.\n", @@ -488,8 +535,10 @@ }, { "cell_type": "markdown", - "id": "be983759", - "metadata": {}, + "id": "3b751f02", + "metadata": { + "editable": true + }, "source": [ "## Solving the equations\n", "\n", @@ -498,8 +547,10 @@ }, { "cell_type": "markdown", - "id": "0863cef7", - "metadata": {}, + "id": "6e23ce6c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "b \\leftarrow b +\\eta \\frac{\\partial C}{\\partial b},\n", @@ -508,16 +559,20 @@ }, { "cell_type": "markdown", - "id": "b689a885", - "metadata": {}, + "id": "a68f94d2", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "4a258203", - "metadata": {}, + "id": "22863a65", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{w} \\leftarrow \\boldsymbol{w} +\\eta \\frac{\\partial C}{\\partial \\boldsymbol{w}},\n", @@ -526,16 +581,20 @@ }, { "cell_type": "markdown", - "id": "ead67e72", - "metadata": {}, + "id": "e2bb412b", + "metadata": { + "editable": true + }, "source": [ "where $\\eta$ is our by now well-known learning rate." ] }, { "cell_type": "markdown", - "id": "8d4d628c", - "metadata": {}, + "id": "83636c52", + "metadata": { + "editable": true + }, "source": [ "## Problems with the Simpler Approach\n", "\n", @@ -555,8 +614,10 @@ }, { "cell_type": "markdown", - "id": "347c4a08", - "metadata": {}, + "id": "f7aac32d", + "metadata": { + "editable": true + }, "source": [ "## A better approach\n", "\n", @@ -569,8 +630,10 @@ }, { "cell_type": "markdown", - "id": "abb58339", - "metadata": {}, + "id": "fae15368", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) \\geq M \\hspace{0.1cm}\\forall i=1,2,\\dots, n.\n", @@ -579,8 +642,10 @@ }, { "cell_type": "markdown", - "id": "0f707d57", - "metadata": {}, + "id": "f8d5b573", + "metadata": { + "editable": true + }, "source": [ "All points are thus at a signed distance from the decision boundary defined by the line $L$. The parameters $b$ and $w_1$ and $w_2$ define this line. \n", "\n", @@ -589,8 +654,10 @@ }, { "cell_type": "markdown", - "id": "d20d1e37", - "metadata": {}, + "id": "90cb8295", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{1}{\\vert \\vert \\boldsymbol{w}\\vert\\vert}y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) \\geq M \\hspace{0.1cm}\\forall i=1,2,\\dots, n,\n", @@ -599,16 +666,20 @@ }, { "cell_type": "markdown", - "id": "1db90e6c", - "metadata": {}, + "id": "b9a33957", + "metadata": { + "editable": true + }, "source": [ "or just" ] }, { "cell_type": "markdown", - "id": "f7434597", - "metadata": {}, + "id": "acaf1bce", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) \\geq M\\vert \\vert \\boldsymbol{w}\\vert\\vert \\hspace{0.1cm}\\forall i=1,2,\\dots,n.\n", @@ -617,8 +688,10 @@ }, { "cell_type": "markdown", - "id": "4d32d348", - "metadata": {}, + "id": "745c9e07", + "metadata": { + "editable": true + }, "source": [ "If we scale the equation so that $\\vert \\vert \\boldsymbol{w}\\vert\\vert = 1/M$, we have to find the minimum of \n", "$\\boldsymbol{w}^T\\boldsymbol{w}=\\vert \\vert \\boldsymbol{w}\\vert\\vert_2^2$ (the norm) subject to the condition" @@ -626,8 +699,10 @@ }, { "cell_type": "markdown", - "id": "d1a75d9f", - "metadata": {}, + "id": "a2e94351", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) \\geq 1 \\hspace{0.1cm}\\forall i=1,2,\\dots,n.\n", @@ -636,8 +711,10 @@ }, { "cell_type": "markdown", - "id": "69f0b39a", - "metadata": {}, + "id": "9c0dc8fb", + "metadata": { + "editable": true + }, "source": [ "We have thus defined our margin as the invers of the norm of\n", "$\\boldsymbol{w}$. We want to minimize the norm in order to have a as large as\n", @@ -647,8 +724,10 @@ }, { "cell_type": "markdown", - "id": "ba07bab7", - "metadata": {}, + "id": "19a4b668", + "metadata": { + "editable": true + }, "source": [ "## A quick Reminder on Lagrangian Multipliers\n", "\n", @@ -658,8 +737,10 @@ }, { "cell_type": "markdown", - "id": "0406de63", - "metadata": {}, + "id": "503733b6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "df=0.\n", @@ -668,16 +749,20 @@ }, { "cell_type": "markdown", - "id": "ec5cf43e", - "metadata": {}, + "id": "f46a1dec", + "metadata": { + "editable": true + }, "source": [ "A necessary and sufficient condition is" ] }, { "cell_type": "markdown", - "id": "b934ace1", - "metadata": {}, + "id": "68b9cbe2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f}{\\partial x} =\\frac{\\partial f}{\\partial y}=\\frac{\\partial f}{\\partial z}=0,\n", @@ -686,16 +771,20 @@ }, { "cell_type": "markdown", - "id": "b658e117", - "metadata": {}, + "id": "261c8643", + "metadata": { + "editable": true + }, "source": [ "due to" ] }, { "cell_type": "markdown", - "id": "1858e8b0", - "metadata": {}, + "id": "02a6477c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "df = \\frac{\\partial f}{\\partial x}dx+\\frac{\\partial f}{\\partial y}dy+\\frac{\\partial f}{\\partial z}dz.\n", @@ -704,8 +793,10 @@ }, { "cell_type": "markdown", - "id": "95cca23b", - "metadata": {}, + "id": "36194bf1", + "metadata": { + "editable": true + }, "source": [ "In many problems the variables $x,y,z$ are often subject to constraints (such as those above for the margin)\n", "so that they are no longer all independent. It is possible at least in principle to use each \n", @@ -719,8 +810,10 @@ }, { "cell_type": "markdown", - "id": "05397bd4", - "metadata": {}, + "id": "bda4cda8", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\phi(x,y,z) = 0,\n", @@ -729,16 +822,20 @@ }, { "cell_type": "markdown", - "id": "982efeca", - "metadata": {}, + "id": "73175784", + "metadata": { + "editable": true + }, "source": [ "resulting in" ] }, { "cell_type": "markdown", - "id": "4b7f2368", - "metadata": {}, + "id": "ca704143", + "metadata": { + "editable": true + }, "source": [ "$$\n", "d\\phi = \\frac{\\partial \\phi}{\\partial x}dx+\\frac{\\partial \\phi}{\\partial y}dy+\\frac{\\partial \\phi}{\\partial z}dz =0.\n", @@ -747,16 +844,20 @@ }, { "cell_type": "markdown", - "id": "4e602e73", - "metadata": {}, + "id": "96609bee", + "metadata": { + "editable": true + }, "source": [ "Now we cannot set anymore" ] }, { "cell_type": "markdown", - "id": "d6c9eab3", - "metadata": {}, + "id": "ea5a988d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f}{\\partial x} =\\frac{\\partial f}{\\partial y}=\\frac{\\partial f}{\\partial z}=0,\n", @@ -765,8 +866,10 @@ }, { "cell_type": "markdown", - "id": "ec87a2b9", - "metadata": {}, + "id": "3234d6b4", + "metadata": { + "editable": true + }, "source": [ "if $df=0$ is wanted\n", "because there are now only two independent variables! Assume $x$ and $y$ are the independent \n", @@ -776,8 +879,10 @@ }, { "cell_type": "markdown", - "id": "8d12bb81", - "metadata": {}, + "id": "7d78dd16", + "metadata": { + "editable": true + }, "source": [ "## Adding the Multiplier\n", "\n", @@ -786,8 +891,10 @@ }, { "cell_type": "markdown", - "id": "10d026d5", - "metadata": {}, + "id": "a29351df", + "metadata": { + "editable": true + }, "source": [ "$$\n", "df = \\frac{\\partial f}{\\partial x}dx+\\frac{\\partial f}{\\partial y}dy+\\frac{\\partial f}{\\partial z}dz,\n", @@ -796,16 +903,20 @@ }, { "cell_type": "markdown", - "id": "6a7c46e4", - "metadata": {}, + "id": "4e8d5392", + "metadata": { + "editable": true + }, "source": [ "a multiplum of $d\\phi$, viz. $\\lambda d\\phi$, resulting in" ] }, { "cell_type": "markdown", - "id": "d211ad3e", - "metadata": {}, + "id": "8ab64081", + "metadata": { + "editable": true + }, "source": [ "$$\n", "df+\\lambda d\\phi = (\\frac{\\partial f}{\\partial z}+\\lambda\n", @@ -816,16 +927,20 @@ }, { "cell_type": "markdown", - "id": "6886ef44", - "metadata": {}, + "id": "e8889edb", + "metadata": { + "editable": true + }, "source": [ "Our multiplier is chosen so that" ] }, { "cell_type": "markdown", - "id": "f9e63f33", - "metadata": {}, + "id": "8e2d8258", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f}{\\partial z}+\\lambda\\frac{\\partial \\phi}{\\partial z} =0.\n", @@ -834,16 +949,20 @@ }, { "cell_type": "markdown", - "id": "5e7e1f95", - "metadata": {}, + "id": "5be4b771", + "metadata": { + "editable": true + }, "source": [ "We need to remember that we took $dx$ and $dy$ to be arbitrary and thus we must have" ] }, { "cell_type": "markdown", - "id": "06f66e7b", - "metadata": {}, + "id": "28951a63", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f}{\\partial x}+\\lambda\\frac{\\partial \\phi}{\\partial x} =0,\n", @@ -852,16 +971,20 @@ }, { "cell_type": "markdown", - "id": "e44affd7", - "metadata": {}, + "id": "edb341b0", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "f7c924ed", - "metadata": {}, + "id": "fcc45030", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f}{\\partial y}+\\lambda\\frac{\\partial \\phi}{\\partial y} =0.\n", @@ -870,8 +993,10 @@ }, { "cell_type": "markdown", - "id": "1b52bf51", - "metadata": {}, + "id": "5c38244b", + "metadata": { + "editable": true + }, "source": [ "When all these equations are satisfied, $df=0$. We have four unknowns, $x,y,z$ and\n", "$\\lambda$. Actually we want only $x,y,z$, $\\lambda$ needs not to be determined, \n", @@ -882,8 +1007,10 @@ }, { "cell_type": "markdown", - "id": "5fbb430c", - "metadata": {}, + "id": "5a1ed2b3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f}{\\partial x_i}+\\sum_k\\lambda_k\\frac{\\partial \\phi_k}{\\partial x_i} =0.\n", @@ -892,8 +1019,10 @@ }, { "cell_type": "markdown", - "id": "19e75f8d", - "metadata": {}, + "id": "b7af7142", + "metadata": { + "editable": true + }, "source": [ "## Setting up the Problem\n", "\n", @@ -902,8 +1031,10 @@ }, { "cell_type": "markdown", - "id": "45f3abca", - "metadata": {}, + "id": "f15f8eda", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\cal L}(\\lambda,b,\\boldsymbol{w})=\\frac{1}{2}\\boldsymbol{w}^T\\boldsymbol{w}-\\sum_{i=1}^n\\lambda_i\\left[y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)-1\\right],\n", @@ -912,8 +1043,10 @@ }, { "cell_type": "markdown", - "id": "e03d742c", - "metadata": {}, + "id": "8dd88f9b", + "metadata": { + "editable": true + }, "source": [ "where $\\lambda_i$ is a so-called Lagrange multiplier subject to the condition $\\lambda_i \\geq 0$.\n", "\n", @@ -922,8 +1055,10 @@ }, { "cell_type": "markdown", - "id": "013f58b3", - "metadata": {}, + "id": "045c6f11", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial {\\cal L}}{\\partial b} = -\\sum_{i} \\lambda_iy_i=0,\n", @@ -932,16 +1067,20 @@ }, { "cell_type": "markdown", - "id": "ac60181e", - "metadata": {}, + "id": "0da19338", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "9f527f31", - "metadata": {}, + "id": "b1ada680", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial {\\cal L}}{\\partial \\boldsymbol{w}} = 0 = \\boldsymbol{w}-\\sum_{i} \\lambda_iy_i\\boldsymbol{x}_i.\n", @@ -950,16 +1089,20 @@ }, { "cell_type": "markdown", - "id": "3195b77e", - "metadata": {}, + "id": "fc41d910", + "metadata": { + "editable": true + }, "source": [ "Inserting these constraints into the equation for ${\\cal L}$ we obtain" ] }, { "cell_type": "markdown", - "id": "226450c0", - "metadata": {}, + "id": "fbccf23d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\cal L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{x}_i^T\\boldsymbol{x}_j,\n", @@ -968,8 +1111,10 @@ }, { "cell_type": "markdown", - "id": "c51cc75d", - "metadata": {}, + "id": "4a2abaae", + "metadata": { + "editable": true + }, "source": [ "subject to the constraints $\\lambda_i\\geq 0$ and $\\sum_i\\lambda_iy_i=0$. \n", "We must in addition satisfy the [Karush-Kuhn-Tucker](https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions) (KKT) condition" @@ -977,8 +1122,10 @@ }, { "cell_type": "markdown", - "id": "f532e0cd", - "metadata": {}, + "id": "ed9c3f06", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\lambda_i\\left[y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) -1\\right] \\hspace{0.1cm}\\forall i.\n", @@ -987,8 +1134,10 @@ }, { "cell_type": "markdown", - "id": "b140f6d9", - "metadata": {}, + "id": "6f6860a6", + "metadata": { + "editable": true + }, "source": [ "1. If $\\lambda_i > 0$, then $y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1$ and we say that $x_i$ is on the boundary.\n", "\n", @@ -999,8 +1148,10 @@ }, { "cell_type": "markdown", - "id": "030ef098", - "metadata": {}, + "id": "a0cbe3aa", + "metadata": { + "editable": true + }, "source": [ "## The problem to solve\n", "\n", @@ -1009,8 +1160,10 @@ }, { "cell_type": "markdown", - "id": "134e888c", - "metadata": {}, + "id": "4a28c76a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\cal L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{x}_i^T\\boldsymbol{x}_j,\n", @@ -1019,16 +1172,20 @@ }, { "cell_type": "markdown", - "id": "8fb795f5", - "metadata": {}, + "id": "29c3740b", + "metadata": { + "editable": true + }, "source": [ "and its constraints in terms of a matrix-vector problem where we minimize w.r.t. $\\lambda$ the following problem" ] }, { "cell_type": "markdown", - "id": "54737881", - "metadata": {}, + "id": "a27ddcbd", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{1}{2} \\boldsymbol{\\lambda}^T\\begin{bmatrix} y_1y_1\\boldsymbol{x}_1^T\\boldsymbol{x}_1 & y_1y_2\\boldsymbol{x}_1^T\\boldsymbol{x}_2 & \\dots & \\dots & y_1y_n\\boldsymbol{x}_1^T\\boldsymbol{x}_n \\\\\n", @@ -1042,8 +1199,10 @@ }, { "cell_type": "markdown", - "id": "81814011", - "metadata": {}, + "id": "62f235b8", + "metadata": { + "editable": true + }, "source": [ "subject to $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$. Here we defined the vectors $\\boldsymbol{\\lambda}^T =[\\lambda_1,\\lambda_2,\\dots,\\lambda_n]$ and \n", "$\\boldsymbol{y}^T=[y_1,y_2,\\dots,y_n]$." @@ -1051,8 +1210,10 @@ }, { "cell_type": "markdown", - "id": "cda4b712", - "metadata": {}, + "id": "5b81af07", + "metadata": { + "editable": true + }, "source": [ "## The last steps\n", "\n", @@ -1062,8 +1223,10 @@ }, { "cell_type": "markdown", - "id": "1371d59a", - "metadata": {}, + "id": "2ae4d5ff", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{w}=\\sum_{i} \\lambda_iy_i\\boldsymbol{x}_i.\n", @@ -1072,16 +1235,20 @@ }, { "cell_type": "markdown", - "id": "fa4889ae", - "metadata": {}, + "id": "b47ad3de", + "metadata": { + "editable": true + }, "source": [ "With our vector $\\boldsymbol{w}$ we can in turn find the value of the intercept $b$ (here in two dimensions) via" ] }, { "cell_type": "markdown", - "id": "a78be679", - "metadata": {}, + "id": "e872de52", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1,\n", @@ -1090,16 +1257,20 @@ }, { "cell_type": "markdown", - "id": "164c6341", - "metadata": {}, + "id": "046fa24f", + "metadata": { + "editable": true + }, "source": [ "resulting in" ] }, { "cell_type": "markdown", - "id": "b0af4f60", - "metadata": {}, + "id": "c1408b1d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "b = \\frac{1}{y_i}-\\boldsymbol{w}^T\\boldsymbol{x}_i,\n", @@ -1108,16 +1279,20 @@ }, { "cell_type": "markdown", - "id": "0f2597ec", - "metadata": {}, + "id": "e50397ce", + "metadata": { + "editable": true + }, "source": [ "or if we write it out in terms of the support vectors only, with $N_s$ being their number, we have" ] }, { "cell_type": "markdown", - "id": "076089c0", - "metadata": {}, + "id": "7741d80a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "b = \\frac{1}{N_s}\\sum_{j\\in N_s}\\left(y_j-\\sum_{i=1}^n\\lambda_iy_i\\boldsymbol{x}_i^T\\boldsymbol{x}_j\\right).\n", @@ -1126,16 +1301,20 @@ }, { "cell_type": "markdown", - "id": "6eb1c414", - "metadata": {}, + "id": "b69cef10", + "metadata": { + "editable": true + }, "source": [ "With our hyperplane coefficients we can use our classifier to assign any observation by simply using" ] }, { "cell_type": "markdown", - "id": "7dbf8128", - "metadata": {}, + "id": "0344d03a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i = \\mathrm{sign}(\\boldsymbol{w}^T\\boldsymbol{x}_i+b).\n", @@ -1144,16 +1323,20 @@ }, { "cell_type": "markdown", - "id": "a03361ca", - "metadata": {}, + "id": "daaf3c59", + "metadata": { + "editable": true + }, "source": [ "Below we discuss how to find the optimal values of $\\lambda_i$. Before we proceed however, we discuss now the so-called soft classifier." ] }, { "cell_type": "markdown", - "id": "2dd830c5", - "metadata": {}, + "id": "60689323", + "metadata": { + "editable": true + }, "source": [ "## A soft classifier\n", "\n", @@ -1172,8 +1355,10 @@ }, { "cell_type": "markdown", - "id": "0dc3f9af", - "metadata": {}, + "id": "9d3fc013", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1,\n", @@ -1182,16 +1367,20 @@ }, { "cell_type": "markdown", - "id": "a9b8b493", - "metadata": {}, + "id": "99cf58e0", + "metadata": { + "editable": true + }, "source": [ "to" ] }, { "cell_type": "markdown", - "id": "39194508", - "metadata": {}, + "id": "8cb29974", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1-\\xi_i,\n", @@ -1200,8 +1389,10 @@ }, { "cell_type": "markdown", - "id": "903b1b09", - "metadata": {}, + "id": "68fb6a76", + "metadata": { + "editable": true + }, "source": [ "with the requirement $\\xi_i\\geq 0$. The total violation is now $\\sum_i\\xi$. \n", "The value $\\xi_i$ in the constraint the last constraint corresponds to the amount by which the prediction\n", @@ -1214,8 +1405,10 @@ }, { "cell_type": "markdown", - "id": "db69e6ee", - "metadata": {}, + "id": "96d747fc", + "metadata": { + "editable": true + }, "source": [ "## Soft optmization problem\n", "\n", @@ -1224,8 +1417,10 @@ }, { "cell_type": "markdown", - "id": "197fb7da", - "metadata": {}, + "id": "d04d1d58", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\cal L}=\\frac{1}{2}\\boldsymbol{w}^T\\boldsymbol{w}-\\sum_{i=1}^n\\lambda_i\\left[y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)-(1-\\xi_)\\right]+C\\sum_{i=1}^n\\xi_i-\\sum_{i=1}^n\\gamma_i\\xi_i,\n", @@ -1234,16 +1429,20 @@ }, { "cell_type": "markdown", - "id": "a254ef6c", - "metadata": {}, + "id": "b000bfc4", + "metadata": { + "editable": true + }, "source": [ "subject to" ] }, { "cell_type": "markdown", - "id": "20f993a9", - "metadata": {}, + "id": "30968487", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b)=1-\\xi_i \\hspace{0.1cm}\\forall i,\n", @@ -1252,8 +1451,10 @@ }, { "cell_type": "markdown", - "id": "a381c227", - "metadata": {}, + "id": "2a6d59b9", + "metadata": { + "editable": true + }, "source": [ "with the requirement $\\xi_i\\geq 0$.\n", "\n", @@ -1262,8 +1463,10 @@ }, { "cell_type": "markdown", - "id": "7ab15cb1", - "metadata": {}, + "id": "084f8ed5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial {\\cal L}}{\\partial b} = -\\sum_{i} \\lambda_iy_i=0,\n", @@ -1272,16 +1475,20 @@ }, { "cell_type": "markdown", - "id": "31416bbc", - "metadata": {}, + "id": "83fe2138", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "9c827b1e", - "metadata": {}, + "id": "34ec7cbc", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial {\\cal L}}{\\partial \\boldsymbol{w}} = 0 = \\boldsymbol{w}-\\sum_{i} \\lambda_iy_i\\boldsymbol{x}_i,\n", @@ -1290,16 +1497,20 @@ }, { "cell_type": "markdown", - "id": "840e9948", - "metadata": {}, + "id": "61885050", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "3e1d7923", - "metadata": {}, + "id": "0549a281", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\lambda_i = C-\\gamma_i \\hspace{0.1cm}\\forall i.\n", @@ -1308,16 +1519,20 @@ }, { "cell_type": "markdown", - "id": "8182840e", - "metadata": {}, + "id": "9b266759", + "metadata": { + "editable": true + }, "source": [ "Inserting these constraints into the equation for ${\\cal L}$ we obtain the same equation as before" ] }, { "cell_type": "markdown", - "id": "8304578d", - "metadata": {}, + "id": "da6c1b06", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\cal L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{x}_i^T\\boldsymbol{x}_j,\n", @@ -1326,8 +1541,10 @@ }, { "cell_type": "markdown", - "id": "a6268362", - "metadata": {}, + "id": "cef40956", + "metadata": { + "editable": true + }, "source": [ "but now subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$ and $0\\leq\\lambda_i \\leq C$. \n", "We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads" @@ -1335,8 +1552,10 @@ }, { "cell_type": "markdown", - "id": "21b23ee4", - "metadata": {}, + "id": "ca490f40", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\lambda_i\\left[y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) -(1-\\xi_)\\right]=0 \\hspace{0.1cm}\\forall i,\n", @@ -1345,8 +1564,10 @@ }, { "cell_type": "markdown", - "id": "9655b95d", - "metadata": {}, + "id": "f586bb61", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\gamma_i\\xi_i = 0,\n", @@ -1355,16 +1576,20 @@ }, { "cell_type": "markdown", - "id": "f4567799", - "metadata": {}, + "id": "2407239c", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "4b9b4e69", - "metadata": {}, + "id": "05c61efd", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i(\\boldsymbol{w}^T\\boldsymbol{x}_i+b) -(1-\\xi_) \\geq 0 \\hspace{0.1cm}\\forall i.\n", @@ -1373,8 +1598,10 @@ }, { "cell_type": "markdown", - "id": "d6b6e35e", - "metadata": {}, + "id": "a032cabe", + "metadata": { + "editable": true + }, "source": [ "## Kernels and non-linearity\n", "\n", @@ -1398,22 +1625,12 @@ { "cell_type": "code", "execution_count": 2, - "id": "a1a38dbc", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "id": "6c0344e3", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "import numpy as np\n", "import os\n", @@ -1465,8 +1682,10 @@ }, { "cell_type": "markdown", - "id": "74f17cd6", - "metadata": {}, + "id": "f8378a43", + "metadata": { + "editable": true + }, "source": [ "## The equations\n", "\n", @@ -1475,8 +1694,10 @@ }, { "cell_type": "markdown", - "id": "59a7758f", - "metadata": {}, + "id": "a4fa21ef", + "metadata": { + "editable": true + }, "source": [ "$$\n", "z = \\phi(x_i) =\\left(x_i^2, y_i^2, \\sqrt{2}x_iy_i\\right).\n", @@ -1485,16 +1706,20 @@ }, { "cell_type": "markdown", - "id": "7511cc97", - "metadata": {}, + "id": "eed132fc", + "metadata": { + "editable": true + }, "source": [ "With our new basis, the equations we solved earlier are basically the same, that is we have now (without the slack option for simplicity)" ] }, { "cell_type": "markdown", - "id": "c18aae49", - "metadata": {}, + "id": "fc2192a2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\cal L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{z}_i^T\\boldsymbol{z}_j,\n", @@ -1503,16 +1728,20 @@ }, { "cell_type": "markdown", - "id": "6f577c4b", - "metadata": {}, + "id": "1dceb1c6", + "metadata": { + "editable": true + }, "source": [ "subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$, and for the support vectors" ] }, { "cell_type": "markdown", - "id": "01d040cc", - "metadata": {}, + "id": "a88c33a5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_i(\\boldsymbol{w}^T\\boldsymbol{z}_i+b)= 1 \\hspace{0.1cm}\\forall i,\n", @@ -1521,8 +1750,10 @@ }, { "cell_type": "markdown", - "id": "a165ba6e", - "metadata": {}, + "id": "b28b421c", + "metadata": { + "editable": true + }, "source": [ "from which we also find $b$.\n", "To compute $\\boldsymbol{z}_i^T\\boldsymbol{z}_j$ we define the kernel $K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)$ as" @@ -1530,8 +1761,10 @@ }, { "cell_type": "markdown", - "id": "7bf9de65", - "metadata": {}, + "id": "e16881ac", + "metadata": { + "editable": true + }, "source": [ "$$\n", "K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=\\boldsymbol{z}_i^T\\boldsymbol{z}_j= \\phi(\\boldsymbol{x}_i)^T\\phi(\\boldsymbol{x}_j).\n", @@ -1540,16 +1773,20 @@ }, { "cell_type": "markdown", - "id": "8c870963", - "metadata": {}, + "id": "ccc8a354", + "metadata": { + "editable": true + }, "source": [ "For the above example, the kernel reads" ] }, { "cell_type": "markdown", - "id": "14d72bac", - "metadata": {}, + "id": "c0cbf60d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=[x_i^2, y_i^2, \\sqrt{2}x_iy_i]^T\\begin{bmatrix} x_j^2 \\\\ y_j^2 \\\\ \\sqrt{2}x_jy_j \\end{bmatrix}=x_i^2x_j^2+2x_ix_jy_iy_j+y_i^2y_j^2.\n", @@ -1558,8 +1795,10 @@ }, { "cell_type": "markdown", - "id": "7e9c91fa", - "metadata": {}, + "id": "35aaea21", + "metadata": { + "editable": true + }, "source": [ "We note that this is nothing but the dot product of the two original\n", "vectors $(\\boldsymbol{x}_i^T\\boldsymbol{x}_j)^2$. Instead of thus computing the\n", @@ -1574,8 +1813,10 @@ }, { "cell_type": "markdown", - "id": "36551459", - "metadata": {}, + "id": "de0351ac", + "metadata": { + "editable": true + }, "source": [ "## The problem to solve\n", "Using our definition of the kernel We can rewrite again the Lagrangian" @@ -1583,8 +1824,10 @@ }, { "cell_type": "markdown", - "id": "1f558a05", - "metadata": {}, + "id": "a9dc0877", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\cal L}=\\sum_i\\lambda_i-\\frac{1}{2}\\sum_{ij}^n\\lambda_i\\lambda_jy_iy_j\\boldsymbol{x}_i^T\\boldsymbol{z}_j,\n", @@ -1593,16 +1836,20 @@ }, { "cell_type": "markdown", - "id": "279ab53a", - "metadata": {}, + "id": "0a1e27d2", + "metadata": { + "editable": true + }, "source": [ "subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$ in terms of a convex optimization problem" ] }, { "cell_type": "markdown", - "id": "672fd6fa", - "metadata": {}, + "id": "f9b7fb95", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{1}{2} \\boldsymbol{\\lambda}^T\\begin{bmatrix} y_1y_1K(\\boldsymbol{x}_1,\\boldsymbol{x}_1) & y_1y_2K(\\boldsymbol{x}_1,\\boldsymbol{x}_2) & \\dots & \\dots & y_1y_nK(\\boldsymbol{x}_1,\\boldsymbol{x}_n) \\\\\n", @@ -1616,8 +1863,10 @@ }, { "cell_type": "markdown", - "id": "42031f08", - "metadata": {}, + "id": "da53e5a2", + "metadata": { + "editable": true + }, "source": [ "subject to $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$. Here we defined the vectors $\\boldsymbol{\\lambda} =[\\lambda_1,\\lambda_2,\\dots,\\lambda_n]$ and \n", "$\\boldsymbol{y}=[y_1,y_2,\\dots,y_n]$. \n", @@ -1628,8 +1877,10 @@ }, { "cell_type": "markdown", - "id": "7a16af05", - "metadata": {}, + "id": "873ed2fc", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -1641,8 +1892,10 @@ }, { "cell_type": "markdown", - "id": "bcf0d58c", - "metadata": {}, + "id": "becdf4e7", + "metadata": { + "editable": true + }, "source": [ "Below we discuss how to solve these equations. Here we note that the matrix $\\boldsymbol{P}$ has matrix elements $p_{ij}=y_iy_jK(\\boldsymbol{x}_i,\\boldsymbol{x}_j)$.\n", "Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up. The constraint $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$ leads to $f=0$ and $\\boldsymbol{A}=\\boldsymbol{y}$. How to set up the matrix $\\boldsymbol{G}$ is discussed later. Here note that the inequalities $0\\leq \\lambda_i \\leq C$ can be split up into\n", @@ -1651,8 +1904,10 @@ }, { "cell_type": "markdown", - "id": "d4c81398", - "metadata": {}, + "id": "4b694b70", + "metadata": { + "editable": true + }, "source": [ "## Different kernels and Mercer's theorem\n", "\n", @@ -1677,8 +1932,10 @@ }, { "cell_type": "markdown", - "id": "16082e86", - "metadata": {}, + "id": "5b69b1fc", + "metadata": { + "editable": true + }, "source": [ "$$\n", "K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=\\phi(\\boldsymbol{x}_i)^T\\phi(\\boldsymbol{x}_j).\n", @@ -1687,8 +1944,10 @@ }, { "cell_type": "markdown", - "id": "0b8c3336", - "metadata": {}, + "id": "389b247b", + "metadata": { + "editable": true + }, "source": [ "So you can use $K$ as a kernel since you know $\\phi$ exists, even if\n", "you don’t know what $\\phi$ is. \n", @@ -1700,8 +1959,10 @@ }, { "cell_type": "markdown", - "id": "ee66be99", - "metadata": {}, + "id": "40d5386c", + "metadata": { + "editable": true + }, "source": [ "## The moons example" ] @@ -1709,86 +1970,12 @@ { "cell_type": "code", "execution_count": 3, - "id": "ae55fede", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Phi(-1.0, -2) = [0.74081822]\n", - "Phi(-1.0, 1) = [0.30119421]\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "id": "9a6dcd4c", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "from __future__ import division, print_function, unicode_literals\n", "\n", @@ -1982,8 +2169,10 @@ }, { "cell_type": "markdown", - "id": "33d09931", - "metadata": {}, + "id": "217a7460", + "metadata": { + "editable": true + }, "source": [ "## Mathematical optimization of convex functions\n", "\n", @@ -1992,8 +2181,10 @@ }, { "cell_type": "markdown", - "id": "18af658e", - "metadata": {}, + "id": "2b6698c5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2005,8 +2196,10 @@ }, { "cell_type": "markdown", - "id": "762e6754", - "metadata": {}, + "id": "3a3b520d", + "metadata": { + "editable": true + }, "source": [ "subject to some constraints for say a selected set $i=1,2,\\dots, n$.\n", "In our case we are optimizing with respect to the Lagrangian multipliers $\\lambda_i$, and the\n", @@ -2020,8 +2213,10 @@ }, { "cell_type": "markdown", - "id": "6699af37", - "metadata": {}, + "id": "86ab3c96", + "metadata": { + "editable": true + }, "source": [ "## How do we solve these problems?\n", "\n", @@ -2038,22 +2233,13 @@ }, { "cell_type": "code", - "execution_count": 5, - "id": "91eb98c8", - "metadata": {}, - "outputs": [ - { - "ename": "ModuleNotFoundError", - "evalue": "No module named 'cvxopt'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mcvxopt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'cvxopt'" - ] - } - ], + "execution_count": 4, + "id": "3576e0d1", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "import numpy\n", "import cvxopt" @@ -2061,16 +2247,20 @@ }, { "cell_type": "markdown", - "id": "0e8869fe", - "metadata": {}, + "id": "6aecf621", + "metadata": { + "editable": true + }, "source": [ "This will make our life much easier. You don't need t write your own optimizer." ] }, { "cell_type": "markdown", - "id": "d2089bcc", - "metadata": {}, + "id": "28339500", + "metadata": { + "editable": true + }, "source": [ "## A simple example\n", "\n", @@ -2079,8 +2269,10 @@ }, { "cell_type": "markdown", - "id": "f6016f93", - "metadata": {}, + "id": "1e1d8445", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2092,16 +2284,20 @@ }, { "cell_type": "markdown", - "id": "5befddeb", - "metadata": {}, + "id": "46380665", + "metadata": { + "editable": true + }, "source": [ "Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem" ] }, { "cell_type": "markdown", - "id": "b181577e", - "metadata": {}, + "id": "6bb9f8a5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2117,16 +2313,20 @@ }, { "cell_type": "markdown", - "id": "76afd26b", - "metadata": {}, + "id": "9fe7090b", + "metadata": { + "editable": true + }, "source": [ "The minimization problem can be rewritten in terms of vectors and matrices as (with $x$ and $y$ being the unknowns)" ] }, { "cell_type": "markdown", - "id": "d6e70295", - "metadata": {}, + "id": "1fcbf1c6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{1}{2}\\begin{bmatrix} x\\\\ y \\end{bmatrix}^T \\begin{bmatrix} 1 & 0\\\\ 0 & 0 \\end{bmatrix} \\begin{bmatrix} x \\\\ y \\end{bmatrix} + \\begin{bmatrix}3\\\\ 4 \\end{bmatrix}^T \\begin{bmatrix}x \\\\ y \\end{bmatrix}.\n", @@ -2135,16 +2335,20 @@ }, { "cell_type": "markdown", - "id": "ae1478ad", - "metadata": {}, + "id": "a1515d47", + "metadata": { + "editable": true + }, "source": [ "Similarly, we can now set up the inequalities (we need to change $\\geq$ to $\\leq$ by multiplying with $-1$ on bot sides) as the following matrix-vector equation" ] }, { "cell_type": "markdown", - "id": "d1af3e76", - "metadata": {}, + "id": "997a5620", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{bmatrix} -1 & 0 \\\\ 0 & -1 \\\\ -1 & -3 \\\\ 2 & 5 \\\\ 3 & 4\\end{bmatrix}\\begin{bmatrix} x \\\\ y\\end{bmatrix} \\preceq \\begin{bmatrix}0 \\\\ 0\\\\ -15 \\\\ 100 \\\\ 80\\end{bmatrix}.\n", @@ -2153,16 +2357,20 @@ }, { "cell_type": "markdown", - "id": "e8fdf43e", - "metadata": {}, + "id": "052555ae", + "metadata": { + "editable": true + }, "source": [ "We have collapsed all the inequalities into a single matrix $\\boldsymbol{G}$. We see also that our matrix" ] }, { "cell_type": "markdown", - "id": "950f39e6", - "metadata": {}, + "id": "b9ed9098", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{P} =\\begin{bmatrix} 1 & 0\\\\ 0 & 0 \\end{bmatrix}\n", @@ -2171,8 +2379,10 @@ }, { "cell_type": "markdown", - "id": "62c0750c", - "metadata": {}, + "id": "dc51e878", + "metadata": { + "editable": true + }, "source": [ "is clearly positive semi-definite (all eigenvalues larger or equal zero). \n", "Finally, the vector $\\boldsymbol{h}$ is defined as" @@ -2180,8 +2390,10 @@ }, { "cell_type": "markdown", - "id": "05f7db4e", - "metadata": {}, + "id": "7aeb6cf5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{h} = \\begin{bmatrix}0 \\\\ 0\\\\ -15 \\\\ 100 \\\\ 80\\end{bmatrix}.\n", @@ -2190,8 +2402,10 @@ }, { "cell_type": "markdown", - "id": "be905e5c", - "metadata": {}, + "id": "9217a43c", + "metadata": { + "editable": true + }, "source": [ "Since we don't have any equalities the matrix $\\boldsymbol{A}$ is set to zero\n", "The following code solves the equations for us" @@ -2199,19 +2413,13 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "84671cc1", - "metadata": {}, - "outputs": [ - { - "ename": "SyntaxError", - "evalue": "invalid character in identifier (, line 5)", - "output_type": "error", - "traceback": [ - "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m5\u001b[0m\n\u001b[0;31m P = matrix(numpy.diag([1,0]), tc=’d’)\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid character in identifier\n" - ] - } - ], + "execution_count": 5, + "id": "78cfa5fd", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "# Import the necessary packages\n", "import numpy\n", @@ -2230,8 +2438,10 @@ }, { "cell_type": "markdown", - "id": "1c9d5533", - "metadata": {}, + "id": "3fd59e06", + "metadata": { + "editable": true + }, "source": [ "## Support Vector Machines and Regression\n", "\n", @@ -2240,16 +2450,20 @@ }, { "cell_type": "markdown", - "id": "a5abe159", - "metadata": {}, + "id": "c5630a0f", + "metadata": { + "editable": true + }, "source": [ "## Summary of course" ] }, { "cell_type": "markdown", - "id": "9e154bb6", - "metadata": {}, + "id": "e791014b", + "metadata": { + "editable": true + }, "source": [ "## What? Me worry? No final exam in this course!\n", "\n", @@ -2261,8 +2475,10 @@ }, { "cell_type": "markdown", - "id": "bca0471a", - "metadata": {}, + "id": "36adcbc3", + "metadata": { + "editable": true + }, "source": [ "## What is the link between Artificial Intelligence and Machine Learning and some general Remarks\n", "\n", @@ -2275,8 +2491,10 @@ }, { "cell_type": "markdown", - "id": "28cb541d", - "metadata": {}, + "id": "8eb9f848", + "metadata": { + "editable": true + }, "source": [ "## Going back to the beginning of the semester\n", "\n", @@ -2298,8 +2516,10 @@ }, { "cell_type": "markdown", - "id": "b7fa1d7d", - "metadata": {}, + "id": "abad119b", + "metadata": { + "editable": true + }, "source": [ "## Not so sharp distinctions\n", "\n", @@ -2325,8 +2545,10 @@ }, { "cell_type": "markdown", - "id": "003a23ee", - "metadata": {}, + "id": "73e937ff", + "metadata": { + "editable": true + }, "source": [ "## Topics we have covered this year\n", "\n", @@ -2339,8 +2561,10 @@ }, { "cell_type": "markdown", - "id": "58b9a8f0", - "metadata": {}, + "id": "490622c0", + "metadata": { + "editable": true + }, "source": [ "## Statistical analysis and optimization of data\n", "\n", @@ -2362,8 +2586,10 @@ }, { "cell_type": "markdown", - "id": "bf2dbf12", - "metadata": {}, + "id": "7a3b32c1", + "metadata": { + "editable": true + }, "source": [ "## Machine learning\n", "\n", @@ -2407,8 +2633,10 @@ }, { "cell_type": "markdown", - "id": "2c79eaf4", - "metadata": {}, + "id": "c81c797f", + "metadata": { + "editable": true + }, "source": [ "## Learning outcomes and overarching aims of this course\n", "\n", @@ -2441,8 +2669,10 @@ }, { "cell_type": "markdown", - "id": "25c294d5", - "metadata": {}, + "id": "d2cf0222", + "metadata": { + "editable": true + }, "source": [ "## Perspective on Machine Learning\n", "\n", @@ -2462,8 +2692,10 @@ }, { "cell_type": "markdown", - "id": "ee41415f", - "metadata": {}, + "id": "bbcc7d29", + "metadata": { + "editable": true + }, "source": [ "## Machine Learning Research\n", "\n", @@ -2483,8 +2715,10 @@ }, { "cell_type": "markdown", - "id": "5e1f3792", - "metadata": {}, + "id": "30c6424f", + "metadata": { + "editable": true + }, "source": [ "## Starting your Machine Learning Project\n", "\n", @@ -2501,8 +2735,10 @@ }, { "cell_type": "markdown", - "id": "2343a871", - "metadata": {}, + "id": "e72f56e6", + "metadata": { + "editable": true + }, "source": [ "## Choose a Model and Algorithm\n", "\n", @@ -2515,8 +2751,10 @@ }, { "cell_type": "markdown", - "id": "b8119c66", - "metadata": {}, + "id": "40ba33b0", + "metadata": { + "editable": true + }, "source": [ "## Preparing Your Data\n", "\n", @@ -2541,8 +2779,10 @@ }, { "cell_type": "markdown", - "id": "9dc83fc3", - "metadata": {}, + "id": "a3f61c6d", + "metadata": { + "editable": true + }, "source": [ "## Which Activation and Weights to Choose in Neural Networks\n", "\n", @@ -2561,8 +2801,10 @@ }, { "cell_type": "markdown", - "id": "c7ab7d9e", - "metadata": {}, + "id": "e27eeae8", + "metadata": { + "editable": true + }, "source": [ "## Optimization Methods and Hyperparameters\n", "1. Stochastic gradient descent\n", @@ -2584,8 +2826,10 @@ }, { "cell_type": "markdown", - "id": "4f361b65", - "metadata": {}, + "id": "5698f25f", + "metadata": { + "editable": true + }, "source": [ "## Resampling\n", "\n", @@ -2600,8 +2844,10 @@ }, { "cell_type": "markdown", - "id": "e40ad98c", - "metadata": {}, + "id": "eb7a215e", + "metadata": { + "editable": true + }, "source": [ "## Other courses on Data science and Machine Learning at UiO\n", "\n", @@ -2626,8 +2872,10 @@ }, { "cell_type": "markdown", - "id": "c6f64d3f", - "metadata": {}, + "id": "a172156e", + "metadata": { + "editable": true + }, "source": [ "## Additional courses of interest\n", "\n", @@ -2638,8 +2886,10 @@ }, { "cell_type": "markdown", - "id": "68b28771", - "metadata": {}, + "id": "39182cca", + "metadata": { + "editable": true + }, "source": [ "## What's the future like?\n", "\n", @@ -2662,8 +2912,10 @@ }, { "cell_type": "markdown", - "id": "b9271af0", - "metadata": {}, + "id": "4cf6b162", + "metadata": { + "editable": true + }, "source": [ "## Types of Machine Learning, a repetition\n", "\n", @@ -2689,8 +2941,10 @@ }, { "cell_type": "markdown", - "id": "966ba86e", - "metadata": {}, + "id": "3c6398b2", + "metadata": { + "editable": true + }, "source": [ "## Why Boltzmann machines?\n", "\n", @@ -2704,8 +2958,10 @@ }, { "cell_type": "markdown", - "id": "c9e3653b", - "metadata": {}, + "id": "16192cc1", + "metadata": { + "editable": true + }, "source": [ "## Boltzmann Machines\n", "\n", @@ -2724,8 +2980,10 @@ }, { "cell_type": "markdown", - "id": "73a5b537", - "metadata": {}, + "id": "048d0418", + "metadata": { + "editable": true + }, "source": [ "## Some similarities and differences from DNNs\n", "\n", @@ -2740,8 +2998,10 @@ }, { "cell_type": "markdown", - "id": "4b8c7811", - "metadata": {}, + "id": "c1793dd2", + "metadata": { + "editable": true + }, "source": [ "## Boltzmann machines (BM)\n", "\n", @@ -2761,8 +3021,10 @@ }, { "cell_type": "markdown", - "id": "89427e4d", - "metadata": {}, + "id": "a4cb8abd", + "metadata": { + "editable": true + }, "source": [ "## A standard BM setup\n", "\n", @@ -2778,8 +3040,10 @@ }, { "cell_type": "markdown", - "id": "a79b7a09", - "metadata": {}, + "id": "cf932eac", + "metadata": { + "editable": true + }, "source": [ "## The structure of the RBM network\n", "\n", @@ -2792,8 +3056,10 @@ }, { "cell_type": "markdown", - "id": "8f9545b1", - "metadata": {}, + "id": "5c167167", + "metadata": { + "editable": true + }, "source": [ "## The network\n", "\n", @@ -2805,8 +3071,10 @@ }, { "cell_type": "markdown", - "id": "f1d71860", - "metadata": {}, + "id": "6775e1c8", + "metadata": { + "editable": true + }, "source": [ "## Goals\n", "\n", @@ -2827,8 +3095,10 @@ }, { "cell_type": "markdown", - "id": "0ea2d42d", - "metadata": {}, + "id": "a770586b", + "metadata": { + "editable": true + }, "source": [ "## Joint distribution\n", "\n", @@ -2837,8 +3107,10 @@ }, { "cell_type": "markdown", - "id": "b9d0e1d1", - "metadata": {}, + "id": "1e478026", + "metadata": { + "editable": true + }, "source": [ "\n", "
\n", @@ -2853,16 +3125,20 @@ }, { "cell_type": "markdown", - "id": "d7065d67", - "metadata": {}, + "id": "da7256cc", + "metadata": { + "editable": true + }, "source": [ "where $Z$ is the normalization constant or partition function, defined as" ] }, { "cell_type": "markdown", - "id": "cbf630db", - "metadata": {}, + "id": "cbde45f7", + "metadata": { + "editable": true + }, "source": [ "\n", "
\n", @@ -2877,16 +3153,20 @@ }, { "cell_type": "markdown", - "id": "baa89cde", - "metadata": {}, + "id": "eabef96c", + "metadata": { + "editable": true + }, "source": [ "It is common to ignore $T_0$ by setting it to one." ] }, { "cell_type": "markdown", - "id": "e90da2c5", - "metadata": {}, + "id": "96a1dd12", + "metadata": { + "editable": true + }, "source": [ "## Network Elements, the energy function\n", "\n", @@ -2902,8 +3182,10 @@ }, { "cell_type": "markdown", - "id": "c35f1e14", - "metadata": {}, + "id": "f50439f5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "E(\\hat{x},\\hat{h}) = -\\sum_{ia}^{NA}b_i^a \\alpha_i^a(x_i)-\\sum_{jd}^{MD}c_j^d \\beta_j^d(h_j)-\\sum_{ijad}^{NAMD}b_i^a \\alpha_i^a(x_i)c_j^d \\beta_j^d(h_j)w_{ij}^{ad}.\n", @@ -2912,8 +3194,10 @@ }, { "cell_type": "markdown", - "id": "f68ce169", - "metadata": {}, + "id": "5e083450", + "metadata": { + "editable": true + }, "source": [ "Here $\\beta_j^d(h_j)$ and $\\alpha_i^a(x_j)$ are so-called transfer functions that map a given input value to a desired feature value. The labels $a$ and $d$ denote that there can be multiple transfer functions per variable. The first sum depends only on the visible units. The second on the hidden ones. **Note** that there is no connection between nodes in a layer.\n", "\n", @@ -2924,8 +3208,10 @@ }, { "cell_type": "markdown", - "id": "1652008b", - "metadata": {}, + "id": "36c9ab3c", + "metadata": { + "editable": true + }, "source": [ "## Defining different types of RBMs\n", "There are different variants of RBMs, and the differences lie in the types of visible and hidden units we choose as well as in the implementation of the energy function $E(\\mathbf{x},\\mathbf{h})$. \n", @@ -2937,8 +3223,10 @@ }, { "cell_type": "markdown", - "id": "cf9a080a", - "metadata": {}, + "id": "0101e73a", + "metadata": { + "editable": true + }, "source": [ "\n", "
\n", @@ -2953,8 +3241,10 @@ }, { "cell_type": "markdown", - "id": "c859d123", - "metadata": {}, + "id": "20c1a798", + "metadata": { + "editable": true + }, "source": [ "where the binary values taken on by the nodes are most commonly 0 and 1.\n", "\n", @@ -2965,8 +3255,10 @@ }, { "cell_type": "markdown", - "id": "a1c9078b", - "metadata": {}, + "id": "813f90dd", + "metadata": { + "editable": true + }, "source": [ "\n", "
\n", @@ -2981,8 +3273,10 @@ }, { "cell_type": "markdown", - "id": "bdfcc47e", - "metadata": {}, + "id": "990e2365", + "metadata": { + "editable": true + }, "source": [ "## More about RBMs\n", "1. Useful when we model continuous data (i.e., we wish $\\mathbf{x}$ to be continuous)\n", @@ -3003,8 +3297,10 @@ }, { "cell_type": "markdown", - "id": "b07f0554", - "metadata": {}, + "id": "ecfab9f8", + "metadata": { + "editable": true + }, "source": [ "## Autoencoders: Overarching view\n", "\n", @@ -3039,8 +3335,10 @@ }, { "cell_type": "markdown", - "id": "b04dfdb3", - "metadata": {}, + "id": "6584ce00", + "metadata": { + "editable": true + }, "source": [ "## Bayesian Machine Learning\n", "\n", @@ -3060,8 +3358,10 @@ }, { "cell_type": "markdown", - "id": "cd2fa1fa", - "metadata": {}, + "id": "d370516b", + "metadata": { + "editable": true + }, "source": [ "## Reinforcement Learning\n", "\n", @@ -3094,8 +3394,10 @@ }, { "cell_type": "markdown", - "id": "f81f5278", - "metadata": {}, + "id": "79a529f1", + "metadata": { + "editable": true + }, "source": [ "## Transfer learning\n", "\n", @@ -3113,8 +3415,10 @@ }, { "cell_type": "markdown", - "id": "0090aea4", - "metadata": {}, + "id": "0e566b6e", + "metadata": { + "editable": true + }, "source": [ "## Adversarial learning\n", "\n", @@ -3133,8 +3437,10 @@ }, { "cell_type": "markdown", - "id": "05cf9456", - "metadata": {}, + "id": "a88bfdd0", + "metadata": { + "editable": true + }, "source": [ "## Dual learning\n", "\n", @@ -3151,8 +3457,10 @@ }, { "cell_type": "markdown", - "id": "7e4f0953", - "metadata": {}, + "id": "2d8849ab", + "metadata": { + "editable": true + }, "source": [ "## Distributed machine learning\n", "\n", @@ -3164,8 +3472,10 @@ }, { "cell_type": "markdown", - "id": "a9c33826", - "metadata": {}, + "id": "7c4e5272", + "metadata": { + "editable": true + }, "source": [ "## Meta learning\n", "\n", @@ -3180,8 +3490,10 @@ }, { "cell_type": "markdown", - "id": "752e5038", - "metadata": {}, + "id": "1374df2f", + "metadata": { + "editable": true + }, "source": [ "## The Challenges Facing Machine Learning\n", "\n", @@ -3208,8 +3520,10 @@ }, { "cell_type": "markdown", - "id": "f7764abd", - "metadata": {}, + "id": "0c08d140", + "metadata": { + "editable": true + }, "source": [ "## Explainable machine learning\n", "\n", @@ -3235,8 +3549,10 @@ }, { "cell_type": "markdown", - "id": "27480bd3", - "metadata": {}, + "id": "2521ec0c", + "metadata": { + "editable": true + }, "source": [ "## Quantum machine learning\n", "\n", @@ -3264,8 +3580,10 @@ }, { "cell_type": "markdown", - "id": "749b7131", - "metadata": {}, + "id": "9da35f3e", + "metadata": { + "editable": true + }, "source": [ "## Quantum machine learning algorithms based on linear algebra\n", "\n", @@ -3285,8 +3603,10 @@ }, { "cell_type": "markdown", - "id": "ee1256ed", - "metadata": {}, + "id": "4a6e2846", + "metadata": { + "editable": true + }, "source": [ "## Quantum reinforcement learning\n", "\n", @@ -3301,8 +3621,10 @@ }, { "cell_type": "markdown", - "id": "a9168474", - "metadata": {}, + "id": "82926d7b", + "metadata": { + "editable": true + }, "source": [ "## Quantum deep learning\n", "\n", @@ -3322,8 +3644,10 @@ }, { "cell_type": "markdown", - "id": "ad7bb318", - "metadata": {}, + "id": "089ee83b", + "metadata": { + "editable": true + }, "source": [ "## Social machine learning\n", "\n", @@ -3341,8 +3665,10 @@ }, { "cell_type": "markdown", - "id": "554ca5d8", - "metadata": {}, + "id": "a9bfdafd", + "metadata": { + "editable": true + }, "source": [ "## The last words?\n", "\n", @@ -3355,8 +3681,10 @@ }, { "cell_type": "markdown", - "id": "7226e95f", - "metadata": {}, + "id": "de7febef", + "metadata": { + "editable": true + }, "source": [ "## Best wishes to you all and thanks so much for your heroic efforts this semester\n", "\n", @@ -3368,25 +3696,7 @@ ] } ], - "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": "3.8.8" - } - }, + "metadata": {}, "nbformat": 4, "nbformat_minor": 5 } diff --git a/doc/src/week47/week47.do.txt b/doc/src/week47/week47.do.txt index e318554a6..d003e4844 100644 --- a/doc/src/week47/week47.do.txt +++ b/doc/src/week47/week47.do.txt @@ -5,7 +5,8 @@ DATE: today !split ===== Overview of week 47 ===== -* _Thursday_: Support Vector Machines, classification and regression. +* _Thursday_: Support Vector Machines, classification and regression. + * "Video of Lecture":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureNovember25.mp4?vrtx=view-as-webpage" * _Friday_: Support Vector Machines and Summary of Course