From 3aa69845c722aa75039134d03e3131b46c957638 Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Mon, 15 Sep 2025 16:29:20 +0200 Subject: [PATCH] update --- doc/HandWrittenNotes/2025/FYSSTKweek38.pdf | Bin 0 -> 1584187 bytes .../_build/.doctrees/environment.pickle | Bin 334020 -> 334020 bytes .../_build/.doctrees/week38.doctree | Bin 198578 -> 198852 bytes .../_build/html/_sources/week38.ipynb | 256 +- doc/LectureNotes/_build/html/searchindex.js | 2 +- doc/LectureNotes/_build/html/week38.html | 9 +- .../_build/jupyter_execute/week38.ipynb | 256 +- doc/LectureNotes/week38.ipynb | 256 +- doc/pub/week38/html/._week38-bs001.html | 6 +- doc/pub/week38/html/week38-reveal.html | 6 +- doc/pub/week38/html/week38-solarized.html | 6 +- doc/pub/week38/html/week38.html | 6 +- .../week38-checkpoint.ipynb | 4610 ++++++++--------- doc/pub/week38/ipynb/ipynb-week38-src.tar.gz | Bin 1022756 -> 1022756 bytes doc/pub/week38/ipynb/week38.ipynb | 252 +- doc/src/week38/week38.do.txt | 4 +- 16 files 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a/doc/LectureNotes/_build/html/_sources/week38.ipynb b/doc/LectureNotes/_build/html/_sources/week38.ipynb index 544d286d0..1d25f9941 100644 --- a/doc/LectureNotes/_build/html/_sources/week38.ipynb +++ b/doc/LectureNotes/_build/html/_sources/week38.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "169923b3", + "id": "8f27372d", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "47013ee7", + "id": "fff8ca30", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "d1fb5464", + "id": "7ee7e714", "metadata": { "editable": true }, @@ -41,13 +41,15 @@ "2. Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff\n", "\n", "3. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at \n", - "\n", - "" + "\n", + "4. [Video of Lecture](https://youtu.be/4Fo7ITVA7V4)\n", + "\n", + "5. [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek38.pdf)" ] }, { "cell_type": "markdown", - "id": "1a34a7ce", + "id": "3b5ac440", "metadata": { "editable": true }, @@ -68,7 +70,7 @@ }, { "cell_type": "markdown", - "id": "c6f56f83", + "id": "6d5dba52", "metadata": { "editable": true }, @@ -96,7 +98,7 @@ }, { "cell_type": "markdown", - "id": "3ece0c04", + "id": "bfc2983a", "metadata": { "editable": true }, @@ -112,7 +114,7 @@ }, { "cell_type": "markdown", - "id": "d36cf6db", + "id": "2b5f5980", "metadata": { "editable": true }, @@ -131,7 +133,7 @@ }, { "cell_type": "markdown", - "id": "5903d2be", + "id": "3464c7e8", "metadata": { "editable": true }, @@ -145,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "37f4e199", + "id": "ed0fd2df", "metadata": { "editable": true }, @@ -157,7 +159,7 @@ }, { "cell_type": "markdown", - "id": "7a7b084f", + "id": "feb9d4c2", "metadata": { "editable": true }, @@ -168,7 +170,7 @@ }, { "cell_type": "markdown", - "id": "1ec511a1", + "id": "eb6d71f8", "metadata": { "editable": true }, @@ -180,7 +182,7 @@ }, { "cell_type": "markdown", - "id": "ffe76935", + "id": "566399f6", "metadata": { "editable": true }, @@ -192,7 +194,7 @@ }, { "cell_type": "markdown", - "id": "e569274a", + "id": "6b33f497", "metadata": { "editable": true }, @@ -208,7 +210,7 @@ }, { "cell_type": "markdown", - "id": "c4dd2623", + "id": "5f2f79f2", "metadata": { "editable": true }, @@ -219,7 +221,7 @@ }, { "cell_type": "markdown", - "id": "df2f8936", + "id": "199121b0", "metadata": { "editable": true }, @@ -242,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "0a3e5956", + "id": "9a1cc529", "metadata": { "editable": true }, @@ -253,7 +255,7 @@ }, { "cell_type": "markdown", - "id": "973e45a3", + "id": "149e63be", "metadata": { "editable": true }, @@ -265,7 +267,7 @@ }, { "cell_type": "markdown", - "id": "ff486d1e", + "id": "6a6fb04a", "metadata": { "editable": true }, @@ -277,7 +279,7 @@ }, { "cell_type": "markdown", - "id": "e4307815", + "id": "79420d06", "metadata": { "editable": true }, @@ -291,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "490b2cbf", + "id": "0e3de992", "metadata": { "editable": true }, @@ -322,7 +324,7 @@ }, { "cell_type": "markdown", - "id": "5d8dd6bc", + "id": "d3ea2897", "metadata": { "editable": true }, @@ -344,7 +346,7 @@ }, { "cell_type": "markdown", - "id": "3594078a", + "id": "da5e3927", "metadata": { "editable": true }, @@ -356,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "43007b7a", + "id": "7ab5488b", "metadata": { "editable": true }, @@ -369,7 +371,7 @@ }, { "cell_type": "markdown", - "id": "3cd4e7da", + "id": "f904a739", "metadata": { "editable": true }, @@ -381,7 +383,7 @@ }, { "cell_type": "markdown", - "id": "5816b21e", + "id": "10fd648b", "metadata": { "editable": true }, @@ -393,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "b58b8607", + "id": "4812c2a4", "metadata": { "editable": true }, @@ -405,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "c843db7f", + "id": "199d8531", "metadata": { "editable": true }, @@ -417,7 +419,7 @@ }, { "cell_type": "markdown", - "id": "e81b1c39", + "id": "96c16676", "metadata": { "editable": true }, @@ -440,7 +442,7 @@ }, { "cell_type": "markdown", - "id": "ea9719e3", + "id": "a2a1a004", "metadata": { "editable": true }, @@ -452,7 +454,7 @@ }, { "cell_type": "markdown", - "id": "c28b598f", + "id": "5aad445b", "metadata": { "editable": true }, @@ -465,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "88063ed7", + "id": "d197c8bb", "metadata": { "editable": true }, @@ -477,7 +479,7 @@ }, { "cell_type": "markdown", - "id": "a34e4c28", + "id": "e2e7462f", "metadata": { "editable": true }, @@ -489,7 +491,7 @@ }, { "cell_type": "markdown", - "id": "1fc7ae0a", + "id": "eb635d3d", "metadata": { "editable": true }, @@ -501,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "30d5a1be", + "id": "445ed13e", "metadata": { "editable": true }, @@ -512,7 +514,7 @@ }, { "cell_type": "markdown", - "id": "1d29fd29", + "id": "319bfc6c", "metadata": { "editable": true }, @@ -524,7 +526,7 @@ }, { "cell_type": "markdown", - "id": "289a116c", + "id": "90abf35a", "metadata": { "editable": true }, @@ -535,7 +537,7 @@ }, { "cell_type": "markdown", - "id": "d1cfbb56", + "id": "04b66fbd", "metadata": { "editable": true }, @@ -547,7 +549,7 @@ }, { "cell_type": "markdown", - "id": "e089fc0e", + "id": "4a27b5a7", "metadata": { "editable": true }, @@ -557,7 +559,7 @@ }, { "cell_type": "markdown", - "id": "32cf9944", + "id": "8d12543f", "metadata": { "editable": true }, @@ -588,7 +590,7 @@ }, { "cell_type": "markdown", - "id": "ee8a9544", + "id": "2e5cd118", "metadata": { "editable": true }, @@ -600,19 +602,19 @@ }, { "cell_type": "markdown", - "id": "4bfeb203", + "id": "c71a5edf", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\theta}=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})},\n", + "C(\\boldsymbol{\\theta})=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})},\n", "$$" ] }, { "cell_type": "markdown", - "id": "256143f9", + "id": "e663bf2e", "metadata": { "editable": true }, @@ -622,19 +624,19 @@ }, { "cell_type": "markdown", - "id": "60d75bb1", + "id": "c4bc4873", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\theta}=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta})\\vert\\vert_2^2}{2\\sigma^2}.\n", + "C(\\boldsymbol{\\theta})=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta})\\vert\\vert_2^2}{2\\sigma^2}.\n", "$$" ] }, { "cell_type": "markdown", - "id": "7b111014", + "id": "f5bc59b8", "metadata": { "editable": true }, @@ -644,7 +646,7 @@ }, { "cell_type": "markdown", - "id": "0f42a0b5", + "id": "4f6ddf4a", "metadata": { "editable": true }, @@ -656,7 +658,7 @@ }, { "cell_type": "markdown", - "id": "39a9276b", + "id": "afda0a6b", "metadata": { "editable": true }, @@ -666,7 +668,7 @@ }, { "cell_type": "markdown", - "id": "84c63927", + "id": "b5335dc0", "metadata": { "editable": true }, @@ -678,7 +680,7 @@ }, { "cell_type": "markdown", - "id": "c087ef22", + "id": "4f86a52d", "metadata": { "editable": true }, @@ -688,7 +690,7 @@ }, { "cell_type": "markdown", - "id": "79503987", + "id": "5cdb1767", "metadata": { "editable": true }, @@ -707,7 +709,7 @@ }, { "cell_type": "markdown", - "id": "c165025b", + "id": "69435d77", "metadata": { "editable": true }, @@ -735,7 +737,7 @@ }, { "cell_type": "markdown", - "id": "efb63405", + "id": "cefbb559", "metadata": { "editable": true }, @@ -761,7 +763,7 @@ }, { "cell_type": "markdown", - "id": "88d4bfd8", + "id": "2659401a", "metadata": { "editable": true }, @@ -778,7 +780,7 @@ }, { "cell_type": "markdown", - "id": "6a0795e0", + "id": "4d5d7748", "metadata": { "editable": true }, @@ -798,7 +800,7 @@ }, { "cell_type": "markdown", - "id": "d815fdf3", + "id": "54df92b3", "metadata": { "editable": true }, @@ -827,7 +829,7 @@ }, { "cell_type": "markdown", - "id": "a5b26ed1", + "id": "5b1a1390", "metadata": { "editable": true }, @@ -852,7 +854,7 @@ }, { "cell_type": "markdown", - "id": "e5783b81", + "id": "39f233e4", "metadata": { "editable": true }, @@ -872,7 +874,7 @@ }, { "cell_type": "markdown", - "id": "9bdfff4f", + "id": "361320d8", "metadata": { "editable": true }, @@ -884,7 +886,7 @@ }, { "cell_type": "markdown", - "id": "bd1e4a83", + "id": "a363db1e", "metadata": { "editable": true }, @@ -894,7 +896,7 @@ }, { "cell_type": "markdown", - "id": "66d14a83", + "id": "92967efc", "metadata": { "editable": true }, @@ -909,7 +911,7 @@ }, { "cell_type": "markdown", - "id": "ac38d462", + "id": "1bffca97", "metadata": { "editable": true }, @@ -922,7 +924,7 @@ }, { "cell_type": "markdown", - "id": "65488a60", + "id": "0dacb6fc", "metadata": { "editable": true }, @@ -935,7 +937,7 @@ }, { "cell_type": "markdown", - "id": "9c8686d8", + "id": "baeedf81", "metadata": { "editable": true }, @@ -947,7 +949,7 @@ }, { "cell_type": "markdown", - "id": "585dbaff", + "id": "20cc7770", "metadata": { "editable": true }, @@ -960,7 +962,7 @@ }, { "cell_type": "markdown", - "id": "a8093a3e", + "id": "f67d3b94", "metadata": { "editable": true }, @@ -971,7 +973,7 @@ }, { "cell_type": "markdown", - "id": "ec844baa", + "id": "17f59fb6", "metadata": { "editable": true }, @@ -985,7 +987,7 @@ }, { "cell_type": "markdown", - "id": "7f2b563b", + "id": "5f899fbe", "metadata": { "editable": true }, @@ -995,7 +997,7 @@ }, { "cell_type": "markdown", - "id": "5a75bbe4", + "id": "19a1f5bb", "metadata": { "editable": true }, @@ -1009,7 +1011,7 @@ }, { "cell_type": "markdown", - "id": 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- "id": "f4ff2861", + "id": "25418113", "metadata": { "editable": true }, @@ -1125,7 +1127,7 @@ }, { "cell_type": "markdown", - "id": "fd66a47c", + "id": "e5d3c3eb", "metadata": { "editable": true }, @@ -1137,7 +1139,7 @@ }, { "cell_type": "markdown", - "id": "51e5434b", + "id": "c504cba4", "metadata": { "editable": true }, @@ -1150,7 +1152,7 @@ }, { "cell_type": "markdown", - "id": "9129f7a5", + "id": "079ded2a", "metadata": { "editable": true }, @@ -1170,7 +1172,7 @@ }, { "cell_type": "markdown", - "id": "e5fa7f9c", + "id": "e8534a50", "metadata": { "editable": true }, @@ -1193,7 +1195,7 @@ }, { "cell_type": "markdown", - "id": "f5bbafe6", + "id": "2fc73431", "metadata": { "editable": true }, @@ -1208,7 +1210,7 @@ }, { "cell_type": "markdown", - "id": "0cc93a0c", + "id": "0f8b0845", "metadata": { "editable": true }, @@ -1220,7 +1222,7 @@ }, { "cell_type": "markdown", - "id": "8dd4f5e0", + "id": "25105753", "metadata": { "editable": true }, @@ -1240,7 +1242,7 @@ }, { "cell_type": 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@@ -1419,7 +1421,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "39fd1fa8", + "id": "3cf4144d", "metadata": { "collapsed": false, "editable": true @@ -1439,7 +1441,7 @@ }, { "cell_type": "markdown", - "id": "237b4db3", + "id": "db5a8f91", "metadata": { "editable": true }, @@ -1457,7 +1459,7 @@ }, { "cell_type": "markdown", - "id": "0c13e5b0", + "id": "327bce6a", "metadata": { "editable": true }, @@ -1469,7 +1471,7 @@ }, { "cell_type": "markdown", - "id": "a086aa7e", + "id": "1c671d4e", "metadata": { "editable": true }, @@ -1486,7 +1488,7 @@ }, { "cell_type": "markdown", - "id": "c3837d89", + "id": "6e05fc43", "metadata": { "editable": true }, @@ -1498,7 +1500,7 @@ }, { "cell_type": "markdown", - "id": "7c7cd0a7", + "id": "c45e0752", "metadata": { "editable": true }, @@ -1508,7 +1510,7 @@ }, { "cell_type": "markdown", - "id": "b9db0cd5", + "id": "bafa4ab6", "metadata": { "editable": true }, @@ -1520,7 +1522,7 @@ }, { "cell_type": "markdown", - "id": "00482b2d", + "id": "ea0bc471", "metadata": { "editable": true }, @@ -1537,7 +1539,7 @@ }, { "cell_type": "markdown", - "id": "2e7c7291", + "id": "08b603f3", "metadata": { "editable": true }, @@ -1549,7 +1551,7 @@ }, { "cell_type": "markdown", - "id": "9a8d29b5", + "id": "4114d10e", "metadata": { "editable": true }, @@ -1559,7 +1561,7 @@ }, { "cell_type": "markdown", - "id": "9a8e2084", + "id": "8890c666", "metadata": { "editable": true }, @@ -1571,7 +1573,7 @@ }, { "cell_type": "markdown", - "id": "4a191c5c", + "id": "7d5b7ce4", "metadata": { "editable": true }, @@ -1581,7 +1583,7 @@ }, { "cell_type": "markdown", - "id": "c37713f8", + "id": "3913c5b9", "metadata": { "editable": true }, @@ -1593,7 +1595,7 @@ }, { "cell_type": "markdown", - "id": "82ca4a7b", + "id": "5e0067b1", "metadata": { "editable": true }, @@ -1603,7 +1605,7 @@ }, { "cell_type": "markdown", - "id": "2765a841", + "id": "326bc8f1", "metadata": { "editable": true }, @@ -1619,7 +1621,7 @@ }, { "cell_type": "markdown", - "id": "321964c1", + "id": "d3713eca", "metadata": { "editable": true }, @@ -1630,7 +1632,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "5942226f", + "id": "01c3b507", "metadata": { "collapsed": false, "editable": true @@ -1695,7 +1697,7 @@ }, { "cell_type": "markdown", - "id": "cf2af19d", + "id": "949e3a5e", "metadata": { "editable": true }, @@ -1706,7 +1708,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "7b371a0c", + "id": "7e7f4926", "metadata": { "collapsed": false, "editable": true @@ -1763,7 +1765,7 @@ }, { "cell_type": "markdown", - "id": "6f583fcd", + "id": "33c5cae5", "metadata": { "editable": true }, @@ -1801,7 +1803,7 @@ }, { "cell_type": "markdown", - "id": "37766c51", + "id": "f931f0f2", "metadata": { "editable": true }, @@ -1828,7 +1830,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "0eac5ca9", + "id": "58daa28d", "metadata": { "collapsed": false, "editable": true @@ -1890,7 +1892,7 @@ }, { "cell_type": "markdown", - "id": "d698096e", + "id": "3bbcf741", "metadata": { "editable": true }, @@ -1915,7 +1917,7 @@ }, { "cell_type": "markdown", - "id": "3e37a4d2", + "id": "4b0ffe06", "metadata": { "editable": true }, @@ -1943,7 +1945,7 @@ }, { "cell_type": "markdown", - "id": "e7e43cf9", + "id": "b11baed6", "metadata": { "editable": true }, @@ -1956,7 +1958,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "7aa6a568", + "id": "39e76d49", "metadata": { "collapsed": false, "editable": true @@ -2056,7 +2058,7 @@ }, { "cell_type": "markdown", - "id": "9a90aec7", + "id": "e7d12ef0", "metadata": { "editable": true }, @@ -2067,7 +2069,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "93b3af24", + "id": "47f6ae18", "metadata": { "collapsed": false, "editable": true @@ -2156,7 +2158,7 @@ }, { "cell_type": "markdown", - "id": "90657c6d", + "id": "9c1d4754", "metadata": { "editable": true }, @@ -2166,7 +2168,7 @@ }, { "cell_type": "markdown", - "id": "a88b86e7", + "id": "b698ac66", "metadata": { "editable": true }, @@ -2179,7 +2181,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "89f45188", + "id": "0a2409b0", "metadata": { "collapsed": false, "editable": true @@ -2257,7 +2259,7 @@ }, { "cell_type": "markdown", - "id": "75496517", + "id": "56f130b5", "metadata": { "editable": true }, diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js index b5568cb04..268076012 100644 --- a/doc/LectureNotes/_build/html/searchindex.js +++ b/doc/LectureNotes/_build/html/searchindex.js @@ -1 +1 @@ -Search.setIndex({"alltitles": {"1a)": [[18, "a"]], "3a)": [[18, "id1"]], "3b)": [[18, "b"]], "4a)": [[18, "id2"]], "4b)": [[18, "id3"]], "A Classification Tree": [[9, "a-classification-tree"]], "A Frequentist approach to data analysis": [[0, "a-frequentist-approach-to-data-analysis"], [28, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[8, "a-better-approach"]], "A first summary": [[28, "a-first-summary"]], "A new Cost Function": [[32, "a-new-cost-function"]], "A quick Reminder on Lagrangian Multipliers": [[8, "a-quick-reminder-on-lagrangian-multipliers"]], "A simple example": [[4, "a-simple-example"]], "A soft classifier": [[8, "a-soft-classifier"]], "A top-down perspective on Neural networks": [[1, "a-top-down-perspective-on-neural-networks"]], "A way to Read the Bias-Variance Tradeoff": [[32, "a-way-to-read-the-bias-variance-tradeoff"]], "ADAM algorithm, taken from Goodfellow et al": [[31, "adam-algorithm-taken-from-goodfellow-et-al"]], "ADAM optimizer": [[13, "adam-optimizer"], [31, "id2"]], "Accuracy": [[31, "accuracy"]], "Activation functions": [[12, "activation-functions"]], "AdaGrad Properties": [[31, "adagrad-properties"]], "AdaGrad Update Rule Derivation": [[31, "adagrad-update-rule-derivation"]], "AdaGrad algorithm, taken from Goodfellow et al": [[31, "adagrad-algorithm-taken-from-goodfellow-et-al"]], "Adam Optimizer": [[31, "adam-optimizer"]], "Adam vs. AdaGrad and RMSProp": [[31, "adam-vs-adagrad-and-rmsprop"]], "Adam: Bias 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"an-optimization-minimization-problem"]], "And finally \\boldsymbol{X}\\boldsymbol{X}^T": [[29, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And finally ADAM": [[31, "and-finally-adam"]], "And what about using neural networks?": [[28, "and-what-about-using-neural-networks"]], "Another Example from Scikit-Learn\u2019s Repository": [[32, "another-example-from-scikit-learn-s-repository"]], "Another Example, now with a polynomial fit": [[30, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[9, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[21, null]], "Assumptions made": [[32, "assumptions-made"]], "Autocorrelation function": [[25, "autocorrelation-function"]], "Automatic differentiation": [[13, "automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[29, "back-to-ridge-and-lasso-regression"], [30, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[11, "back-to-the-cancer-data"]], 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Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[28, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"]], "Example 2": [[29, "example-2"]], "Example 3": [[29, "example-3"]], "Example 4": [[29, "example-4"]], "Example Matrix": [[29, "example-matrix"], [30, "example-matrix"]], "Example code for Bias-Variance tradeoff": [[32, "example-code-for-bias-variance-tradeoff"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[28, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[28, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[29, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[29, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"]], "Examples": [[28, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Creating the report document": [[20, "exercise-1-creating-the-report-document"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: Adding good figures": [[20, "exercise-2-adding-good-figures"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 3: Writing an abstract and introduction": [[20, "exercise-3-writing-an-abstract-and-introduction"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 4: Making the code available and presentable": [[20, "exercise-4-making-the-code-available-and-presentable"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise 5: Referencing": [[20, "exercise-5-referencing"]], "Exercise: Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Exercises week 38": [[19, null]], "Exercises week 39": [[20, null]], "Expectation value and variance": [[32, "expectation-value-and-variance"]], "Expectation value and variance for \\boldsymbol{\\theta}": [[32, "expectation-value-and-variance-for-boldsymbol-theta"]], "Expectation values": [[25, "expectation-values"]], "Extending to more than one variable": [[30, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[28, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"]], "Finding the Limit": [[32, "finding-the-limit"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[29, "fixing-the-singularity"], [30, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[23, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[29, "frequently-used-scaling-functions"], [31, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[30, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Functionality in Scikit-Learn": [[29, "functionality-in-scikit-learn"], [31, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [29, "further-properties-important-for-our-analyses-later"], [30, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[22, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[28, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[28, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [28, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[28, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting started with project 1": [[20, "getting-started-with-project-1"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"]], "Gradient Descent Example": [[30, "id1"], [31, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"]], "Gradient descent and Ridge": [[30, "gradient-descent-and-ridge"], [31, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[31, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[30, "gradient-descent-example"], [31, "gradient-descent-example"]], "Grading": [[26, "grading"], [26, "id2"], [28, "grading"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Identifying Terms": [[32, "identifying-terms"]], "Important Matrix and vector handling packages": [[22, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[29, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[31, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"]], "In summary": [[26, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [31, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[11, "incremental-pca"]], "Independent and Identically Distributed (iid)": [[32, "independent-and-identically-distributed-iid"]], "Installing R, C++, cython or Julia": [[28, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[28, "installing-r-c-cython-numba-etc"]], "Instructor information": [[26, "instructor-information"]], "Interpretations and optimizing our parameters": [[28, "interpretations-and-optimizing-our-parameters"], [28, "id2"], [28, "id3"], [29, "interpretations-and-optimizing-our-parameters"], [29, "id1"], [29, "id2"]], "Interpreting the Ridge results": [[29, "interpreting-the-ridge-results"], [30, "interpreting-the-ridge-results"], [30, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [29, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [21, "introduction"], [22, "introduction"]], "Introduction to numerical projects": [[23, "introduction-to-numerical-projects"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[22, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[30, "lasso-regression"]], "Lasso case": [[30, "lasso-case"]], "Layers": [[1, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"], [18, "learning-goals"], [19, "learning-goals"], [20, "learning-goals"]], "Learning outcomes": [[21, "learning-outcomes"], [28, "learning-outcomes"]], "Lectures and ComputerLab": [[28, "lectures-and-computerlab"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[22, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[29, "linear-regression-problems"], [30, "linear-regression-problems"]], "Linear Regression and the SVD": [[30, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[5, "linking-the-regression-analysis-with-a-statistical-interpretation"], [32, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [29, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[27, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[28, "machine-learning"]], "Machine learning": [[21, "machine-learning"]], "Main textbooks": [[28, "main-textbooks"]], "Making a tree": [[9, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[10, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[29, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[29, "material-for-exercises-week-35"]], "Material for lab sessions sessions Tuesday and Wednesday": [[30, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[30, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[31, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[31, "material-for-the-lab-sessions"], [32, "material-for-the-lab-sessions"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [29, "mathematical-interpretation-of-ordinary-least-squares"], [30, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [29, "mathematics-of-the-svd-and-implications"], [30, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[28, "matrices-in-python"]], "Matrix multiplication": [[1, "matrix-multiplication"]], "Matrix-vector notation and activation": [[12, "matrix-vector-notation-and-activation"]], "Maximum Likelihood Estimation (MLE)": [[32, "maximum-likelihood-estimation-mle"]], "Meet the covariance!": [[25, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [29, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[29, "meet-the-hessian-matrix"]], "Meet the Pandas": [[28, "meet-the-pandas"]], "Memory Usage and Scalability": [[31, "memory-usage-and-scalability"]], "Memory constraints": [[31, "memory-constraints"]], "Min-Max Scaling": [[29, "min-max-scaling"]], "Momentum based GD": [[13, "momentum-based-gd"], [31, "momentum-based-gd"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More examples on bootstrap and cross-validation and errors": [[32, "more-examples-on-bootstrap-and-cross-validation-and-errors"]], "More interpretations": [[29, "more-interpretations"], [30, "more-interpretations"], [30, "id5"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[30, "more-on-steepest-descent"]], "More on convex functions": [[30, "more-on-convex-functions"]], "More preprocessing": [[29, "more-preprocessing"], [31, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[31, "motivation-for-adaptive-step-sizes"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"]], "Network requirements": [[2, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural networks": [[12, null]], "Non-Convex Problems": [[31, "non-convex-problems"]], "Note about SVD Calculations": [[29, "note-about-svd-calculations"], [30, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[30, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[25, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[22, "numpy-and-arrays"], [28, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[28, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[30, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null]], "Optimizing our parameters": [[28, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[28, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"]], "Organizing our data": [[0, "organizing-our-data"], [28, "organizing-our-data"]], "Other Matrix and Vector Operations": [[22, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning at UiO": [[28, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning at UiO, contn": [[28, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[28, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[28, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[28, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[31, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[28, "own-code-for-ordinary-least-squares"], [29, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[28, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[23, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for the Runge function": [[23, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[23, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[23, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing our own code for Lasso regression": [[23, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f: Stochastic gradient descent": [[23, "part-f-stochastic-gradient-descent"]], "Part g: Bias-variance trade-off and resampling techniques": [[23, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[23, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[2, "partial-differential-equations"]], "Plans for week 35": [[29, "plans-for-week-35"]], "Plans for week 36": [[30, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[31, "plans-for-week-37-lecture-monday"]], "Plans for week 38, lecture Monday September 15": [[32, "plans-for-week-38-lecture-monday-september-15"]], "Plotting the Histogram": [[32, "plotting-the-histogram"]], "Practical tips": [[13, "practical-tips"], [31, "practical-tips"]], "Practicalities": [[26, "practicalities"], [26, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[23, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[29, "preprocessing-our-data"]], "Prerequisites": [[28, "prerequisites"]], "Prerequisites and background": [[21, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[25, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[30, "program-example-for-gradient-descent-with-ridge-regression"], [31, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[23, null]], "Properties of PDFs": [[25, "properties-of-pdfs"]], "Pros and cons": [[31, "pros-and-cons"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[21, "python-installers"], [28, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[31, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[31, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[31, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[25, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[28, "reading-material"]], "Reading recommendations:": [[29, "reading-recommendations"]], "Reading suggestions week 34": [[28, "reading-suggestions-week-34"]], "Readings and Videos": [[32, "readings-and-videos"]], "Readings and Videos:": [[31, "readings-and-videos"]], "Recurrent neural networks": [[12, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[4, null]], "Reducing the number of degrees of freedom, overarching view": [[0, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [29, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reformulating the problem": [[2, "reformulating-the-problem"]], "Regression Case": [[10, "regression-case"]], "Regression analysis and resampling methods": [[23, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[28, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[28, "regression-analysis-overarching-aims-ii"]], "Regularization": [[1, "regularization"]], "Reminder from last week": [[29, "reminder-from-last-week"]], "Reminder on Newton-Raphson\u2019s method": [[30, "reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[6, "reminder-on-statistics"]], "Reminder on different scaling methods": [[31, "reminder-on-different-scaling-methods"]], "Replace or not": [[13, "replace-or-not"], [31, "replace-or-not"]], "Required Technologies": [[21, "required-technologies"]], "Resampling Methods": [[6, null]], "Resampling and the Bias-Variance Trade-off": [[19, "resampling-and-the-bias-variance-trade-off"]], "Resampling approaches can be computationally expensive": [[32, "resampling-approaches-can-be-computationally-expensive"]], "Resampling methods": [[6, "id1"], [32, "resampling-methods"], [32, "id2"]], "Resampling methods: Bootstrap": [[32, "resampling-methods-bootstrap"]], "Resampling methods: Bootstrap approach": [[32, "resampling-methods-bootstrap-approach"]], "Resampling methods: Bootstrap background": [[32, "resampling-methods-bootstrap-background"]], "Resampling methods: Bootstrap steps": [[32, "resampling-methods-bootstrap-steps"]], "Resampling methods: More Bootstrap background": [[32, "resampling-methods-more-bootstrap-background"]], "Residual Error": [[29, "residual-error"], [30, "residual-error"]], "Resources on differential equations and deep learning": [[2, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[30, "revisiting-ordinary-least-squares"]], "Revisiting 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"simple-program"]], "Slightly different approach": [[31, "slightly-different-approach"]], "Sneaking in automatic differentiation using Autograd": [[31, "sneaking-in-automatic-differentiation-using-autograd"]], "Software and needed installations": [[23, "software-and-needed-installations"], [28, "software-and-needed-installations"]], "Solving Differential Equations with Deep Learning": [[2, null]], "Solving the one dimensional Poisson equation": [[2, "solving-the-one-dimensional-poisson-equation"]], "Solving the wave equation with Neural Networks": [[2, "solving-the-wave-equation-with-neural-networks"]], "Some famous Matrices": [[22, "some-famous-matrices"]], "Some simple problems": [[13, "some-simple-problems"], [30, "some-simple-problems"]], "Some useful matrix and vector expressions": [[29, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[0, "splitting-our-data-in-training-and-test-data"], [29, 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Trees and other Methods": [[9, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Challenge: Choosing a Fixed Learning Rate": [[31, "challenge-choosing-a-fixed-learning-rate"]], "Choose cost function and optimizer": [[1, "choose-cost-function-and-optimizer"]], "Classical PCA Theorem": [[11, "classical-pca-theorem"]], "Clustering and Unsupervised Learning": [[14, null]], "Code Example for Cross-validation and k-fold Cross-validation": [[32, "code-example-for-cross-validation-and-k-fold-cross-validation"]], "Code example for the Bootstrap method": [[32, "code-example-for-the-bootstrap-method"]], "Code for SVD and Inversion of Matrices": [[5, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[31, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[14, "codes-and-approaches"]], "Codes for the SVD": [[5, "codes-for-the-svd"], [29, "codes-for-the-svd"], [30, "codes-for-the-svd"]], "Coding Setup and Linear 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"convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[3, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[12, "convolutional-neural-network"]], "Convolutional Neural Networks": [[3, null]], "Correlation Function and Design/Feature Matrix": [[29, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[11, "correlation-matrix"], [29, "correlation-matrix"]], "Correlation Matrix with Pandas": [[29, "correlation-matrix-with-pandas"]], "Course Format": [[28, "course-format"]], "Course setting": [[24, null]], "Covariance Matrix Examples": [[29, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[29, "covariance-and-correlation-matrix"]], "Cross-validation": [[6, "cross-validation"]], "Cross-validation in brief": [[32, "cross-validation-in-brief"]], "Deadlines for projects (tentative)": [[28, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep Neural Networks": [[31, "deep-neural-networks"]], "Deep learning methods": [[28, "deep-learning-methods"]], "Define model and architecture": [[1, "define-model-and-architecture"]], "Defining the cost function": [[1, "defining-the-cost-function"]], "Definitions": [[19, "definitions"]], "Deliverables": [[15, "deliverables"], [16, "deliverables"], [19, "deliverables"], [20, "deliverables"]], "Derivation of the AdaGrad Algorithm": [[31, "derivation-of-the-adagrad-algorithm"]], "Derivatives and the chain rule": [[12, "derivatives-and-the-chain-rule"]], "Derivatives, example 1": [[29, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"], [32, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[16, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[17, "deriving-and-implementing-ridge-regression"]], "Deriving the Lasso Regression Equations": [[29, "deriving-the-lasso-regression-equations"], [30, "deriving-the-lasso-regression-equations"], [30, "id6"]], "Deriving the Ridge Regression Equations": [[29, "deriving-the-ridge-regression-equations"], [30, "deriving-the-ridge-regression-equations"], [30, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[12, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[1, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[11, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[8, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[9, "disadvantages"]], "Discriminative Modeling": [[28, "discriminative-modeling"]], "Domains and probabilities": [[25, "domains-and-probabilities"]], "Dropout": [[1, "dropout"]], "Economy-size SVD": [[29, "economy-size-svd"], [30, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[25, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[31, "empirical-evidence-convergence-time-and-memory-in-practice"]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[28, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"]], "Example 2": [[29, "example-2"]], "Example 3": [[29, "example-3"]], "Example 4": [[29, "example-4"]], "Example Matrix": [[29, "example-matrix"], [30, "example-matrix"]], "Example code for Bias-Variance tradeoff": [[32, "example-code-for-bias-variance-tradeoff"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[28, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[28, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[29, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[29, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"]], "Examples": [[28, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Creating the report document": [[20, "exercise-1-creating-the-report-document"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: Adding good figures": [[20, "exercise-2-adding-good-figures"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 3: Writing an abstract and introduction": [[20, "exercise-3-writing-an-abstract-and-introduction"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 4: Making the code available and presentable": [[20, "exercise-4-making-the-code-available-and-presentable"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise 5: Referencing": [[20, "exercise-5-referencing"]], "Exercise: Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Exercises week 38": [[19, null]], "Exercises week 39": [[20, null]], "Expectation value and variance": [[32, "expectation-value-and-variance"]], "Expectation value and variance for \\boldsymbol{\\theta}": [[32, "expectation-value-and-variance-for-boldsymbol-theta"]], "Expectation values": [[25, "expectation-values"]], "Extending to more than one variable": [[30, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[28, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"]], "Finding the Limit": [[32, "finding-the-limit"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[29, "fixing-the-singularity"], [30, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[23, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[29, "frequently-used-scaling-functions"], [31, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[30, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Functionality in Scikit-Learn": [[29, "functionality-in-scikit-learn"], [31, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [29, "further-properties-important-for-our-analyses-later"], [30, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[22, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[28, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[28, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [28, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[28, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting started with project 1": [[20, "getting-started-with-project-1"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"]], "Gradient Descent Example": [[30, "id1"], [31, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"]], "Gradient descent and Ridge": [[30, "gradient-descent-and-ridge"], [31, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[31, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[30, "gradient-descent-example"], [31, "gradient-descent-example"]], "Grading": [[26, "grading"], [26, "id2"], [28, "grading"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Identifying Terms": [[32, "identifying-terms"]], "Important Matrix and vector handling packages": [[22, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[29, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[31, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"]], "In summary": [[26, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [31, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[11, "incremental-pca"]], "Independent and Identically Distributed (iid)": [[32, "independent-and-identically-distributed-iid"]], "Installing R, C++, cython or Julia": [[28, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[28, "installing-r-c-cython-numba-etc"]], "Instructor information": [[26, "instructor-information"]], "Interpretations and optimizing our parameters": [[28, "interpretations-and-optimizing-our-parameters"], [28, "id2"], [28, "id3"], [29, "interpretations-and-optimizing-our-parameters"], [29, "id1"], [29, "id2"]], "Interpreting the Ridge results": [[29, "interpreting-the-ridge-results"], [30, "interpreting-the-ridge-results"], [30, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [29, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [21, "introduction"], [22, "introduction"]], "Introduction to numerical projects": [[23, "introduction-to-numerical-projects"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[22, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[30, "lasso-regression"]], "Lasso case": [[30, "lasso-case"]], "Layers": [[1, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"], [18, "learning-goals"], [19, "learning-goals"], [20, "learning-goals"]], "Learning outcomes": [[21, "learning-outcomes"], [28, "learning-outcomes"]], "Lectures and ComputerLab": [[28, "lectures-and-computerlab"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[22, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[29, "linear-regression-problems"], [30, "linear-regression-problems"]], "Linear Regression and the SVD": [[30, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[5, "linking-the-regression-analysis-with-a-statistical-interpretation"], [32, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [29, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[27, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[28, "machine-learning"]], "Machine learning": [[21, "machine-learning"]], "Main textbooks": [[28, "main-textbooks"]], "Making a tree": [[9, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[10, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[29, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[29, "material-for-exercises-week-35"]], "Material for lab sessions sessions Tuesday and Wednesday": [[30, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[30, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[31, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[31, "material-for-the-lab-sessions"], [32, "material-for-the-lab-sessions"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [29, "mathematical-interpretation-of-ordinary-least-squares"], [30, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [29, "mathematics-of-the-svd-and-implications"], [30, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[28, "matrices-in-python"]], "Matrix multiplication": [[1, "matrix-multiplication"]], "Matrix-vector notation and activation": [[12, "matrix-vector-notation-and-activation"]], "Maximum Likelihood Estimation (MLE)": [[32, "maximum-likelihood-estimation-mle"]], "Meet the covariance!": [[25, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [29, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[29, "meet-the-hessian-matrix"]], "Meet the Pandas": [[28, "meet-the-pandas"]], "Memory Usage and Scalability": [[31, "memory-usage-and-scalability"]], "Memory constraints": [[31, "memory-constraints"]], "Min-Max Scaling": [[29, "min-max-scaling"]], "Momentum based GD": [[13, "momentum-based-gd"], [31, "momentum-based-gd"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More examples on bootstrap and cross-validation and errors": [[32, "more-examples-on-bootstrap-and-cross-validation-and-errors"]], "More interpretations": [[29, "more-interpretations"], [30, "more-interpretations"], [30, "id5"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[30, "more-on-steepest-descent"]], "More on convex functions": [[30, "more-on-convex-functions"]], "More preprocessing": [[29, "more-preprocessing"], [31, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[31, "motivation-for-adaptive-step-sizes"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"]], "Network requirements": [[2, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural networks": [[12, null]], "Non-Convex Problems": [[31, "non-convex-problems"]], "Note about SVD Calculations": [[29, "note-about-svd-calculations"], [30, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[30, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[25, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[22, "numpy-and-arrays"], [28, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[28, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[30, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null]], "Optimizing our parameters": [[28, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[28, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"]], "Organizing our data": [[0, "organizing-our-data"], [28, "organizing-our-data"]], "Other Matrix and Vector Operations": [[22, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning at UiO": [[28, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning at UiO, contn": [[28, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[28, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[28, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[28, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[31, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[28, "own-code-for-ordinary-least-squares"], [29, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[28, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[23, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for the Runge function": [[23, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[23, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[23, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing 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"practicalities"], [26, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[23, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[29, "preprocessing-our-data"]], "Prerequisites": [[28, "prerequisites"]], "Prerequisites and background": [[21, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[25, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[30, "program-example-for-gradient-descent-with-ridge-regression"], [31, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine 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"reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[6, "reminder-on-statistics"]], "Reminder on different scaling methods": [[31, "reminder-on-different-scaling-methods"]], "Replace or not": [[13, "replace-or-not"], [31, "replace-or-not"]], "Required Technologies": [[21, "required-technologies"]], "Resampling Methods": [[6, null]], "Resampling and the Bias-Variance Trade-off": [[19, "resampling-and-the-bias-variance-trade-off"]], "Resampling approaches can be computationally expensive": [[32, "resampling-approaches-can-be-computationally-expensive"]], "Resampling methods": [[6, "id1"], [32, "resampling-methods"], [32, "id2"]], "Resampling methods: Bootstrap": [[32, "resampling-methods-bootstrap"]], "Resampling methods: Bootstrap approach": [[32, "resampling-methods-bootstrap-approach"]], "Resampling methods: Bootstrap background": [[32, "resampling-methods-bootstrap-background"]], "Resampling methods: Bootstrap steps": [[32, "resampling-methods-bootstrap-steps"]], "Resampling methods: More Bootstrap background": [[32, "resampling-methods-more-bootstrap-background"]], "Residual Error": [[29, "residual-error"], [30, "residual-error"]], "Resources on differential equations and deep learning": [[2, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[30, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[13, "revisiting-our-linear-regression-solvers"]], "Rewriting the Covariance and/or Correlation Matrix": [[29, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the \\delta-function": [[32, "rewriting-the-delta-function"]], "Rewriting the fitting procedure as a linear algebra problem": [[28, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[28, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[30, "ridge-regression"]], "Ridge and LASSO Regression": [[29, "ridge-and-lasso-regression"], [30, "ridge-and-lasso-regression"], [30, "id2"]], "Ridge and Lasso Regression": [[5, null], [5, "id1"]], "SGD example": [[31, "sgd-example"]], "SGD vs Full-Batch GD: Convergence Speed and Memory Comparison": [[31, "sgd-vs-full-batch-gd-convergence-speed-and-memory-comparison"]], "SVD analysis": [[30, "svd-analysis"]], "Same code but now with momentum gradient descent": [[13, "same-code-but-now-with-momentum-gradient-descent"], [31, "same-code-but-now-with-momentum-gradient-descent"], [31, "id3"], [31, "id4"]], "Schedule first week": [[28, "schedule-first-week"]], "Schematic Regression Procedure": [[9, "schematic-regression-procedure"]], "Second moment of the gradient": [[31, "second-moment-of-the-gradient"]], "September 15-19": [[19, "september-15-19"]], "Setting up the Back propagation algorithm": [[12, "setting-up-the-back-propagation-algorithm"]], "Setting up the Matrix to be inverted": [[29, "setting-up-the-matrix-to-be-inverted"], [30, "setting-up-the-matrix-to-be-inverted"]], "Setting up the network using Autograd; The full program": [[2, "setting-up-the-network-using-autograd-the-full-program"]], "Similar (second order function now) problem but now with AdaGrad": [[13, "similar-second-order-function-now-problem-but-now-with-adagrad"], [31, "similar-second-order-function-now-problem-but-now-with-adagrad"]], "Simple Python Code to read in Data and perform Classification": [[9, "simple-python-code-to-read-in-data-and-perform-classification"]], "Simple case": [[29, "simple-case"], [30, "simple-case"]], "Simple code for solving the above problem": [[30, "simple-code-for-solving-the-above-problem"]], "Simple example code": [[31, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[30, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric interpretation": [[30, 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--git a/doc/LectureNotes/_build/html/week38.html b/doc/LectureNotes/_build/html/week38.html index 183739715..6f81f5ea5 100644 --- a/doc/LectureNotes/_build/html/week38.html +++ b/doc/LectureNotes/_build/html/week38.html @@ -452,9 +452,10 @@ doconce format html week38.do.txt --no_mako -->

  • Statistical interpretation of OLS and various expectation values

  • Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff

  • The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at https://youtu.be/J_41Hld6tTU

    • +

  • Video of Lecture

    • +

  • Whiteboard notes

    • - - +

    Readings and Videos#

      @@ -684,12 +685,12 @@ is equivalent to the maximization/minimization of the function itself.

      We could now define a new cost function to minimize, namely the negative logarithm of the above PDF

      \[ -C(\boldsymbol{\theta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}, +C(\boldsymbol{\theta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}, \]

      which becomes

      \[ -C(\boldsymbol{\theta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}. +C(\boldsymbol{\theta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}. \]

      Taking the derivative of the new cost function with respect to the parameters \(\theta\) we recognize our familiar OLS equation, namely

      diff --git a/doc/LectureNotes/_build/jupyter_execute/week38.ipynb b/doc/LectureNotes/_build/jupyter_execute/week38.ipynb index 7dd2e229a..c9b413443 100644 --- a/doc/LectureNotes/_build/jupyter_execute/week38.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/week38.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "169923b3", + "id": "8f27372d", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "47013ee7", + "id": "fff8ca30", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "d1fb5464", + "id": "7ee7e714", "metadata": { "editable": true }, @@ -41,13 +41,15 @@ "2. Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff\n", "\n", "3. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at \n", - "\n", - "" + "\n", + "4. [Video of Lecture](https://youtu.be/4Fo7ITVA7V4)\n", + "\n", + "5. [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek38.pdf)" ] }, { "cell_type": "markdown", - "id": "1a34a7ce", + "id": "3b5ac440", "metadata": { "editable": true }, @@ -68,7 +70,7 @@ }, { "cell_type": "markdown", - "id": "c6f56f83", + "id": "6d5dba52", "metadata": { "editable": true }, @@ -96,7 +98,7 @@ }, { "cell_type": "markdown", - "id": "3ece0c04", + "id": "bfc2983a", "metadata": { "editable": true }, @@ -112,7 +114,7 @@ }, { "cell_type": "markdown", - "id": "d36cf6db", + "id": "2b5f5980", "metadata": { "editable": true }, @@ -131,7 +133,7 @@ }, { "cell_type": "markdown", - "id": "5903d2be", + "id": "3464c7e8", "metadata": { "editable": true }, @@ -145,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "37f4e199", + "id": "ed0fd2df", "metadata": { "editable": true }, @@ -157,7 +159,7 @@ }, { "cell_type": "markdown", - "id": "7a7b084f", + "id": "feb9d4c2", "metadata": { "editable": true }, @@ -168,7 +170,7 @@ }, { "cell_type": "markdown", - "id": "1ec511a1", + "id": "eb6d71f8", "metadata": { "editable": true }, @@ -180,7 +182,7 @@ }, { "cell_type": "markdown", - "id": "ffe76935", + "id": "566399f6", "metadata": { "editable": true }, @@ -192,7 +194,7 @@ }, { "cell_type": "markdown", - "id": "e569274a", + "id": "6b33f497", "metadata": { "editable": true }, @@ -208,7 +210,7 @@ }, { "cell_type": "markdown", - "id": "c4dd2623", + "id": "5f2f79f2", "metadata": { "editable": true }, @@ -219,7 +221,7 @@ }, { "cell_type": "markdown", - "id": "df2f8936", + "id": "199121b0", "metadata": { "editable": true }, @@ -242,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "0a3e5956", + "id": "9a1cc529", "metadata": { "editable": true }, @@ -253,7 +255,7 @@ }, { "cell_type": "markdown", - "id": "973e45a3", + "id": "149e63be", "metadata": { "editable": true }, @@ -265,7 +267,7 @@ }, { "cell_type": "markdown", - "id": "ff486d1e", + "id": "6a6fb04a", "metadata": { "editable": true }, @@ -277,7 +279,7 @@ }, { "cell_type": "markdown", - "id": "e4307815", + "id": "79420d06", "metadata": { "editable": true }, @@ -291,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "490b2cbf", + "id": "0e3de992", "metadata": { "editable": true }, @@ -322,7 +324,7 @@ }, { "cell_type": "markdown", - "id": "5d8dd6bc", + "id": "d3ea2897", "metadata": { "editable": true }, @@ -344,7 +346,7 @@ }, { "cell_type": "markdown", - "id": "3594078a", + "id": "da5e3927", "metadata": { "editable": true }, @@ -356,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "43007b7a", + "id": "7ab5488b", "metadata": { "editable": true }, @@ -369,7 +371,7 @@ }, { "cell_type": "markdown", - "id": "3cd4e7da", + "id": "f904a739", "metadata": { "editable": true }, @@ -381,7 +383,7 @@ }, { "cell_type": "markdown", - "id": "5816b21e", + "id": "10fd648b", "metadata": { "editable": true }, @@ -393,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "b58b8607", + "id": "4812c2a4", "metadata": { "editable": true }, @@ -405,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "c843db7f", + "id": "199d8531", "metadata": { "editable": true }, @@ -417,7 +419,7 @@ }, { "cell_type": "markdown", - "id": "e81b1c39", + "id": "96c16676", "metadata": { "editable": true }, @@ -440,7 +442,7 @@ }, { "cell_type": "markdown", - "id": "ea9719e3", + "id": "a2a1a004", "metadata": { "editable": true }, @@ -452,7 +454,7 @@ }, { "cell_type": "markdown", - "id": "c28b598f", + "id": "5aad445b", "metadata": { "editable": true }, @@ -465,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "88063ed7", + "id": "d197c8bb", "metadata": { "editable": true }, @@ -477,7 +479,7 @@ }, { "cell_type": "markdown", - "id": "a34e4c28", + "id": "e2e7462f", "metadata": { "editable": true }, @@ -489,7 +491,7 @@ }, { "cell_type": "markdown", - "id": "1fc7ae0a", + "id": "eb635d3d", "metadata": { "editable": true }, @@ -501,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "30d5a1be", + "id": "445ed13e", "metadata": { "editable": true }, @@ -512,7 +514,7 @@ }, { "cell_type": "markdown", - "id": "1d29fd29", + "id": "319bfc6c", "metadata": { "editable": true }, @@ -524,7 +526,7 @@ }, { "cell_type": "markdown", - "id": "289a116c", + "id": "90abf35a", "metadata": { "editable": true }, @@ -535,7 +537,7 @@ }, { "cell_type": "markdown", - "id": "d1cfbb56", + "id": "04b66fbd", "metadata": { "editable": true }, @@ -547,7 +549,7 @@ }, { "cell_type": "markdown", - "id": "e089fc0e", + "id": "4a27b5a7", "metadata": { "editable": true }, @@ -557,7 +559,7 @@ }, { "cell_type": "markdown", - "id": "32cf9944", + "id": "8d12543f", "metadata": { "editable": true }, @@ -588,7 +590,7 @@ }, { "cell_type": "markdown", - "id": "ee8a9544", + "id": "2e5cd118", "metadata": { "editable": true }, @@ -600,19 +602,19 @@ }, { "cell_type": "markdown", - "id": "4bfeb203", + "id": "c71a5edf", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\theta}=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})},\n", + "C(\\boldsymbol{\\theta})=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})},\n", "$$" ] }, { "cell_type": "markdown", - "id": "256143f9", + "id": "e663bf2e", "metadata": { "editable": true }, @@ -622,19 +624,19 @@ }, { "cell_type": "markdown", - "id": "60d75bb1", + "id": "c4bc4873", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\theta}=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta})\\vert\\vert_2^2}{2\\sigma^2}.\n", + "C(\\boldsymbol{\\theta})=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta})\\vert\\vert_2^2}{2\\sigma^2}.\n", "$$" ] }, { "cell_type": "markdown", - "id": "7b111014", + "id": "f5bc59b8", "metadata": { "editable": true }, @@ -644,7 +646,7 @@ }, { "cell_type": "markdown", - "id": "0f42a0b5", + "id": "4f6ddf4a", "metadata": { "editable": true }, @@ -656,7 +658,7 @@ }, { "cell_type": "markdown", - "id": "39a9276b", + "id": "afda0a6b", "metadata": { "editable": true }, @@ -666,7 +668,7 @@ }, { "cell_type": "markdown", - "id": "84c63927", + "id": "b5335dc0", "metadata": { "editable": true }, @@ -678,7 +680,7 @@ }, { "cell_type": "markdown", - "id": "c087ef22", + "id": "4f86a52d", "metadata": { "editable": true }, @@ -688,7 +690,7 @@ }, { "cell_type": "markdown", - "id": "79503987", + "id": "5cdb1767", "metadata": { "editable": true }, @@ -707,7 +709,7 @@ }, { "cell_type": "markdown", - "id": "c165025b", + "id": "69435d77", "metadata": { "editable": true }, @@ -735,7 +737,7 @@ }, { "cell_type": "markdown", - "id": "efb63405", + "id": "cefbb559", "metadata": { "editable": true }, @@ -761,7 +763,7 @@ }, { "cell_type": "markdown", - "id": "88d4bfd8", + "id": "2659401a", "metadata": { "editable": true }, @@ -778,7 +780,7 @@ }, { "cell_type": "markdown", - "id": "6a0795e0", + "id": "4d5d7748", "metadata": { "editable": true }, @@ -798,7 +800,7 @@ }, { "cell_type": "markdown", - "id": "d815fdf3", + "id": "54df92b3", "metadata": { "editable": true }, @@ -827,7 +829,7 @@ }, { "cell_type": "markdown", - "id": "a5b26ed1", + "id": "5b1a1390", "metadata": { "editable": true }, @@ -852,7 +854,7 @@ }, { "cell_type": "markdown", - "id": "e5783b81", + "id": "39f233e4", "metadata": { "editable": true }, @@ -872,7 +874,7 @@ }, { "cell_type": "markdown", - "id": "9bdfff4f", + "id": "361320d8", "metadata": { "editable": true }, @@ -884,7 +886,7 @@ }, { "cell_type": "markdown", - "id": "bd1e4a83", + "id": "a363db1e", "metadata": { "editable": true }, @@ -894,7 +896,7 @@ }, { "cell_type": "markdown", - "id": "66d14a83", + "id": "92967efc", "metadata": { "editable": true }, @@ -909,7 +911,7 @@ }, { "cell_type": "markdown", - "id": "ac38d462", + "id": "1bffca97", "metadata": { "editable": true }, @@ -922,7 +924,7 @@ }, { "cell_type": "markdown", - "id": "65488a60", + "id": "0dacb6fc", "metadata": { "editable": true }, @@ -935,7 +937,7 @@ }, { "cell_type": "markdown", - "id": "9c8686d8", + "id": "baeedf81", "metadata": { "editable": true }, @@ -947,7 +949,7 @@ }, { "cell_type": "markdown", - "id": "585dbaff", + "id": "20cc7770", "metadata": { "editable": true }, @@ -960,7 +962,7 @@ }, { "cell_type": "markdown", - "id": "a8093a3e", + "id": "f67d3b94", "metadata": { "editable": true }, @@ -971,7 +973,7 @@ }, { "cell_type": "markdown", - "id": "ec844baa", + "id": "17f59fb6", "metadata": { "editable": true }, @@ -985,7 +987,7 @@ }, { "cell_type": "markdown", - "id": "7f2b563b", + "id": "5f899fbe", "metadata": { "editable": true }, @@ -995,7 +997,7 @@ }, { "cell_type": "markdown", - "id": "5a75bbe4", + "id": "19a1f5bb", "metadata": { "editable": true }, @@ -1009,7 +1011,7 @@ }, { "cell_type": "markdown", - "id": "8d00a9ff", + "id": "1db8fcf2", "metadata": { "editable": true }, @@ -1022,7 +1024,7 @@ }, { "cell_type": "markdown", - "id": "cae54a40", + "id": "bfadf7e5", "metadata": { "editable": true }, @@ -1035,7 +1037,7 @@ }, { "cell_type": "markdown", - "id": "ef87a15a", + "id": "7c65ce24", "metadata": { "editable": true }, @@ -1045,7 +1047,7 @@ }, { "cell_type": "markdown", - "id": "5bfaef5d", + "id": "8cd5650a", "metadata": { "editable": true }, @@ -1058,7 +1060,7 @@ }, { "cell_type": "markdown", - "id": "0aab5f59", + "id": "11fdc936", "metadata": { "editable": true }, @@ -1068,7 +1070,7 @@ }, { "cell_type": "markdown", - "id": "71269afb", + "id": "ed88642e", "metadata": { "editable": true }, @@ -1081,7 +1083,7 @@ }, { "cell_type": "markdown", - "id": "4d809fab", + "id": "82c61b81", "metadata": { "editable": true }, @@ -1093,7 +1095,7 @@ }, { "cell_type": "markdown", - "id": "734f7c5e", + "id": "bc43db46", "metadata": { "editable": true }, @@ -1112,7 +1114,7 @@ }, { "cell_type": "markdown", - "id": "f4ff2861", + "id": "25418113", "metadata": { "editable": true }, @@ -1125,7 +1127,7 @@ }, { "cell_type": "markdown", - "id": "fd66a47c", + "id": "e5d3c3eb", "metadata": { "editable": true }, @@ -1137,7 +1139,7 @@ }, { "cell_type": "markdown", - "id": "51e5434b", + "id": "c504cba4", "metadata": { "editable": true }, @@ -1150,7 +1152,7 @@ }, { "cell_type": "markdown", - "id": "9129f7a5", + "id": "079ded2a", "metadata": { "editable": true }, @@ -1170,7 +1172,7 @@ }, { "cell_type": "markdown", - "id": "e5fa7f9c", + "id": "e8534a50", "metadata": { "editable": true }, @@ -1193,7 +1195,7 @@ }, { "cell_type": "markdown", - "id": "f5bbafe6", + "id": "2fc73431", "metadata": { "editable": true }, @@ -1208,7 +1210,7 @@ }, { "cell_type": "markdown", - "id": "0cc93a0c", + "id": "0f8b0845", "metadata": { "editable": true }, @@ -1220,7 +1222,7 @@ }, { "cell_type": "markdown", - "id": "8dd4f5e0", + "id": "25105753", "metadata": { "editable": true }, @@ -1240,7 +1242,7 @@ }, { "cell_type": "markdown", - "id": "f51c546c", + "id": "89be6eea", "metadata": { "editable": true }, @@ -1260,7 +1262,7 @@ }, { "cell_type": "markdown", - "id": "e44fcf6d", + "id": "6c240b38", "metadata": { "editable": true }, @@ -1284,7 +1286,7 @@ }, { "cell_type": "markdown", - "id": "3bd69373", + "id": "fbd95a5c", "metadata": { "editable": true }, @@ -1305,7 +1307,7 @@ }, { "cell_type": "markdown", - "id": "e7f867d9", + "id": "dc50d43a", "metadata": { "editable": true }, @@ -1335,7 +1337,7 @@ }, { "cell_type": "markdown", - "id": "5c2c3909", + "id": "283068cc", "metadata": { "editable": true }, @@ -1359,7 +1361,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "a32faf6a", + "id": "ff4790ba", "metadata": { "collapsed": false, "editable": true @@ -1398,7 +1400,7 @@ }, { "cell_type": "markdown", - "id": "bc95505d", + "id": "3e6adc2f", "metadata": { "editable": true }, @@ -1408,7 +1410,7 @@ }, { "cell_type": "markdown", - "id": "355f62af", + "id": "6ec8223c", "metadata": { "editable": true }, @@ -1419,7 +1421,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "39fd1fa8", + "id": "3cf4144d", "metadata": { "collapsed": false, "editable": true @@ -1439,7 +1441,7 @@ }, { "cell_type": "markdown", - "id": "237b4db3", + "id": "db5a8f91", "metadata": { "editable": true }, @@ -1457,7 +1459,7 @@ }, { "cell_type": "markdown", - "id": "0c13e5b0", + "id": "327bce6a", "metadata": { "editable": true }, @@ -1469,7 +1471,7 @@ }, { "cell_type": "markdown", - "id": "a086aa7e", + "id": "1c671d4e", "metadata": { "editable": true }, @@ -1486,7 +1488,7 @@ }, { "cell_type": "markdown", - "id": "c3837d89", + "id": "6e05fc43", "metadata": { "editable": true }, @@ -1498,7 +1500,7 @@ }, { "cell_type": "markdown", - "id": "7c7cd0a7", + "id": "c45e0752", "metadata": { "editable": true }, @@ -1508,7 +1510,7 @@ }, { "cell_type": "markdown", - "id": "b9db0cd5", + "id": "bafa4ab6", "metadata": { "editable": true }, @@ -1520,7 +1522,7 @@ }, { "cell_type": "markdown", - "id": "00482b2d", + "id": "ea0bc471", "metadata": { "editable": true }, @@ -1537,7 +1539,7 @@ }, { "cell_type": "markdown", - "id": "2e7c7291", + "id": "08b603f3", "metadata": { "editable": true }, @@ -1549,7 +1551,7 @@ }, { "cell_type": "markdown", - "id": "9a8d29b5", + "id": "4114d10e", "metadata": { "editable": true }, @@ -1559,7 +1561,7 @@ }, { "cell_type": "markdown", - "id": "9a8e2084", + "id": "8890c666", "metadata": { "editable": true }, @@ -1571,7 +1573,7 @@ }, { "cell_type": "markdown", - "id": "4a191c5c", + "id": "7d5b7ce4", "metadata": { "editable": true }, @@ -1581,7 +1583,7 @@ }, { "cell_type": "markdown", - "id": "c37713f8", + "id": "3913c5b9", "metadata": { "editable": true }, @@ -1593,7 +1595,7 @@ }, { "cell_type": "markdown", - "id": "82ca4a7b", + "id": "5e0067b1", "metadata": { "editable": true }, @@ -1603,7 +1605,7 @@ }, { "cell_type": "markdown", - "id": "2765a841", + "id": "326bc8f1", "metadata": { "editable": true }, @@ -1619,7 +1621,7 @@ }, { "cell_type": "markdown", - "id": "321964c1", + "id": "d3713eca", "metadata": { "editable": true }, @@ -1630,7 +1632,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "5942226f", + "id": "01c3b507", "metadata": { "collapsed": false, "editable": true @@ -1695,7 +1697,7 @@ }, { "cell_type": "markdown", - "id": "cf2af19d", + "id": "949e3a5e", "metadata": { "editable": true }, @@ -1706,7 +1708,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "7b371a0c", + "id": "7e7f4926", "metadata": { "collapsed": false, "editable": true @@ -1763,7 +1765,7 @@ }, { "cell_type": "markdown", - "id": "6f583fcd", + "id": "33c5cae5", "metadata": { "editable": true }, @@ -1801,7 +1803,7 @@ }, { "cell_type": "markdown", - "id": "37766c51", + "id": "f931f0f2", "metadata": { "editable": true }, @@ -1828,7 +1830,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "0eac5ca9", + "id": "58daa28d", "metadata": { "collapsed": false, "editable": true @@ -1890,7 +1892,7 @@ }, { "cell_type": "markdown", - "id": "d698096e", + "id": "3bbcf741", "metadata": { "editable": true }, @@ -1915,7 +1917,7 @@ }, { "cell_type": "markdown", - "id": "3e37a4d2", + "id": "4b0ffe06", "metadata": { "editable": true }, @@ -1943,7 +1945,7 @@ }, { "cell_type": "markdown", - "id": "e7e43cf9", + "id": "b11baed6", "metadata": { "editable": true }, @@ -1956,7 +1958,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "7aa6a568", + "id": "39e76d49", "metadata": { "collapsed": false, "editable": true @@ -2056,7 +2058,7 @@ }, { "cell_type": "markdown", - "id": "9a90aec7", + "id": "e7d12ef0", "metadata": { "editable": true }, @@ -2067,7 +2069,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "93b3af24", + "id": "47f6ae18", "metadata": { "collapsed": false, "editable": true @@ -2156,7 +2158,7 @@ }, { "cell_type": "markdown", - "id": "90657c6d", + "id": "9c1d4754", "metadata": { "editable": true }, @@ -2166,7 +2168,7 @@ }, { "cell_type": "markdown", - "id": "a88b86e7", + "id": "b698ac66", "metadata": { "editable": true }, @@ -2179,7 +2181,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "89f45188", + "id": "0a2409b0", "metadata": { "collapsed": false, "editable": true @@ -2257,7 +2259,7 @@ }, { "cell_type": "markdown", - "id": "75496517", + "id": "56f130b5", "metadata": { "editable": true }, diff --git a/doc/LectureNotes/week38.ipynb b/doc/LectureNotes/week38.ipynb index 544d286d0..1d25f9941 100644 --- a/doc/LectureNotes/week38.ipynb +++ b/doc/LectureNotes/week38.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "169923b3", + "id": "8f27372d", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "47013ee7", + "id": "fff8ca30", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "d1fb5464", + "id": "7ee7e714", "metadata": { "editable": true }, @@ -41,13 +41,15 @@ "2. Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff\n", "\n", "3. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at \n", - "\n", - "" + "\n", + "4. [Video of Lecture](https://youtu.be/4Fo7ITVA7V4)\n", + "\n", + "5. [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek38.pdf)" ] }, { "cell_type": "markdown", - "id": "1a34a7ce", + "id": "3b5ac440", "metadata": { "editable": true }, @@ -68,7 +70,7 @@ }, { "cell_type": "markdown", - "id": "c6f56f83", + "id": "6d5dba52", "metadata": { "editable": true }, @@ -96,7 +98,7 @@ }, { "cell_type": "markdown", - "id": "3ece0c04", + "id": "bfc2983a", "metadata": { "editable": true }, @@ -112,7 +114,7 @@ }, { "cell_type": "markdown", - "id": "d36cf6db", + "id": "2b5f5980", "metadata": { "editable": true }, @@ -131,7 +133,7 @@ }, { "cell_type": "markdown", - "id": "5903d2be", + "id": "3464c7e8", "metadata": { "editable": true }, @@ -145,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "37f4e199", + "id": "ed0fd2df", "metadata": { "editable": true }, @@ -157,7 +159,7 @@ }, { "cell_type": "markdown", - "id": "7a7b084f", + "id": "feb9d4c2", "metadata": { "editable": true }, @@ -168,7 +170,7 @@ }, { "cell_type": "markdown", - "id": "1ec511a1", + "id": "eb6d71f8", "metadata": { "editable": true }, @@ -180,7 +182,7 @@ }, { "cell_type": "markdown", - "id": "ffe76935", + "id": "566399f6", "metadata": { "editable": true }, @@ -192,7 +194,7 @@ }, { "cell_type": "markdown", - "id": "e569274a", + "id": "6b33f497", "metadata": { "editable": true }, @@ -208,7 +210,7 @@ }, { "cell_type": "markdown", - "id": "c4dd2623", + "id": "5f2f79f2", "metadata": { "editable": true }, @@ -219,7 +221,7 @@ }, { "cell_type": "markdown", - "id": "df2f8936", + "id": "199121b0", "metadata": { "editable": true }, @@ -242,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "0a3e5956", + "id": "9a1cc529", "metadata": { "editable": true }, @@ -253,7 +255,7 @@ }, { "cell_type": "markdown", - "id": "973e45a3", + "id": "149e63be", "metadata": { "editable": true }, @@ -265,7 +267,7 @@ }, { "cell_type": "markdown", - "id": "ff486d1e", + "id": "6a6fb04a", "metadata": { "editable": true }, @@ -277,7 +279,7 @@ }, { "cell_type": "markdown", - "id": "e4307815", + "id": "79420d06", "metadata": { "editable": true }, @@ -291,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "490b2cbf", + "id": "0e3de992", "metadata": { "editable": true }, @@ -322,7 +324,7 @@ }, { "cell_type": "markdown", - "id": "5d8dd6bc", + "id": "d3ea2897", "metadata": { "editable": true }, @@ -344,7 +346,7 @@ }, { "cell_type": "markdown", - "id": "3594078a", + "id": "da5e3927", "metadata": { "editable": true }, @@ -356,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "43007b7a", + "id": "7ab5488b", "metadata": { "editable": true }, @@ -369,7 +371,7 @@ }, { "cell_type": "markdown", - "id": "3cd4e7da", + "id": "f904a739", "metadata": { "editable": true }, @@ -381,7 +383,7 @@ }, { "cell_type": "markdown", - "id": "5816b21e", + "id": "10fd648b", "metadata": { "editable": true }, @@ -393,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "b58b8607", + "id": "4812c2a4", "metadata": { "editable": true }, @@ -405,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "c843db7f", + "id": "199d8531", "metadata": { "editable": true }, @@ -417,7 +419,7 @@ }, { "cell_type": "markdown", - "id": "e81b1c39", + "id": "96c16676", "metadata": { "editable": true }, @@ -440,7 +442,7 @@ }, { "cell_type": "markdown", - "id": "ea9719e3", + "id": "a2a1a004", "metadata": { "editable": true }, @@ -452,7 +454,7 @@ }, { "cell_type": "markdown", - "id": "c28b598f", + "id": "5aad445b", "metadata": { "editable": true }, @@ -465,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "88063ed7", + "id": "d197c8bb", "metadata": { "editable": true }, @@ -477,7 +479,7 @@ }, { "cell_type": "markdown", - "id": "a34e4c28", + "id": "e2e7462f", "metadata": { "editable": true }, @@ -489,7 +491,7 @@ }, { "cell_type": "markdown", - "id": "1fc7ae0a", + "id": "eb635d3d", "metadata": { "editable": true }, @@ -501,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "30d5a1be", + "id": "445ed13e", "metadata": { "editable": true }, @@ -512,7 +514,7 @@ }, { "cell_type": "markdown", - "id": "1d29fd29", + "id": "319bfc6c", "metadata": { "editable": true }, @@ -524,7 +526,7 @@ }, { "cell_type": "markdown", - "id": "289a116c", + "id": "90abf35a", "metadata": { "editable": true }, @@ -535,7 +537,7 @@ }, { "cell_type": "markdown", - "id": "d1cfbb56", + "id": "04b66fbd", "metadata": { "editable": true }, @@ -547,7 +549,7 @@ }, { "cell_type": "markdown", - "id": "e089fc0e", + "id": "4a27b5a7", "metadata": { "editable": true }, @@ -557,7 +559,7 @@ }, { "cell_type": "markdown", - "id": "32cf9944", + "id": "8d12543f", "metadata": { "editable": true }, @@ -588,7 +590,7 @@ }, { "cell_type": "markdown", - "id": "ee8a9544", + "id": "2e5cd118", "metadata": { "editable": true }, @@ -600,19 +602,19 @@ }, { "cell_type": "markdown", - "id": "4bfeb203", + "id": "c71a5edf", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\theta}=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})},\n", + "C(\\boldsymbol{\\theta})=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})},\n", "$$" ] }, { "cell_type": "markdown", - "id": "256143f9", + "id": "e663bf2e", "metadata": { "editable": true }, @@ -622,19 +624,19 @@ }, { "cell_type": "markdown", - "id": "60d75bb1", + "id": "c4bc4873", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\theta}=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta})\\vert\\vert_2^2}{2\\sigma^2}.\n", + "C(\\boldsymbol{\\theta})=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta})\\vert\\vert_2^2}{2\\sigma^2}.\n", "$$" ] }, { "cell_type": "markdown", - "id": "7b111014", + "id": "f5bc59b8", "metadata": { "editable": true }, @@ -644,7 +646,7 @@ }, { "cell_type": "markdown", - "id": "0f42a0b5", + "id": "4f6ddf4a", "metadata": { "editable": true }, @@ -656,7 +658,7 @@ }, { "cell_type": "markdown", - "id": "39a9276b", + "id": "afda0a6b", "metadata": { "editable": true }, @@ -666,7 +668,7 @@ }, { "cell_type": "markdown", - "id": "84c63927", + "id": "b5335dc0", "metadata": { "editable": true }, @@ -678,7 +680,7 @@ }, { "cell_type": "markdown", - "id": "c087ef22", + "id": "4f86a52d", "metadata": { "editable": true }, @@ -688,7 +690,7 @@ }, { "cell_type": "markdown", - "id": "79503987", + "id": "5cdb1767", "metadata": { "editable": true }, @@ -707,7 +709,7 @@ }, { "cell_type": "markdown", - "id": "c165025b", + "id": "69435d77", "metadata": { "editable": true }, @@ -735,7 +737,7 @@ }, { "cell_type": "markdown", - "id": "efb63405", + "id": "cefbb559", "metadata": { "editable": true }, @@ -761,7 +763,7 @@ }, { "cell_type": "markdown", - "id": "88d4bfd8", + "id": "2659401a", "metadata": { "editable": true }, @@ -778,7 +780,7 @@ }, { "cell_type": "markdown", - "id": "6a0795e0", + "id": "4d5d7748", "metadata": { "editable": true }, @@ -798,7 +800,7 @@ }, { "cell_type": "markdown", - "id": "d815fdf3", + "id": "54df92b3", "metadata": { "editable": true }, @@ -827,7 +829,7 @@ }, { "cell_type": "markdown", - "id": "a5b26ed1", + "id": "5b1a1390", "metadata": { "editable": true }, @@ -852,7 +854,7 @@ }, { "cell_type": "markdown", - "id": "e5783b81", + "id": "39f233e4", "metadata": { "editable": true }, @@ -872,7 +874,7 @@ }, { "cell_type": "markdown", - "id": "9bdfff4f", + "id": "361320d8", "metadata": { "editable": true }, @@ -884,7 +886,7 @@ }, { "cell_type": "markdown", - "id": "bd1e4a83", + "id": "a363db1e", "metadata": { "editable": true }, @@ -894,7 +896,7 @@ }, { "cell_type": "markdown", - "id": "66d14a83", + "id": "92967efc", "metadata": { "editable": true }, @@ -909,7 +911,7 @@ }, { "cell_type": "markdown", - "id": "ac38d462", + "id": "1bffca97", "metadata": { "editable": true }, @@ -922,7 +924,7 @@ }, { "cell_type": "markdown", - "id": "65488a60", + "id": "0dacb6fc", "metadata": { "editable": true }, @@ -935,7 +937,7 @@ }, { "cell_type": "markdown", - "id": "9c8686d8", + "id": "baeedf81", "metadata": { "editable": true }, @@ -947,7 +949,7 @@ }, { "cell_type": "markdown", - "id": "585dbaff", + "id": "20cc7770", "metadata": { "editable": true }, @@ -960,7 +962,7 @@ }, { "cell_type": "markdown", - "id": "a8093a3e", + "id": "f67d3b94", "metadata": { "editable": true }, @@ -971,7 +973,7 @@ }, { "cell_type": "markdown", - "id": "ec844baa", + "id": "17f59fb6", "metadata": { "editable": true }, @@ -985,7 +987,7 @@ }, { "cell_type": "markdown", - "id": "7f2b563b", + "id": "5f899fbe", "metadata": { "editable": true }, @@ -995,7 +997,7 @@ }, { "cell_type": "markdown", - "id": "5a75bbe4", + "id": "19a1f5bb", "metadata": { "editable": true }, @@ -1009,7 +1011,7 @@ }, { "cell_type": "markdown", - "id": "8d00a9ff", + "id": "1db8fcf2", "metadata": { "editable": true }, @@ -1022,7 +1024,7 @@ }, { "cell_type": "markdown", - "id": "cae54a40", + "id": "bfadf7e5", "metadata": { "editable": true }, @@ -1035,7 +1037,7 @@ }, { "cell_type": "markdown", - "id": "ef87a15a", + "id": "7c65ce24", "metadata": { "editable": true }, @@ -1045,7 +1047,7 @@ }, { "cell_type": "markdown", - "id": "5bfaef5d", + "id": "8cd5650a", "metadata": { "editable": true }, @@ -1058,7 +1060,7 @@ }, { "cell_type": "markdown", - "id": "0aab5f59", + "id": "11fdc936", "metadata": { "editable": true }, @@ -1068,7 +1070,7 @@ }, { "cell_type": "markdown", - "id": "71269afb", + "id": "ed88642e", "metadata": { "editable": true }, @@ -1081,7 +1083,7 @@ }, { "cell_type": "markdown", - "id": "4d809fab", + "id": "82c61b81", "metadata": { "editable": true }, @@ -1093,7 +1095,7 @@ }, { "cell_type": "markdown", - "id": "734f7c5e", + "id": "bc43db46", "metadata": { "editable": true }, @@ -1112,7 +1114,7 @@ }, { "cell_type": "markdown", - "id": "f4ff2861", + "id": "25418113", "metadata": { "editable": true }, @@ -1125,7 +1127,7 @@ }, { "cell_type": "markdown", - "id": "fd66a47c", + "id": "e5d3c3eb", "metadata": { "editable": true }, @@ -1137,7 +1139,7 @@ }, { "cell_type": "markdown", - "id": "51e5434b", + "id": "c504cba4", "metadata": { "editable": true }, @@ -1150,7 +1152,7 @@ }, { "cell_type": "markdown", - "id": "9129f7a5", + "id": "079ded2a", "metadata": { "editable": true }, @@ -1170,7 +1172,7 @@ }, { "cell_type": "markdown", - "id": "e5fa7f9c", + "id": "e8534a50", "metadata": { "editable": true }, @@ -1193,7 +1195,7 @@ }, { "cell_type": "markdown", - "id": "f5bbafe6", + "id": "2fc73431", "metadata": { "editable": true }, @@ -1208,7 +1210,7 @@ }, { "cell_type": "markdown", - "id": "0cc93a0c", + "id": "0f8b0845", "metadata": { "editable": true }, @@ -1220,7 +1222,7 @@ }, { "cell_type": "markdown", - "id": "8dd4f5e0", + "id": "25105753", "metadata": { "editable": true }, @@ -1240,7 +1242,7 @@ }, { "cell_type": "markdown", - "id": "f51c546c", + "id": "89be6eea", "metadata": { "editable": true }, @@ -1260,7 +1262,7 @@ }, { "cell_type": "markdown", - "id": "e44fcf6d", + "id": "6c240b38", "metadata": { "editable": true }, @@ -1284,7 +1286,7 @@ }, { "cell_type": "markdown", - "id": "3bd69373", + "id": "fbd95a5c", "metadata": { "editable": true }, @@ -1305,7 +1307,7 @@ }, { "cell_type": "markdown", - "id": "e7f867d9", + "id": "dc50d43a", "metadata": { "editable": true }, @@ -1335,7 +1337,7 @@ }, { "cell_type": "markdown", - "id": "5c2c3909", + "id": "283068cc", "metadata": { "editable": true }, @@ -1359,7 +1361,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "a32faf6a", + "id": "ff4790ba", "metadata": { "collapsed": false, "editable": true @@ -1398,7 +1400,7 @@ }, { "cell_type": "markdown", - "id": "bc95505d", + "id": "3e6adc2f", "metadata": { "editable": true }, @@ -1408,7 +1410,7 @@ }, { "cell_type": "markdown", - "id": "355f62af", + "id": "6ec8223c", "metadata": { "editable": true }, @@ -1419,7 +1421,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "39fd1fa8", + "id": "3cf4144d", "metadata": { "collapsed": false, "editable": true @@ -1439,7 +1441,7 @@ }, { "cell_type": "markdown", - "id": "237b4db3", + "id": "db5a8f91", "metadata": { "editable": true }, @@ -1457,7 +1459,7 @@ }, { "cell_type": "markdown", - "id": "0c13e5b0", + "id": "327bce6a", "metadata": { "editable": true }, @@ -1469,7 +1471,7 @@ }, { "cell_type": "markdown", - "id": "a086aa7e", + "id": "1c671d4e", "metadata": { "editable": true }, @@ -1486,7 +1488,7 @@ }, { "cell_type": "markdown", - "id": "c3837d89", + "id": "6e05fc43", "metadata": { "editable": true }, @@ -1498,7 +1500,7 @@ }, { "cell_type": "markdown", - "id": "7c7cd0a7", + "id": "c45e0752", "metadata": { "editable": true }, @@ -1508,7 +1510,7 @@ }, { "cell_type": "markdown", - "id": "b9db0cd5", + "id": "bafa4ab6", "metadata": { "editable": true }, @@ -1520,7 +1522,7 @@ }, { "cell_type": "markdown", - "id": "00482b2d", + "id": "ea0bc471", "metadata": { "editable": true }, @@ -1537,7 +1539,7 @@ }, { "cell_type": "markdown", - "id": "2e7c7291", + "id": "08b603f3", "metadata": { "editable": true }, @@ -1549,7 +1551,7 @@ }, { "cell_type": "markdown", - "id": "9a8d29b5", + "id": "4114d10e", "metadata": { "editable": true }, @@ -1559,7 +1561,7 @@ }, { "cell_type": "markdown", - "id": "9a8e2084", + "id": "8890c666", "metadata": { "editable": true }, @@ -1571,7 +1573,7 @@ }, { "cell_type": "markdown", - "id": "4a191c5c", + "id": "7d5b7ce4", "metadata": { "editable": true }, @@ -1581,7 +1583,7 @@ }, { "cell_type": "markdown", - "id": "c37713f8", + "id": "3913c5b9", "metadata": { "editable": true }, @@ -1593,7 +1595,7 @@ }, { "cell_type": "markdown", - "id": "82ca4a7b", + "id": "5e0067b1", "metadata": { "editable": true }, @@ -1603,7 +1605,7 @@ }, { "cell_type": "markdown", - "id": "2765a841", + "id": "326bc8f1", "metadata": { "editable": true }, @@ -1619,7 +1621,7 @@ }, { "cell_type": "markdown", - "id": "321964c1", + "id": "d3713eca", "metadata": { "editable": true }, @@ -1630,7 +1632,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "5942226f", + "id": "01c3b507", "metadata": { "collapsed": false, "editable": true @@ -1695,7 +1697,7 @@ }, { "cell_type": "markdown", - "id": "cf2af19d", + "id": "949e3a5e", "metadata": { "editable": true }, @@ -1706,7 +1708,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "7b371a0c", + "id": "7e7f4926", "metadata": { "collapsed": false, "editable": true @@ -1763,7 +1765,7 @@ }, { "cell_type": "markdown", - "id": "6f583fcd", + "id": "33c5cae5", "metadata": { "editable": true }, @@ -1801,7 +1803,7 @@ }, { "cell_type": "markdown", - "id": "37766c51", + "id": "f931f0f2", "metadata": { "editable": true }, @@ -1828,7 +1830,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "0eac5ca9", + "id": "58daa28d", "metadata": { "collapsed": false, "editable": true @@ -1890,7 +1892,7 @@ }, { "cell_type": "markdown", - "id": "d698096e", + "id": "3bbcf741", "metadata": { "editable": true }, @@ -1915,7 +1917,7 @@ }, { "cell_type": "markdown", - "id": "3e37a4d2", + "id": "4b0ffe06", "metadata": { "editable": true }, @@ -1943,7 +1945,7 @@ }, { "cell_type": "markdown", - "id": "e7e43cf9", + "id": "b11baed6", "metadata": { "editable": true }, @@ -1956,7 +1958,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "7aa6a568", + "id": "39e76d49", "metadata": { "collapsed": false, "editable": true @@ -2056,7 +2058,7 @@ }, { "cell_type": "markdown", - "id": "9a90aec7", + "id": "e7d12ef0", "metadata": { "editable": true }, @@ -2067,7 +2069,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "93b3af24", + "id": "47f6ae18", "metadata": { "collapsed": false, "editable": true @@ -2156,7 +2158,7 @@ }, { "cell_type": "markdown", - "id": "90657c6d", + "id": "9c1d4754", "metadata": { "editable": true }, @@ -2166,7 +2168,7 @@ }, { "cell_type": "markdown", - "id": "a88b86e7", + "id": "b698ac66", "metadata": { "editable": true }, @@ -2179,7 +2181,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "89f45188", + "id": "0a2409b0", "metadata": { "collapsed": false, "editable": true @@ -2257,7 +2259,7 @@ }, { "cell_type": "markdown", - "id": "75496517", + "id": "56f130b5", "metadata": { "editable": true }, diff --git a/doc/pub/week38/html/._week38-bs001.html b/doc/pub/week38/html/._week38-bs001.html index ed985caeb..a04cfdd61 100644 --- a/doc/pub/week38/html/._week38-bs001.html +++ b/doc/pub/week38/html/._week38-bs001.html @@ -259,9 +259,9 @@ MathJax.Hub.Config({
      1. Statistical interpretation of OLS and various expectation values
      2. Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff
        3. -
      3. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at https://youtu.be/J_41Hld6tTU - -
        4. +
      4. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at https://youtu.be/J_41Hld6tTU
        5. +
      5. Video of Lecture
        6. +
      6. Whiteboard notes
      diff --git a/doc/pub/week38/html/week38-reveal.html b/doc/pub/week38/html/week38-reveal.html index 94ba9db0a..0271e775a 100644 --- a/doc/pub/week38/html/week38-reveal.html +++ b/doc/pub/week38/html/week38-reveal.html @@ -200,9 +200,9 @@ MathJax.Hub.Config({

      1. Statistical interpretation of OLS and various expectation values

      2. Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff
        3. -

      3. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at https://youtu.be/J_41Hld6tTU - -
        4. +

      4. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at https://youtu.be/J_41Hld6tTU
        5. +

      5. Video of Lecture
        6. +

      6. Whiteboard notes
    diff --git a/doc/pub/week38/html/week38-solarized.html b/doc/pub/week38/html/week38-solarized.html index bb7857a3f..43f7fbd86 100644 --- a/doc/pub/week38/html/week38-solarized.html +++ b/doc/pub/week38/html/week38-solarized.html @@ -238,9 +238,9 @@ MathJax.Hub.Config({
    1. Statistical interpretation of OLS and various expectation values
    2. Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff
      3. -
    3. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at https://youtu.be/J_41Hld6tTU - -
      4. +
    4. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at https://youtu.be/J_41Hld6tTU
      5. +
    5. Video of Lecture
      6. +
    6. Whiteboard notes
    diff --git a/doc/pub/week38/html/week38.html b/doc/pub/week38/html/week38.html index fb0c0fad3..57e0831cb 100644 --- a/doc/pub/week38/html/week38.html +++ b/doc/pub/week38/html/week38.html @@ -315,9 +315,9 @@ MathJax.Hub.Config({
    1. Statistical interpretation of OLS and various expectation values
    2. Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff
      3. -
    3. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at https://youtu.be/J_41Hld6tTU - -
      4. +
    4. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at https://youtu.be/J_41Hld6tTU
      5. +
    5. Video of Lecture
      6. +
    6. Whiteboard notes
    diff --git a/doc/pub/week38/ipynb/.ipynb_checkpoints/week38-checkpoint.ipynb b/doc/pub/week38/ipynb/.ipynb_checkpoints/week38-checkpoint.ipynb index 43e3b26d9..9f7e9120b 100644 --- a/doc/pub/week38/ipynb/.ipynb_checkpoints/week38-checkpoint.ipynb +++ b/doc/pub/week38/ipynb/.ipynb_checkpoints/week38-checkpoint.ipynb @@ -2,172 +2,1914 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "id": "799137cd", + "metadata": { + "editable": true + }, "source": [ - "\n", - "# Data Analysis and Machine Learning: Logistic Regression\n", - "\n", - " \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", - "\n", -<<<<<<< HEAD - "Date: **Sep 16, 2020**\n", -======= - "Date: **Sep 18, 2020**\n", ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - "\n", - "Copyright 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", - "\n", - "\n", - "\n", - "\n", -<<<<<<< HEAD - "## To do for log reg\n", - "\n", - "* Develop code for log reg step by step, with link to gradient descent part\n", - "\n", - "* show how to read and set up design matrix\n", - "\n", - "* use breast cancer data as example\n", - "\n", - "* develop other classification examples, pulsar example\n", -======= - "## Plans for week 38\n", - "\n", - "* Thursday: Summary of regression methods and discussion of project 1. We revisit also cross-validation and bootstrap as resampling techniques with examples. Recommended reading: [Hastie et al](https://www.springer.com/gp/book/9780387848570) chapters 3 and 7.1-7.6 and 7.10-7.12.\n", - "\n", - "* Friday: Logistic Regression. Recommended reading: [Hastie et al](https://www.springer.com/gp/book/9780387848570) chapters 4.1-4.4 and [Murphy](https://mitpress.mit.edu/books/machine-learning-1) chapter 8.1-8.2\n", - "\n", - "## Thursday September 17\n", - "\n", - "[Video of Lecture](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureSeptember17.mp4?vrtx=view-as-webpage) and [link to handwritten notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesSeptember17.pdf).\n", - "\n", - "## Ridge and LASSO Regression, reminder\n", - "\n", - "The expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is \n", - "our optimization problem is" + "\n", + "" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "f5b17715", + "metadata": { + "editable": true + }, + "source": [ + "# Week 38: Statistical analysis, bias-variance tradeoff and resampling methods\n", + "**Morten Hjorth-Jensen**, Department of Physics and Center for Computing in Science Education, University of Oslo, Norway\n", + "\n", + "Date: **September 15-19, 2025**" + ] + }, + { + "cell_type": "markdown", + "id": "cc859721", + "metadata": { + "editable": true + }, + "source": [ + "## Plans for week 38, lecture Monday September 15\n", + "\n", + "**Material for the lecture on Monday September 15.**\n", + "\n", + "1. Statistical interpretation of OLS and various expectation values\n", + "\n", + "2. Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff\n", + "\n", + "3. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at \n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "a3ecb019", + "metadata": { + "editable": true + }, + "source": [ + "## Readings and Videos\n", + "1. Raschka et al, pages 175-192\n", + "\n", + "2. Hastie et al Chapter 7, here we recommend 7.1-7.5 and 7.10 (cross-validation) and 7.11 (bootstrap). See .\n", + "\n", + "3. [Video on bias-variance tradeoff](https://www.youtube.com/watch?v=EuBBz3bI-aA)\n", + "\n", + "4. [Video on Bootstrapping](https://www.youtube.com/watch?v=Xz0x-8-cgaQ)\n", + "\n", + "5. [Video on cross validation](https://www.youtube.com/watch?v=fSytzGwwBVw)\n", + "\n", + "For the lab session, the following video on cross validation (from 2024), could be helpful, see " + ] + }, + { + "cell_type": "markdown", + "id": "f128464d", + "metadata": { + "editable": true + }, + "source": [ + "## Linking the regression analysis with a statistical interpretation\n", + "\n", + "We will now couple the discussions of ordinary least squares, Ridge\n", + "and Lasso regression with a statistical interpretation, that is we\n", + "move from a linear algebra analysis to a statistical analysis. In\n", + "particular, we will focus on what the regularization terms can result\n", + "in. We will amongst other things show that the regularization\n", + "parameter can reduce considerably the variance of the parameters\n", + "$\\theta$.\n", + "\n", + "On of the advantages of doing linear regression is that we actually end up with\n", + "analytical expressions for several statistical quantities. \n", + "Standard least squares and Ridge regression allow us to\n", + "derive quantities like the variance and other expectation values in a\n", + "rather straightforward way.\n", + "\n", + "It is assumed that $\\varepsilon_i\n", + "\\sim \\mathcal{N}(0, \\sigma^2)$ and the $\\varepsilon_{i}$ are\n", + "independent, i.e.:" + ] + }, + { + "cell_type": "markdown", + "id": "981db0b8", + "metadata": { + "editable": true + }, "source": [ "$$\n", - "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in {\\mathbb{R}}^{p}}}\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right\\}.\n", + "\\begin{align*} \n", + "\\mbox{Cov}(\\varepsilon_{i_1},\n", + "\\varepsilon_{i_2}) & = \\left\\{ \\begin{array}{lcc} \\sigma^2 & \\mbox{if}\n", + "& i_1 = i_2, \\\\ 0 & \\mbox{if} & i_1 \\not= i_2. \\end{array} \\right.\n", + "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "85cc8db5", + "metadata": { + "editable": true + }, "source": [ - "or we can state it as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", - "{\\mathbb{R}}^{p}}}\\frac{1}{n}\\sum_{i=0}^{n-1}\\left(y_i-\\tilde{y}_i\\right)^2=\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where we have used the definition of a norm-2 vector, that is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\vert\\vert \\boldsymbol{x}\\vert\\vert_2 = \\sqrt{\\sum_i x_i^2}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "By minimizing the above equation with respect to the parameters\n", - "$\\boldsymbol{\\beta}$ we could then obtain an analytical expression for the\n", - "parameters $\\boldsymbol{\\beta}$. We can add a regularization parameter $\\lambda$ by\n", - "defining a new cost function to be optimized, that is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", - "{\\mathbb{R}}^{p}}}\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_2^2\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which leads to the Ridge regression minimization problem where we\n", - "require that $\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_2^2\\le t$, where $t$ is\n", - "a finite number larger than zero. By defining" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "C(\\boldsymbol{X},\\boldsymbol{\\beta})=\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_1,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "we have a new optimization equation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", - "{\\mathbb{R}}^{p}}}\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_1\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which leads to Lasso regression. Lasso stands for least absolute shrinkage and selection operator. \n", + "The randomness of $\\varepsilon_i$ implies that\n", + "$\\mathbf{y}_i$ is also a random variable. In particular,\n", + "$\\mathbf{y}_i$ is normally distributed, because $\\varepsilon_i \\sim\n", + "\\mathcal{N}(0, \\sigma^2)$ and $\\mathbf{X}_{i,\\ast} \\, \\boldsymbol{\\theta}$ is a\n", + "non-random scalar. To specify the parameters of the distribution of\n", + "$\\mathbf{y}_i$ we need to calculate its first two moments. \n", "\n", - "Here we have defined the norm-1 as" + "Recall that $\\boldsymbol{X}$ is a matrix of dimensionality $n\\times p$. The\n", + "notation above $\\mathbf{X}_{i,\\ast}$ means that we are looking at the\n", + "row number $i$ and perform a sum over all values $p$." ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "96a431a6", + "metadata": { + "editable": true + }, + "source": [ + "## Assumptions made\n", + "\n", + "The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off)\n", + "that there exists a function $f(\\boldsymbol{x})$ and a normal distributed error $\\boldsymbol{\\varepsilon}\\sim \\mathcal{N}(0, \\sigma^2)$\n", + "which describe our data" + ] + }, + { + "cell_type": "markdown", + "id": "b6bf35de", + "metadata": { + "editable": true + }, "source": [ "$$\n", - "\\vert\\vert \\boldsymbol{x}\\vert\\vert_1 = \\sum_i \\vert x_i\\vert.\n", + "\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n", "$$" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "a4133715", + "metadata": { + "editable": true + }, + "source": [ + "We approximate this function with our model from the solution of the linear regression equations, that is our\n", + "function $f$ is approximated by $\\boldsymbol{\\tilde{y}}$ where we want to minimize $(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2$, our MSE, with" + ] + }, + { + "cell_type": "markdown", + "id": "9d8eea64", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\theta}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "0707109a", + "metadata": { + "editable": true + }, + "source": [ + "## Expectation value and variance\n", + "\n", + "We can calculate the expectation value of $\\boldsymbol{y}$ for a given element $i$" + ] + }, + { + "cell_type": "markdown", + "id": "c84ee75e", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{align*} \n", + "\\mathbb{E}(y_i) & =\n", + "\\mathbb{E}(\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\theta}) + \\mathbb{E}(\\varepsilon_i)\n", + "\\, \\, \\, = \\, \\, \\, \\mathbf{X}_{i, \\ast} \\, \\theta, \n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "eceb2fb1", + "metadata": { + "editable": true + }, + "source": [ + "while\n", + "its variance is" + ] + }, + { + "cell_type": "markdown", + "id": "571c857b", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{align*} \\mbox{Var}(y_i) & = \\mathbb{E} \\{ [y_i\n", + "- \\mathbb{E}(y_i)]^2 \\} \\, \\, \\, = \\, \\, \\, \\mathbb{E} ( y_i^2 ) -\n", + "[\\mathbb{E}(y_i)]^2 \\\\ & = \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\,\n", + "\\theta + \\varepsilon_i )^2] - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\theta})^2 \\\\ &\n", + "= \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\theta})^2 + 2 \\varepsilon_i\n", + "\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\theta} + \\varepsilon_i^2 ] - ( \\mathbf{X}_{i,\n", + "\\ast} \\, \\theta)^2 \\\\ & = ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\theta})^2 + 2\n", + "\\mathbb{E}(\\varepsilon_i) \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\theta} +\n", + "\\mathbb{E}(\\varepsilon_i^2 ) - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\theta})^2 \n", + "\\\\ & = \\mathbb{E}(\\varepsilon_i^2 ) \\, \\, \\, = \\, \\, \\,\n", + "\\mbox{Var}(\\varepsilon_i) \\, \\, \\, = \\, \\, \\, \\sigma^2. \n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "fa94afa6", + "metadata": { + "editable": true + }, + "source": [ + "Hence, $y_i \\sim \\mathcal{N}( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\theta}, \\sigma^2)$, that is $\\boldsymbol{y}$ follows a normal distribution with \n", + "mean value $\\boldsymbol{X}\\boldsymbol{\\theta}$ and variance $\\sigma^2$ (not be confused with the singular values of the SVD)." + ] + }, + { + "cell_type": "markdown", + "id": "ae5807fe", + "metadata": { + "editable": true + }, + "source": [ + "## Expectation value and variance for $\\boldsymbol{\\theta}$\n", + "\n", + "With the OLS expressions for the optimal parameters $\\boldsymbol{\\hat{\\theta}}$ we can evaluate the expectation value" + ] + }, + { + "cell_type": "markdown", + "id": "9b7dbfc6", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}(\\boldsymbol{\\hat{\\theta}}) = \\mathbb{E}[ (\\mathbf{X}^{\\top} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbb{E}[ \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\mathbf{X}^{T}\\mathbf{X}\\boldsymbol{\\theta}=\\boldsymbol{\\theta}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a469ecb5", + "metadata": { + "editable": true + }, + "source": [ + "This means that the estimator of the regression parameters is unbiased.\n", + "\n", + "We can also calculate the variance\n", + "\n", + "The variance of the optimal value $\\boldsymbol{\\hat{\\theta}}$ is" + ] + }, + { + "cell_type": "markdown", + "id": "a22a5899", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray*}\n", + "\\mbox{Var}(\\boldsymbol{\\hat{\\theta}}) & = & \\mathbb{E} \\{ [\\boldsymbol{\\theta} - \\mathbb{E}(\\boldsymbol{\\theta})] [\\boldsymbol{\\theta} - \\mathbb{E}(\\boldsymbol{\\theta})]^{T} \\}\n", + "\\\\\n", + "& = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\theta}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\theta}]^{T} \\}\n", + "\\\\\n", + "% & = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}]^{T} \\} - \\boldsymbol{\\theta} \\, \\boldsymbol{\\theta}^{T}\n", + "% \\\\\n", + "% & = & \\mathbb{E} \\{ (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} \\, \\mathbf{Y}^{T} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\} - \\boldsymbol{\\theta} \\, \\boldsymbol{\\theta}^{T}\n", + "% \\\\\n", + "& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\mathbb{E} \\{ \\mathbf{Y} \\, \\mathbf{Y}^{T} \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\theta} \\, \\boldsymbol{\\theta}^{T}\n", + "\\\\\n", + "& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\{ \\mathbf{X} \\, \\boldsymbol{\\theta} \\, \\boldsymbol{\\theta}^{T} \\, \\mathbf{X}^{T} + \\sigma^2 \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\theta} \\, \\boldsymbol{\\theta}^{T}\n", + "% \\\\\n", + "% & = & (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T \\, \\mathbf{X} \\, \\boldsymbol{\\theta} \\, \\boldsymbol{\\theta}^T \\, \\mathbf{X}^T \\, \\mathbf{X} \\, (\\mathbf{X}^T % \\mathbf{X})^{-1}\n", + "% \\\\\n", + "% & & + \\, \\, \\sigma^2 \\, (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T \\, \\mathbf{X} \\, (\\mathbf{X}^T \\mathbf{X})^{-1} - \\boldsymbol{\\theta} \\boldsymbol{\\theta}^T\n", + "\\\\\n", + "& = & \\boldsymbol{\\theta} \\, \\boldsymbol{\\theta}^{T} + \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\theta} \\, \\boldsymbol{\\theta}^{T}\n", + "\\, \\, \\, = \\, \\, \\, \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1},\n", + "\\end{eqnarray*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "f7b64841", + "metadata": { + "editable": true + }, + "source": [ + "where we have used that $\\mathbb{E} (\\mathbf{Y} \\mathbf{Y}^{T}) =\n", + "\\mathbf{X} \\, \\boldsymbol{\\theta} \\, \\boldsymbol{\\theta}^{T} \\, \\mathbf{X}^{T} +\n", + "\\sigma^2 \\, \\mathbf{I}_{nn}$. From $\\mbox{Var}(\\boldsymbol{\\theta}) = \\sigma^2\n", + "\\, (\\mathbf{X}^{T} \\mathbf{X})^{-1}$, one obtains an estimate of the\n", + "variance of the estimate of the $j$-th regression coefficient:\n", + "$\\boldsymbol{\\sigma}^2 (\\boldsymbol{\\theta}_j ) = \\boldsymbol{\\sigma}^2 [(\\mathbf{X}^{T} \\mathbf{X})^{-1}]_{jj} $. This may be used to\n", + "construct a confidence interval for the estimates.\n", + "\n", + "In a similar way, we can obtain analytical expressions for say the\n", + "expectation values of the parameters $\\boldsymbol{\\theta}$ and their variance\n", + "when we employ Ridge regression, allowing us again to define a confidence interval. \n", + "\n", + "It is rather straightforward to show that" + ] + }, + { + "cell_type": "markdown", + "id": "26d50d5c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E} \\big[ \\boldsymbol{\\theta}^{\\mathrm{Ridge}} \\big]=(\\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I}_{pp})^{-1} (\\mathbf{X}^{\\top} \\mathbf{X})\\boldsymbol{\\theta}^{\\mathrm{OLS}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "e2e18a10", + "metadata": { + "editable": true + }, + "source": [ + "We see clearly that \n", + "$\\mathbb{E} \\big[ \\boldsymbol{\\theta}^{\\mathrm{Ridge}} \\big] \\not= \\boldsymbol{\\theta}^{\\mathrm{OLS}}$ for any $\\lambda > 0$. We say then that the ridge estimator is biased.\n", + "\n", + "We can also compute the variance as" + ] + }, + { + "cell_type": "markdown", + "id": "9a97e0bb", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mbox{Var}[\\boldsymbol{\\theta}^{\\mathrm{Ridge}}]=\\sigma^2[ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1} \\mathbf{X}^{T} \\mathbf{X} \\{ [ \\mathbf{X}^{\\top} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "53cef62d", + "metadata": { + "editable": true + }, + "source": [ + "and it is easy to see that if the parameter $\\lambda$ goes to infinity then the variance of Ridge parameters $\\boldsymbol{\\theta}$ goes to zero. \n", + "\n", + "With this, we can compute the difference" + ] + }, + { + "cell_type": "markdown", + "id": "c8ec4ab0", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mbox{Var}[\\boldsymbol{\\theta}^{\\mathrm{OLS}}]-\\mbox{Var}(\\boldsymbol{\\theta}^{\\mathrm{Ridge}})=\\sigma^2 [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}[ 2\\lambda\\mathbf{I} + \\lambda^2 (\\mathbf{X}^{T} \\mathbf{X})^{-1} ] \\{ [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "1e5e5e07", + "metadata": { + "editable": true + }, + "source": [ + "The difference is non-negative definite since each component of the\n", + "matrix product is non-negative definite. \n", + "This means the variance we obtain with the standard OLS will always for $\\lambda > 0$ be larger than the variance of $\\boldsymbol{\\theta}$ obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below." + ] + }, + { + "cell_type": "markdown", + "id": "b1ea4ea7", + "metadata": { + "editable": true + }, + "source": [ + "## Deriving OLS from a probability distribution\n", + "\n", + "Our basic assumption when we derived the OLS equations was to assume\n", + "that our output is determined by a given continuous function\n", + "$f(\\boldsymbol{x})$ and a random noise $\\boldsymbol{\\epsilon}$ given by the normal\n", + "distribution with zero mean value and an undetermined variance\n", + "$\\sigma^2$.\n", + "\n", + "We found above that the outputs $\\boldsymbol{y}$ have a mean value given by\n", + "$\\boldsymbol{X}\\hat{\\boldsymbol{\\theta}}$ and variance $\\sigma^2$. Since the entries to\n", + "the design matrix are not stochastic variables, we can assume that the\n", + "probability distribution of our targets is also a normal distribution\n", + "but now with mean value $\\boldsymbol{X}\\hat{\\boldsymbol{\\theta}}$. This means that a\n", + "single output $y_i$ is given by the Gaussian distribution" + ] + }, + { + "cell_type": "markdown", + "id": "d9c8dd38", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "y_i\\sim \\mathcal{N}(\\boldsymbol{X}_{i,*}\\boldsymbol{\\theta}, \\sigma^2)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\theta})^2}{2\\sigma^2}\\right]}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "7abb690f", + "metadata": { + "editable": true + }, + "source": [ + "## Independent and Identically Distributed (iid)\n", + "\n", + "We assume now that the various $y_i$ values are stochastically distributed according to the above Gaussian distribution. \n", + "We define this distribution as" + ] + }, + { + "cell_type": "markdown", + "id": "417c8406", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(y_i, \\boldsymbol{X}\\vert\\boldsymbol{\\theta})=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\theta})^2}{2\\sigma^2}\\right]},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "fb01419c", + "metadata": { + "editable": true + }, + "source": [ + "which reads as finding the likelihood of an event $y_i$ with the input variables $\\boldsymbol{X}$ given the parameters (to be determined) $\\boldsymbol{\\theta}$.\n", + "\n", + "Since these events are assumed to be independent and identicall distributed we can build the probability distribution function (PDF) for all possible event $\\boldsymbol{y}$ as the product of the single events, that is we have" + ] + }, + { + "cell_type": "markdown", + "id": "dbe14673", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{y},\\boldsymbol{X}\\vert\\boldsymbol{\\theta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\theta})^2}{2\\sigma^2}\\right]}=\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta}).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a19153fe", + "metadata": { + "editable": true + }, + "source": [ + "We will write this in a more compact form reserving $\\boldsymbol{D}$ for the domain of events, including the ouputs (targets) and the inputs. That is\n", + "in case we have a simple one-dimensional input and output case" + ] + }, + { + "cell_type": "markdown", + "id": "017ca4ca", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\\dots, (x_{n-1},y_{n-1})].\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "85c7bc4a", + "metadata": { + "editable": true + }, + "source": [ + "In the more general case the various inputs should be replaced by the possible features represented by the input data set $\\boldsymbol{X}$. \n", + "We can now rewrite the above probability as" + ] + }, + { + "cell_type": "markdown", + "id": "ad6066d5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{D}\\vert\\boldsymbol{\\theta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\theta})^2}{2\\sigma^2}\\right]}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "7d9872d8", + "metadata": { + "editable": true + }, + "source": [ + "It is a conditional probability (see below) and reads as the likelihood of a domain of events $\\boldsymbol{D}$ given a set of parameters $\\boldsymbol{\\theta}$." + ] + }, + { + "cell_type": "markdown", + "id": "e3973752", + "metadata": { + "editable": true + }, + "source": [ + "## Maximum Likelihood Estimation (MLE)\n", + "\n", + "In statistics, maximum likelihood estimation (MLE) is a method of\n", + "estimating the parameters of an assumed probability distribution,\n", + "given some observed data. This is achieved by maximizing a likelihood\n", + "function so that, under the assumed statistical model, the observed\n", + "data is the most probable. \n", + "\n", + "We will assume here that our events are given by the above Gaussian\n", + "distribution and we will determine the optimal parameters $\\theta$ by\n", + "maximizing the above PDF. However, computing the derivatives of a\n", + "product function is cumbersome and can easily lead to overflow and/or\n", + "underflowproblems, with potentials for loss of numerical precision.\n", + "\n", + "In practice, it is more convenient to maximize the logarithm of the\n", + "PDF because it is a monotonically increasing function of the argument.\n", + "Alternatively, and this will be our option, we will minimize the\n", + "negative of the logarithm since this is a monotonically decreasing\n", + "function.\n", + "\n", + "Note also that maximization/minimization of the logarithm of the PDF\n", + "is equivalent to the maximization/minimization of the function itself." + ] + }, + { + "cell_type": "markdown", + "id": "5adedf8a", + "metadata": { + "editable": true + }, + "source": [ + "## A new Cost Function\n", + "\n", + "We could now define a new cost function to minimize, namely the negative logarithm of the above PDF" + ] + }, + { + "cell_type": "markdown", + "id": "23e01c9e", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{\\theta})=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "94cc3cc3", + "metadata": { + "editable": true + }, + "source": [ + "which becomes" + ] + }, + { + "cell_type": "markdown", + "id": "0e3f94c9", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{\\theta})=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta})\\vert\\vert_2^2}{2\\sigma^2}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "b8dcd25e", + "metadata": { + "editable": true + }, + "source": [ + "Taking the derivative of the *new* cost function with respect to the parameters $\\theta$ we recognize our familiar OLS equation, namely" + ] + }, + { + "cell_type": "markdown", + "id": "9140542c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta}\\right) =0,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "294a8ce0", + "metadata": { + "editable": true + }, + "source": [ + "which leads to the well-known OLS equation for the optimal paramters $\\theta$" + ] + }, + { + "cell_type": "markdown", + "id": "a8c1b097", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\hat{\\boldsymbol{\\theta}}^{\\mathrm{OLS}}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}!\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4180c17f", + "metadata": { + "editable": true + }, + "source": [ + "Next week we will make a similar analysis for Ridge and Lasso regression" + ] + }, + { + "cell_type": "markdown", + "id": "6a48bb05", + "metadata": { + "editable": true + }, + "source": [ + "## Why resampling methods\n", + "\n", + "Before we proceed, we need to rethink what we have been doing. In our\n", + "eager to fit the data, we have omitted several important elements in\n", + "our regression analysis. In what follows we will\n", + "1. look at statistical properties, including a discussion of mean values, variance and the so-called bias-variance tradeoff\n", + "\n", + "2. introduce resampling techniques like cross-validation, bootstrapping and jackknife and more\n", + "\n", + "and discuss how to select a given model (one of the difficult parts in machine learning)." + ] + }, + { + "cell_type": "markdown", + "id": "d053a5c8", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods\n", + "Resampling methods are an indispensable tool in modern\n", + "statistics. They involve repeatedly drawing samples from a training\n", + "set and refitting a model of interest on each sample in order to\n", + "obtain additional information about the fitted model. For example, in\n", + "order to estimate the variability of a linear regression fit, we can\n", + "repeatedly draw different samples from the training data, fit a linear\n", + "regression to each new sample, and then examine the extent to which\n", + "the resulting fits differ. Such an approach may allow us to obtain\n", + "information that would not be available from fitting the model only\n", + "once using the original training sample.\n", + "\n", + "Two resampling methods are often used in Machine Learning analyses,\n", + "1. The **bootstrap method**\n", + "\n", + "2. and **Cross-Validation**\n", + "\n", + "In addition there are several other methods such as the Jackknife and the Blocking methods. We will discuss in particular\n", + "cross-validation and the bootstrap method." + ] + }, + { + "cell_type": "markdown", + "id": "8cb550a1", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling approaches can be computationally expensive\n", + "\n", + "Resampling approaches can be computationally expensive, because they\n", + "involve fitting the same statistical method multiple times using\n", + "different subsets of the training data. However, due to recent\n", + "advances in computing power, the computational requirements of\n", + "resampling methods generally are not prohibitive. In this chapter, we\n", + "discuss two of the most commonly used resampling methods,\n", + "cross-validation and the bootstrap. Both methods are important tools\n", + "in the practical application of many statistical learning\n", + "procedures. For example, cross-validation can be used to estimate the\n", + "test error associated with a given statistical learning method in\n", + "order to evaluate its performance, or to select the appropriate level\n", + "of flexibility. The process of evaluating a model’s performance is\n", + "known as model assessment, whereas the process of selecting the proper\n", + "level of flexibility for a model is known as model selection. The\n", + "bootstrap is widely used." + ] + }, + { + "cell_type": "markdown", + "id": "96be5396", + "metadata": { + "editable": true + }, + "source": [ + "## Why resampling methods ?\n", + "**Statistical analysis.**\n", + "\n", + "* Our simulations can be treated as *computer experiments*. This is particularly the case for Monte Carlo methods which are widely used in statistical analyses.\n", + "\n", + "* The results can be analysed with the same statistical tools as we would use when analysing experimental data.\n", + "\n", + "* As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors." + ] + }, + { + "cell_type": "markdown", + "id": "f8a288b4", + "metadata": { + "editable": true + }, + "source": [ + "## Statistical analysis\n", + "\n", + "* As in other experiments, many numerical experiments have two classes of errors:\n", + "\n", + " * Statistical errors\n", + "\n", + " * Systematical errors\n", + "\n", + "* Statistical errors can be estimated using standard tools from statistics\n", + "\n", + "* Systematical errors are method specific and must be treated differently from case to case." + ] + }, + { + "cell_type": "markdown", + "id": "ee8bd2f9", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods\n", + "\n", + "With all these analytical equations for both the OLS and Ridge\n", + "regression, we will now outline how to assess a given model. This will\n", + "lead to a discussion of the so-called bias-variance tradeoff (see\n", + "below) and so-called resampling methods.\n", + "\n", + "One of the quantities we have discussed as a way to measure errors is\n", + "the mean-squared error (MSE), mainly used for fitting of continuous\n", + "functions. Another choice is the absolute error.\n", + "\n", + "In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data,\n", + "we discuss the\n", + "1. prediction error or simply the **test error** $\\mathrm{Err_{Test}}$, where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the \n", + "\n", + "2. training error $\\mathrm{Err_{Train}}$, which is the average loss over the training data.\n", + "\n", + "As our model becomes more and more complex, more of the training data tends to used. The training may thence adapt to more complicated structures in the data. This may lead to a decrease in the bias (see below for code example) and a slight increase of the variance for the test error.\n", + "For a certain level of complexity the test error will reach minimum, before starting to increase again. The\n", + "training error reaches a saturation." + ] + }, + { + "cell_type": "markdown", + "id": "1037fcf3", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: Bootstrap\n", + "Bootstrapping is a [non-parametric approach](https://en.wikipedia.org/wiki/Nonparametric_statistics) to statistical inference\n", + "that substitutes computation for more traditional distributional\n", + "assumptions and asymptotic results. Bootstrapping offers a number of\n", + "advantages: \n", + "1. The bootstrap is quite general, although there are some cases in which it fails. \n", + "\n", + "2. Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small. \n", + "\n", + "3. It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically. \n", + "\n", + "4. It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples).\n", + "\n", + "The textbook by [Davison on the Bootstrap Methods and their Applications](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A) provides many more insights and proofs. In this course we will take a more practical approach and use the results and theorems provided in the literature. For those interested in reading more about the bootstrap methods, we recommend the above text and the one by [Efron and Tibshirani](https://www.routledge.com/An-Introduction-to-the-Bootstrap/Efron-Tibshirani/p/book/9780412042317).\n", + "\n", + "Before we proceed however, we need to remind ourselves about a central theorem in statistics, namely the so-called **central limit theorem**." + ] + }, + { + "cell_type": "markdown", + "id": "2653d9e3", + "metadata": { + "editable": true + }, + "source": [ + "## The Central Limit Theorem\n", + "\n", + "Suppose we have a PDF $p(x)$ from which we generate a series $N$\n", + "of averages $\\mathbb{E}[x_i]$. Each mean value $\\mathbb{E}[x_i]$\n", + "is viewed as the average of a specific measurement, e.g., throwing \n", + "dice 100 times and then taking the average value, or producing a certain\n", + "amount of random numbers. \n", + "For notational ease, we set $\\mathbb{E}[x_i]=x_i$ in the discussion\n", + "which follows. We do the same for $\\mathbb{E}[z]=z$.\n", + "\n", + "If we compute the mean $z$ of $m$ such mean values $x_i$" + ] + }, + { + "cell_type": "markdown", + "id": "33e4596e", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "z=\\frac{x_1+x_2+\\dots+x_m}{m},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "137d3cd6", + "metadata": { + "editable": true + }, + "source": [ + "the question we pose is which is the PDF of the new variable $z$." + ] + }, + { + "cell_type": "markdown", + "id": "4c9853b7", + "metadata": { + "editable": true + }, + "source": [ + "## Finding the Limit\n", + "\n", + "The probability of obtaining an average value $z$ is the product of the \n", + "probabilities of obtaining arbitrary individual mean values $x_i$,\n", + "but with the constraint that the average is $z$. We can express this through\n", + "the following expression" + ] + }, + { + "cell_type": "markdown", + "id": "493028c4", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\tilde{p}(z)=\\int dx_1p(x_1)\\int dx_2p(x_2)\\dots\\int dx_mp(x_m)\n", + " \\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m}),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "c819e616", + "metadata": { + "editable": true + }, + "source": [ + "where the $\\delta$-function enbodies the constraint that the mean is $z$.\n", + "All measurements that lead to each individual $x_i$ are expected to\n", + "be independent, which in turn means that we can express $\\tilde{p}$ as the \n", + "product of individual $p(x_i)$. The independence assumption is important in the derivation of the central limit theorem." + ] + }, + { + "cell_type": "markdown", + "id": "f0385e1a", + "metadata": { + "editable": true + }, + "source": [ + "## Rewriting the $\\delta$-function\n", + "\n", + "If we use the integral expression for the $\\delta$-function" + ] + }, + { + "cell_type": "markdown", + "id": "4310a9b4", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m})=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n", + " dq\\exp{\\left(iq(z-\\frac{x_1+x_2+\\dots+x_m}{m})\\right)},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "1e3932be", + "metadata": { + "editable": true + }, + "source": [ + "and inserting $e^{i\\mu q-i\\mu q}$ where $\\mu$ is the mean value\n", + "we arrive at" + ] + }, + { + "cell_type": "markdown", + "id": "91e64919", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\tilde{p}(z)=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n", + " dq\\exp{\\left(iq(z-\\mu)\\right)}\\left[\\int_{-\\infty}^{\\infty}\n", + " dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "c83a8ca5", + "metadata": { + "editable": true + }, + "source": [ + "with the integral over $x$ resulting in" + ] + }, + { + "cell_type": "markdown", + "id": "16c94c48", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}=\n", + " \\int_{-\\infty}^{\\infty}dxp(x)\n", + " \\left[1+\\frac{iq(\\mu-x)}{m}-\\frac{q^2(\\mu-x)^2}{2m^2}+\\dots\\right].\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "63bc9d16", + "metadata": { + "editable": true + }, + "source": [ + "## Identifying Terms\n", + "\n", + "The second term on the rhs disappears since this is just the mean and \n", + "employing the definition of $\\sigma^2$ we have" + ] + }, + { + "cell_type": "markdown", + "id": "710fedd5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\int_{-\\infty}^{\\infty}dxp(x)e^{\\left(iq(\\mu-x)/m\\right)}=\n", + " 1-\\frac{q^2\\sigma^2}{2m^2}+\\dots,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "8c47e8f8", + "metadata": { + "editable": true + }, + "source": [ + "resulting in" + ] + }, + { + "cell_type": "markdown", + "id": "c0e43db3", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\left[\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m\\approx\n", + " \\left[1-\\frac{q^2\\sigma^2}{2m^2}+\\dots \\right]^m,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "e9a40705", + "metadata": { + "editable": true + }, + "source": [ + "and in the limit $m\\rightarrow \\infty$ we obtain" + ] + }, + { + "cell_type": "markdown", + "id": "de6040d9", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\tilde{p}(z)=\\frac{1}{\\sqrt{2\\pi}(\\sigma/\\sqrt{m})}\n", + " \\exp{\\left(-\\frac{(z-\\mu)^2}{2(\\sigma/\\sqrt{m})^2}\\right)},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "f2907638", + "metadata": { + "editable": true + }, + "source": [ + "which is the normal distribution with variance\n", + "$\\sigma^2_m=\\sigma^2/m$, where $\\sigma$ is the variance of the PDF $p(x)$\n", + "and $\\mu$ is also the mean of the PDF $p(x)$." + ] + }, + { + "cell_type": "markdown", + "id": "9e53d173", + "metadata": { + "editable": true + }, + "source": [ + "## Wrapping it up\n", + "\n", + "Thus, the central limit theorem states that the PDF $\\tilde{p}(z)$ of\n", + "the average of $m$ random values corresponding to a PDF $p(x)$ \n", + "is a normal distribution whose mean is the \n", + "mean value of the PDF $p(x)$ and whose variance is the variance\n", + "of the PDF $p(x)$ divided by $m$, the number of values used to compute $z$.\n", + "\n", + "The central limit theorem leads to the well-known expression for the\n", + "standard deviation, given by" + ] + }, + { + "cell_type": "markdown", + "id": "959c77be", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\sigma_m=\n", + "\\frac{\\sigma}{\\sqrt{m}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6470ab77", + "metadata": { + "editable": true + }, + "source": [ + "The latter is true only if the average value is known exactly. This is obtained in the limit\n", + "$m\\rightarrow \\infty$ only. Because the mean and the variance are measured quantities we obtain \n", + "the familiar expression in statistics (the so-called Bessel correction)" + ] + }, + { + "cell_type": "markdown", + "id": "720c157a", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\sigma_m\\approx \n", + "\\frac{\\sigma}{\\sqrt{m-1}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "62c153d3", + "metadata": { + "editable": true + }, + "source": [ + "In many cases however the above estimate for the standard deviation,\n", + "in particular if correlations are strong, may be too simplistic. Keep\n", + "in mind that we have assumed that the variables $x$ are independent\n", + "and identically distributed. This is obviously not always the\n", + "case. For example, the random numbers (or better pseudorandom numbers)\n", + "we generate in various calculations do always exhibit some\n", + "correlations.\n", + "\n", + "The theorem is satisfied by a large class of PDFs. Note however that for a\n", + "finite $m$, it is not always possible to find a closed form /analytic expression for\n", + "$\\tilde{p}(x)$." + ] + }, + { + "cell_type": "markdown", + "id": "cfd10bd9", + "metadata": { + "editable": true + }, + "source": [ + "## Confidence Intervals\n", + "\n", + "Confidence intervals are used in statistics and represent a type of estimate\n", + "computed from the observed data. This gives a range of values for an\n", + "unknown parameter such as the parameters $\\boldsymbol{\\theta}$ from linear regression.\n", + "\n", + "With the OLS expressions for the parameters $\\boldsymbol{\\theta}$ we found \n", + "$\\mathbb{E}(\\boldsymbol{\\theta}) = \\boldsymbol{\\theta}$, which means that the estimator of the regression parameters is unbiased.\n", + "\n", + "In the exercises this week we show that the variance of the estimate of the $j$-th regression coefficient is\n", + "$\\boldsymbol{\\sigma}^2 (\\boldsymbol{\\theta}_j ) = \\boldsymbol{\\sigma}^2 [(\\mathbf{X}^{T} \\mathbf{X})^{-1}]_{jj} $.\n", + "\n", + "This quantity can be used to\n", + "construct a confidence interval for the estimates." + ] + }, + { + "cell_type": "markdown", + "id": "40dc022d", + "metadata": { + "editable": true + }, + "source": [ + "## Standard Approach based on the Normal Distribution\n", + "\n", + "We will assume that the parameters $\\theta$ follow a normal\n", + "distribution. We can then define the confidence interval. Here we will be using as\n", + "shorthands $\\mu_{\\theta}$ for the above mean value and $\\sigma_{\\theta}$\n", + "for the standard deviation. We have then a confidence interval" + ] + }, + { + "cell_type": "markdown", + "id": "242bfa08", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\left(\\mu_{\\theta}\\pm \\frac{z\\sigma_{\\theta}}{\\sqrt{n}}\\right),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "7dd4616b", + "metadata": { + "editable": true + }, + "source": [ + "where $z$ defines the level of certainty (or confidence). For a normal\n", + "distribution typical parameters are $z=2.576$ which corresponds to a\n", + "confidence of $99\\%$ while $z=1.96$ corresponds to a confidence of\n", + "$95\\%$. A confidence level of $95\\%$ is commonly used and it is\n", + "normally referred to as a *two-sigmas* confidence level, that is we\n", + "approximate $z\\approx 2$.\n", + "\n", + "For more discussions of confidence intervals (and in particular linked with a discussion of the bootstrap method), see chapter 5 of the textbook by [Davison on the Bootstrap Methods and their Applications](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A)\n", + "\n", + "In this text you will also find an in-depth discussion of the\n", + "Bootstrap method, why it works and various theorems related to it." + ] + }, + { + "cell_type": "markdown", + "id": "00b509e4", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: Bootstrap background\n", + "\n", + "Since $\\widehat{\\theta} = \\widehat{\\theta}(\\boldsymbol{X})$ is a function of random variables,\n", + "$\\widehat{\\theta}$ itself must be a random variable. Thus it has\n", + "a pdf, call this function $p(\\boldsymbol{t})$. The aim of the bootstrap is to\n", + "estimate $p(\\boldsymbol{t})$ by the relative frequency of\n", + "$\\widehat{\\theta}$. You can think of this as using a histogram\n", + "in the place of $p(\\boldsymbol{t})$. If the relative frequency closely\n", + "resembles $p(\\vec{t})$, then using numerics, it is straight forward to\n", + "estimate all the interesting parameters of $p(\\boldsymbol{t})$ using point\n", + "estimators." + ] + }, + { + "cell_type": "markdown", + "id": "941834ae", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: More Bootstrap background\n", + "\n", + "In the case that $\\widehat{\\theta}$ has\n", + "more than one component, and the components are independent, we use the\n", + "same estimator on each component separately. If the probability\n", + "density function of $X_i$, $p(x)$, had been known, then it would have\n", + "been straightforward to do this by: \n", + "1. Drawing lots of numbers from $p(x)$, suppose we call one such set of numbers $(X_1^*, X_2^*, \\cdots, X_n^*)$. \n", + "\n", + "2. Then using these numbers, we could compute a replica of $\\widehat{\\theta}$ called $\\widehat{\\theta}^*$. \n", + "\n", + "By repeated use of the above two points, many\n", + "estimates of $\\widehat{\\theta}$ can be obtained. The\n", + "idea is to use the relative frequency of $\\widehat{\\theta}^*$\n", + "(think of a histogram) as an estimate of $p(\\boldsymbol{t})$." + ] + }, + { + "cell_type": "markdown", + "id": "69ba3346", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: Bootstrap approach\n", + "\n", + "But\n", + "unless there is enough information available about the process that\n", + "generated $X_1,X_2,\\cdots,X_n$, $p(x)$ is in general\n", + "unknown. Therefore, [Efron in 1979](https://projecteuclid.org/euclid.aos/1176344552) asked the\n", + "question: What if we replace $p(x)$ by the relative frequency\n", + "of the observation $X_i$?\n", + "\n", + "If we draw observations in accordance with\n", + "the relative frequency of the observations, will we obtain the same\n", + "result in some asymptotic sense? The answer is yes." + ] + }, + { + "cell_type": "markdown", + "id": "99f1499e", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: Bootstrap steps\n", + "\n", + "The independent bootstrap works like this: \n", + "\n", + "1. Draw with replacement $n$ numbers for the observed variables $\\boldsymbol{x} = (x_1,x_2,\\cdots,x_n)$. \n", + "\n", + "2. Define a vector $\\boldsymbol{x}^*$ containing the values which were drawn from $\\boldsymbol{x}$. \n", + "\n", + "3. Using the vector $\\boldsymbol{x}^*$ compute $\\widehat{\\theta}^*$ by evaluating $\\widehat \\theta$ under the observations $\\boldsymbol{x}^*$. \n", + "\n", + "4. Repeat this process $k$ times. \n", + "\n", + "When you are done, you can draw a histogram of the relative frequency\n", + "of $\\widehat \\theta^*$. This is your estimate of the probability\n", + "distribution $p(t)$. Using this probability distribution you can\n", + "estimate any statistics thereof. In principle you never draw the\n", + "histogram of the relative frequency of $\\widehat{\\theta}^*$. Instead\n", + "you use the estimators corresponding to the statistic of interest. For\n", + "example, if you are interested in estimating the variance of $\\widehat\n", + "\\theta$, apply the etsimator $\\widehat \\sigma^2$ to the values\n", + "$\\widehat \\theta^*$." + ] + }, + { + "cell_type": "markdown", + "id": "c817851a", + "metadata": { + "editable": true + }, + "source": [ + "## Code example for the Bootstrap method\n", + "\n", + "The following code starts with a Gaussian distribution with mean value\n", + "$\\mu =100$ and variance $\\sigma=15$. We use this to generate the data\n", + "used in the bootstrap analysis. The bootstrap analysis returns a data\n", + "set after a given number of bootstrap operations (as many as we have\n", + "data points). This data set consists of estimated mean values for each\n", + "bootstrap operation. The histogram generated by the bootstrap method\n", + "shows that the distribution for these mean values is also a Gaussian,\n", + "centered around the mean value $\\mu=100$ but with standard deviation\n", + "$\\sigma/\\sqrt{n}$, where $n$ is the number of bootstrap samples (in\n", + "this case the same as the number of original data points). The value\n", + "of the standard deviation is what we expect from the central limit\n", + "theorem." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "4b9647f3", + "metadata": { + "collapsed": false, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import numpy as np\n", + "from time import time\n", + "from scipy.stats import norm\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Returns mean of bootstrap samples \n", + "# Bootstrap algorithm\n", + "def bootstrap(data, datapoints):\n", + " t = np.zeros(datapoints)\n", + " n = len(data)\n", + " # non-parametric bootstrap \n", + " for i in range(datapoints):\n", + " t[i] = np.mean(data[np.random.randint(0,n,n)])\n", + " # analysis \n", + " print(\"Bootstrap Statistics :\")\n", + " print(\"original bias std. error\")\n", + " print(\"%8g %8g %14g %15g\" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))\n", + " return t\n", + "\n", + "# We set the mean value to 100 and the standard deviation to 15\n", + "mu, sigma = 100, 15\n", + "datapoints = 10000\n", + "# We generate random numbers according to the normal distribution\n", + "x = mu + sigma*np.random.randn(datapoints)\n", + "# bootstrap returns the data sample \n", + "t = bootstrap(x, datapoints)" + ] + }, + { + "cell_type": "markdown", + "id": "26cf7fd4", + "metadata": { + "editable": true + }, + "source": [ + "We see that our new variance and from that the standard deviation, agrees with the central limit theorem." + ] + }, + { + "cell_type": "markdown", + "id": "b2205188", + "metadata": { + "editable": true + }, + "source": [ + "## Plotting the Histogram" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "be6f7ced", + "metadata": { + "collapsed": false, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# the histogram of the bootstrapped data (normalized data if density = True)\n", + "n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)\n", + "# add a 'best fit' line \n", + "y = norm.pdf(binsboot, np.mean(t), np.std(t))\n", + "lt = plt.plot(binsboot, y, 'b', linewidth=1)\n", + "plt.xlabel('x')\n", + "plt.ylabel('Probability')\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "69bcb406", + "metadata": { + "editable": true + }, + "source": [ + "## The bias-variance tradeoff\n", + "\n", + "We will discuss the bias-variance tradeoff in the context of\n", + "continuous predictions such as regression. However, many of the\n", + "intuitions and ideas discussed here also carry over to classification\n", + "tasks. Consider a dataset $\\mathcal{D}$ consisting of the data\n", + "$\\mathbf{X}_\\mathcal{D}=\\{(y_j, \\boldsymbol{x}_j), j=0\\ldots n-1\\}$. \n", + "\n", + "Let us assume that the true data is generated from a noisy model" + ] + }, + { + "cell_type": "markdown", + "id": "ce87dc4f", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "b8d1371c", + "metadata": { + "editable": true + }, + "source": [ + "where $\\epsilon$ is normally distributed with mean zero and standard deviation $\\sigma^2$.\n", + "\n", + "In our derivation of the ordinary least squares method we defined then\n", + "an approximation to the function $f$ in terms of the parameters\n", + "$\\boldsymbol{\\theta}$ and the design matrix $\\boldsymbol{X}$ which embody our model,\n", + "that is $\\boldsymbol{\\tilde{y}}=\\boldsymbol{X}\\boldsymbol{\\theta}$. \n", + "\n", + "Thereafter we found the parameters $\\boldsymbol{\\theta}$ by optimizing the means squared error via the so-called cost function" + ] + }, + { + "cell_type": "markdown", + "id": "c95f3051", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{X},\\boldsymbol{\\theta}) =\\frac{1}{n}\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2=\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right].\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "107fab0a", + "metadata": { + "editable": true + }, + "source": [ + "We can rewrite this as" + ] + }, + { + "cell_type": "markdown", + "id": "d56b4bd7", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\frac{1}{n}\\sum_i(f_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\sigma^2.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4712d813", + "metadata": { + "editable": true + }, + "source": [ + "The three terms represent the square of the bias of the learning\n", + "method, which can be thought of as the error caused by the simplifying\n", + "assumptions built into the method. The second term represents the\n", + "variance of the chosen model and finally the last terms is variance of\n", + "the error $\\boldsymbol{\\epsilon}$.\n", + "\n", + "To derive this equation, we need to recall that the variance of $\\boldsymbol{y}$ and $\\boldsymbol{\\epsilon}$ are both equal to $\\sigma^2$. The mean value of $\\boldsymbol{\\epsilon}$ is by definition equal to zero. Furthermore, the function $f$ is not a stochastics variable, idem for $\\boldsymbol{\\tilde{y}}$.\n", + "We use a more compact notation in terms of the expectation value" + ] + }, + { + "cell_type": "markdown", + "id": "43a58a59", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}})^2\\right],\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6333f694", + "metadata": { + "editable": true + }, + "source": [ + "and adding and subtracting $\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]$ we get" + ] + }, + { + "cell_type": "markdown", + "id": "24e27c2b", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}}+\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right],\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "0462c197", + "metadata": { + "editable": true + }, + "source": [ + "which, using the abovementioned expectation values can be rewritten as" + ] + }, + { + "cell_type": "markdown", + "id": "965cd453", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right]+\\mathrm{Var}\\left[\\boldsymbol{\\tilde{y}}\\right]+\\sigma^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4426c74e", + "metadata": { + "editable": true + }, + "source": [ + "that is the rewriting in terms of the so-called bias, the variance of the model $\\boldsymbol{\\tilde{y}}$ and the variance of $\\boldsymbol{\\epsilon}$." + ] + }, + { + "cell_type": "markdown", + "id": "d68ec470", + "metadata": { + "editable": true + }, + "source": [ + "## A way to Read the Bias-Variance Tradeoff\n", + "\n", + "\n", + "\n", + "\n", + "

    Figure 1:

    \n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "0198c371", + "metadata": { + "editable": true + }, + "source": [ + "## Example code for Bias-Variance tradeoff" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "af517050", + "metadata": { + "collapsed": false, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.utils import resample\n", + "\n", + "np.random.seed(2018)\n", + "\n", + "n = 500\n", + "n_boostraps = 100\n", + "degree = 18 # A quite high value, just to show.\n", + "noise = 0.1\n", + "\n", + "# Make data set.\n", + "x = np.linspace(-1, 3, n).reshape(-1, 1)\n", + "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2) + np.random.normal(0, 0.1, x.shape)\n", + "\n", + "# Hold out some test data that is never used in training.\n", + "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n", + "\n", + "# Combine x transformation and model into one operation.\n", + "# Not neccesary, but convenient.\n", + "model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n", + "\n", + "# The following (m x n_bootstraps) matrix holds the column vectors y_pred\n", + "# for each bootstrap iteration.\n", + "y_pred = np.empty((y_test.shape[0], n_boostraps))\n", + "for i in range(n_boostraps):\n", + " x_, y_ = resample(x_train, y_train)\n", + "\n", + " # Evaluate the new model on the same test data each time.\n", + " y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n", + "\n", + "# Note: Expectations and variances taken w.r.t. different training\n", + "# data sets, hence the axis=1. Subsequent means are taken across the test data\n", + "# set in order to obtain a total value, but before this we have error/bias/variance\n", + "# calculated per data point in the test set.\n", + "# Note 2: The use of keepdims=True is important in the calculation of bias as this \n", + "# maintains the column vector form. Dropping this yields very unexpected results.\n", + "error = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n", + "bias = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n", + "variance = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n", + "print('Error:', error)\n", + "print('Bias^2:', bias)\n", + "print('Var:', variance)\n", + "print('{} >= {} + {} = {}'.format(error, bias, variance, bias+variance))\n", + "\n", + "plt.plot(x[::5, :], y[::5, :], label='f(x)')\n", + "plt.scatter(x_test, y_test, label='Data points')\n", + "plt.scatter(x_test, np.mean(y_pred, axis=1), label='Pred')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "2b502d1d", + "metadata": { + "editable": true + }, + "source": [ + "## Understanding what happens" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9a5194fb", + "metadata": { + "collapsed": false, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.utils import resample\n", + "\n", + "np.random.seed(2018)\n", + "\n", + "n = 40\n", + "n_boostraps = 100\n", + "maxdegree = 14\n", + "\n", + "\n", + "# Make data set.\n", + "x = np.linspace(-3, 3, n).reshape(-1, 1)\n", + "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n", + "error = np.zeros(maxdegree)\n", + "bias = np.zeros(maxdegree)\n", + "variance = np.zeros(maxdegree)\n", + "polydegree = np.zeros(maxdegree)\n", + "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n", + "\n", + "for degree in range(maxdegree):\n", + " model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n", + " y_pred = np.empty((y_test.shape[0], n_boostraps))\n", + " for i in range(n_boostraps):\n", + " x_, y_ = resample(x_train, y_train)\n", + " y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n", + "\n", + " polydegree[degree] = degree\n", + " error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n", + " bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n", + " variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n", + " print('Polynomial degree:', degree)\n", + " print('Error:', error[degree])\n", + " print('Bias^2:', bias[degree])\n", + " print('Var:', variance[degree])\n", + " print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n", + "\n", + "plt.plot(polydegree, error, label='Error')\n", + "plt.plot(polydegree, bias, label='bias')\n", + "plt.plot(polydegree, variance, label='Variance')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "727c7723", + "metadata": { + "editable": true + }, + "source": [ + "## Summing up\n", + "\n", + "The bias-variance tradeoff summarizes the fundamental tension in\n", + "machine learning, particularly supervised learning, between the\n", + "complexity of a model and the amount of training data needed to train\n", + "it. Since data is often limited, in practice it is often useful to\n", + "use a less-complex model with higher bias, that is a model whose asymptotic\n", + "performance is worse than another model because it is easier to\n", + "train and less sensitive to sampling noise arising from having a\n", + "finite-sized training dataset (smaller variance). \n", + "\n", + "The above equations tell us that in\n", + "order to minimize the expected test error, we need to select a\n", + "statistical learning method that simultaneously achieves low variance\n", + "and low bias. Note that variance is inherently a nonnegative quantity,\n", + "and squared bias is also nonnegative. Hence, we see that the expected\n", + "test MSE can never lie below $Var(\\epsilon)$, the irreducible error.\n", + "\n", + "What do we mean by the variance and bias of a statistical learning\n", + "method? The variance refers to the amount by which our model would change if we\n", + "estimated it using a different training data set. Since the training\n", + "data are used to fit the statistical learning method, different\n", + "training data sets will result in a different estimate. But ideally the\n", + "estimate for our model should not vary too much between training\n", + "sets. However, if a method has high variance then small changes in\n", + "the training data can result in large changes in the model. In general, more\n", + "flexible statistical methods have higher variance.\n", + "\n", + "You may also find this recent [article](https://www.pnas.org/content/116/32/15849) of interest." + ] + }, + { + "cell_type": "markdown", + "id": "7e90566c", + "metadata": { + "editable": true + }, + "source": [ + "## Another Example from Scikit-Learn's Repository\n", + "\n", + "This example demonstrates the problems of underfitting and overfitting and\n", + "how we can use linear regression with polynomial features to approximate\n", + "nonlinear functions. The plot shows the function that we want to approximate,\n", + "which is a part of the cosine function. In addition, the samples from the\n", + "real function and the approximations of different models are displayed. The\n", + "models have polynomial features of different degrees. We can see that a\n", + "linear function (polynomial with degree 1) is not sufficient to fit the\n", + "training samples. This is called **underfitting**. A polynomial of degree 4\n", + "approximates the true function almost perfectly. However, for higher degrees\n", + "the model will **overfit** the training data, i.e. it learns the noise of the\n", + "training data.\n", + "We evaluate quantitatively overfitting and underfitting by using\n", + "cross-validation. We calculate the mean squared error (MSE) on the validation\n", + "set, the higher, the less likely the model generalizes correctly from the\n", + "training data." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "7c760f15", + "metadata": { + "collapsed": false, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "\n", + "\n", + "#print(__doc__)\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.pipeline import Pipeline\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.model_selection import cross_val_score\n", + "\n", + "\n", + "def true_fun(X):\n", + " return np.cos(1.5 * np.pi * X)\n", + "\n", + "np.random.seed(0)\n", + "\n", + "n_samples = 30\n", + "degrees = [1, 4, 15]\n", + "\n", + "X = np.sort(np.random.rand(n_samples))\n", + "y = true_fun(X) + np.random.randn(n_samples) * 0.1\n", + "\n", + "plt.figure(figsize=(14, 5))\n", + "for i in range(len(degrees)):\n", + " ax = plt.subplot(1, len(degrees), i + 1)\n", + " plt.setp(ax, xticks=(), yticks=())\n", + "\n", + " polynomial_features = PolynomialFeatures(degree=degrees[i],\n", + " include_bias=False)\n", + " linear_regression = LinearRegression()\n", + " pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n", + " (\"linear_regression\", linear_regression)])\n", + " pipeline.fit(X[:, np.newaxis], y)\n", + "\n", + " # Evaluate the models using crossvalidation\n", + " scores = cross_val_score(pipeline, X[:, np.newaxis], y,\n", + " scoring=\"neg_mean_squared_error\", cv=10)\n", + "\n", + " X_test = np.linspace(0, 1, 100)\n", + " plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n", + " plt.plot(X_test, true_fun(X_test), label=\"True function\")\n", + " plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n", + " plt.xlabel(\"x\")\n", + " plt.ylabel(\"y\")\n", + " plt.xlim((0, 1))\n", + " plt.ylim((-2, 2))\n", + " plt.legend(loc=\"best\")\n", + " plt.title(\"Degree {}\\nMSE = {:.2e}(+/- {:.2e})\".format(\n", + " degrees[i], -scores.mean(), scores.std()))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "2619ab70", + "metadata": { + "editable": true + }, "source": [ - "\n", "## Various steps in cross-validation\n", "\n", "When the repetitive splitting of the data set is done randomly,\n", @@ -183,56 +1925,15 @@ "test set over the splits. Still the division into the $k$ subsets\n", "involves a degree of randomness. This may be fully excluded when\n", "choosing $k=n$. This particular case is referred to as leave-one-out\n", - "cross-validation (LOOCV). \n", - "\n", - "\n", - "## How to set up the cross-validation for Ridge and/or Lasso\n", - "\n", - "* Define a range of interest for the penalty parameter.\n", - "\n", - "* Divide the data set into training and test set comprising samples $\\{1, \\ldots, n\\} \\setminus i$ and $\\{ i \\}$, respectively.\n", - "\n", - "* Fit the linear regression model by means of ridge estimation for each $\\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\\boldsymbol{\\sigma}_{-i}^2(\\lambda)$, as" + "cross-validation (LOOCV)." ] }, { "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "\\boldsymbol{\\beta}_{-i}(\\lambda) & = ( \\boldsymbol{X}_{-i, \\ast}^{T}\n", - "\\boldsymbol{X}_{-i, \\ast} + \\lambda \\boldsymbol{I}_{pp})^{-1}\n", - "\\boldsymbol{X}_{-i, \\ast}^{T} \\boldsymbol{y}_{-i}\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "* Evaluate the prediction performance of these models on the test set by $\\log\\{L[y_i, \\boldsymbol{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]\\}$. Or, by the prediction error $|y_i - \\boldsymbol{X}_{i, \\ast} \\boldsymbol{\\beta}_{-i}(\\lambda)|$, the relative error, the error squared or the R2 score function.\n", - "\n", - "* Repeat the first three steps such that each sample plays the role of the test set once.\n", - "\n", - "* Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "\\frac{1}{n} \\sum_{i = 1}^n \\log\\{L[y_i, \\mathbf{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]\\}.\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, + "id": "3e4d0bdb", + "metadata": { + "editable": true + }, "source": [ "## Cross-validation in brief\n", "\n", @@ -252,9 +1953,16 @@ "\n", "d. Retain the evaluation score and discard the model\n", "\n", - "\n", - "5. Summarize the model using the sample of model evaluation scores\n", - "\n", + "5. Summarize the model using the sample of model evaluation scores" + ] + }, + { + "cell_type": "markdown", + "id": "65d5f3f5", + "metadata": { + "editable": true + }, + "source": [ "## Code Example for Cross-validation and $k$-fold Cross-validation\n", "\n", "The code here uses Ridge regression with cross-validation (CV) resampling and $k$-fold CV in order to fit a specific polynomial." @@ -262,12 +1970,17 @@ }, { "cell_type": "code", - "execution_count": 1, - "metadata": {}, + "execution_count": 6, + "id": "66c55986", + "metadata": { + "collapsed": false, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, "outputs": [], "source": [ - "%matplotlib inline\n", - "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.model_selection import KFold\n", @@ -361,1365 +2074,26 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8bd8e7a8", + "metadata": { + "editable": true + }, "source": [ - "## Bias-Variance tradeoff with Bootstrap" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", - "from sklearn.preprocessing import PolynomialFeatures\n", - "from sklearn.model_selection import train_test_split\n", - "from sklearn.pipeline import make_pipeline\n", - "from sklearn.utils import resample\n", - "\n", - "np.random.seed(2018)\n", - "\n", - "n = 40\n", - "n_boostraps = 100\n", - "maxdegree = 14\n", - "\n", - "\n", - "# Make data set.\n", - "x = np.linspace(-3, 3, n).reshape(-1, 1)\n", - "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n", - "error = np.zeros(maxdegree)\n", - "bias = np.zeros(maxdegree)\n", - "variance = np.zeros(maxdegree)\n", - "polydegree = np.zeros(maxdegree)\n", - "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n", - "\n", - "for degree in range(maxdegree):\n", - " model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n", - " y_pred = np.empty((y_test.shape[0], n_boostraps))\n", - " for i in range(n_boostraps):\n", - " x_, y_ = resample(x_train, y_train)\n", - " y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n", - "\n", - " polydegree[degree] = degree\n", - " error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n", - " bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n", - " variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n", - " print('Polynomial degree:', degree)\n", - " print('Error:', error[degree])\n", - " print('Bias^2:', bias[degree])\n", - " print('Var:', variance[degree])\n", - " print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n", - "\n", - "plt.plot(polydegree, error, label='Error')\n", - "plt.plot(polydegree, bias, label='bias')\n", - "plt.plot(polydegree, variance, label='Variance')\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Another Example from Scikit-Learn's Repository" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "\"\"\"\n", - "============================\n", - "Underfitting vs. Overfitting\n", - "============================\n", - "\n", - "This example demonstrates the problems of underfitting and overfitting and\n", - "how we can use linear regression with polynomial features to approximate\n", - "nonlinear functions. The plot shows the function that we want to approximate,\n", - "which is a part of the cosine function. In addition, the samples from the\n", - "real function and the approximations of different models are displayed. The\n", - "models have polynomial features of different degrees. We can see that a\n", - "linear function (polynomial with degree 1) is not sufficient to fit the\n", - "training samples. This is called **underfitting**. A polynomial of degree 4\n", - "approximates the true function almost perfectly. However, for higher degrees\n", - "the model will **overfit** the training data, i.e. it learns the noise of the\n", - "training data.\n", - "We evaluate quantitatively **overfitting** / **underfitting** by using\n", - "cross-validation. We calculate the mean squared error (MSE) on the validation\n", - "set, the higher, the less likely the model generalizes correctly from the\n", - "training data.\n", - "\"\"\"\n", - "\n", - "print(__doc__)\n", - "\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from sklearn.pipeline import Pipeline\n", - "from sklearn.preprocessing import PolynomialFeatures\n", - "from sklearn.linear_model import LinearRegression\n", - "from sklearn.model_selection import cross_val_score\n", - "\n", - "\n", - "def true_fun(X):\n", - " return np.cos(1.5 * np.pi * X)\n", - "\n", - "np.random.seed(0)\n", - "\n", - "n_samples = 30\n", - "degrees = [1, 4, 15]\n", - "\n", - "X = np.sort(np.random.rand(n_samples))\n", - "y = true_fun(X) + np.random.randn(n_samples) * 0.1\n", - "\n", - "plt.figure(figsize=(14, 5))\n", - "for i in range(len(degrees)):\n", - " ax = plt.subplot(1, len(degrees), i + 1)\n", - " plt.setp(ax, xticks=(), yticks=())\n", - "\n", - " polynomial_features = PolynomialFeatures(degree=degrees[i],\n", - " include_bias=False)\n", - " linear_regression = LinearRegression()\n", - " pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n", - " (\"linear_regression\", linear_regression)])\n", - " pipeline.fit(X[:, np.newaxis], y)\n", - "\n", - " # Evaluate the models using crossvalidation\n", - " scores = cross_val_score(pipeline, X[:, np.newaxis], y,\n", - " scoring=\"neg_mean_squared_error\", cv=10)\n", - "\n", - " X_test = np.linspace(0, 1, 100)\n", - " plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n", - " plt.plot(X_test, true_fun(X_test), label=\"True function\")\n", - " plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n", - " plt.xlabel(\"x\")\n", - " plt.ylabel(\"y\")\n", - " plt.xlim((0, 1))\n", - " plt.ylim((-2, 2))\n", - " plt.legend(loc=\"best\")\n", - " plt.title(\"Degree {}\\nMSE = {:.2e}(+/- {:.2e})\".format(\n", - " degrees[i], -scores.mean(), scores.std()))\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Cross-validation with Ridge" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from sklearn.model_selection import KFold\n", - "from sklearn.linear_model import Ridge\n", - "from sklearn.model_selection import cross_val_score\n", - "from sklearn.preprocessing import PolynomialFeatures\n", - "\n", - "# A seed just to ensure that the random numbers are the same for every run.\n", - "np.random.seed(3155)\n", - "# Generate the data.\n", - "n = 100\n", - "x = np.linspace(-3, 3, n).reshape(-1, 1)\n", - "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n", - "# Decide degree on polynomial to fit\n", - "poly = PolynomialFeatures(degree = 10)\n", - "\n", - "# Decide which values of lambda to use\n", - "nlambdas = 500\n", - "lambdas = np.logspace(-3, 5, nlambdas)\n", - "# Initialize a KFold instance\n", - "k = 5\n", - "kfold = KFold(n_splits = k)\n", - "estimated_mse_sklearn = np.zeros(nlambdas)\n", - "i = 0\n", - "for lmb in lambdas:\n", - " ridge = Ridge(alpha = lmb)\n", - " estimated_mse_folds = cross_val_score(ridge, x, y, scoring='neg_mean_squared_error', cv=kfold)\n", - " estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)\n", - " i += 1\n", - "plt.figure()\n", - "plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')\n", - "plt.xlabel('log10(lambda)')\n", - "plt.ylabel('MSE')\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The Ising model\n", - "\n", - "The one-dimensional Ising model with nearest neighbor interaction, no\n", - "external field and a constant coupling constant $J$ is given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " H = -J \\sum_{k}^L s_k s_{k + 1},\n", - "\\label{_auto1} \\tag{1}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins\n", - "in the system is determined by $L$. For the one-dimensional system\n", - "there is no phase transition.\n", - "\n", - "We will look at a system of $L = 40$ spins with a coupling constant of\n", - "$J = 1$. To get enough training data we will generate 10000 states\n", - "with their respective energies." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", - "import seaborn as sns\n", - "import scipy.linalg as scl\n", - "from sklearn.model_selection import train_test_split\n", - "import tqdm\n", - "sns.set(color_codes=True)\n", - "cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n", - "\n", - "L = 40\n", - "n = int(1e4)\n", - "\n", - "spins = np.random.choice([-1, 1], size=(n, L))\n", - "J = 1.0\n", - "\n", - "energies = np.zeros(n)\n", - "\n", - "for i in range(n):\n", - " energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we use ordinary least squares\n", - "regression to predict the energy for the nearest neighbor\n", - "one-dimensional Ising model on a ring, i.e., the endpoints wrap\n", - "around. We will use linear regression to fit a value for\n", - "the coupling constant to achieve this.\n", - "\n", - "## Reformulating the problem to suit regression\n", - "\n", - "A more general form for the one-dimensional Ising model is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n", - "\\label{_auto2} \\tag{2}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we allow for interactions beyond the nearest neighbors and a state dependent\n", - "coupling constant. This latter expression can be formulated as\n", - "a matrix-product" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " \\boldsymbol{H} = \\boldsymbol{X} J,\n", - "\\label{_auto3} \\tag{3}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $X_{jk} = s_j s_k$ and $J$ is a matrix which consists of the\n", - "elements $-J_{jk}$. This form of writing the energy fits perfectly\n", - "with the form utilized in linear regression, that is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon},\n", - "\\label{_auto4} \\tag{4}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We split the data in training and test data as discussed in the previous example" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "X = np.zeros((n, L ** 2))\n", - "for i in range(n):\n", - " X[i] = np.outer(spins[i], spins[i]).ravel()\n", - "y = energies\n", - "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Linear regression\n", - "\n", - "In the ordinary least squares method we choose the cost function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " C(\\boldsymbol{X}, \\boldsymbol{\\beta})= \\frac{1}{n}\\left\\{(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})\\right\\}.\n", - "\\label{_auto5} \\tag{5}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We then find the extremal point of $C$ by taking the derivative with respect to $\\boldsymbol{\\beta}$ as discussed above.\n", - "This yields the expression for $\\boldsymbol{\\beta}$ to be" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\boldsymbol{\\beta} = \\frac{\\boldsymbol{X}^T \\boldsymbol{y}}{\\boldsymbol{X}^T \\boldsymbol{X}},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which immediately imposes some requirements on $\\boldsymbol{X}$ as there must exist\n", - "an inverse of $\\boldsymbol{X}^T \\boldsymbol{X}$. If the expression we are modeling contains an\n", - "intercept, i.e., a constant term, we must make sure that the\n", - "first column of $\\boldsymbol{X}$ consists of $1$. We do this here" + "## More examples on bootstrap and cross-validation and errors" ] }, { "cell_type": "code", "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "X_train_own = np.concatenate(\n", - " (np.ones(len(X_train))[:, np.newaxis], X_train),\n", - " axis=1\n", - ")\n", - "X_test_own = np.concatenate(\n", - " (np.ones(len(X_test))[:, np.newaxis], X_test),\n", - " axis=1\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "def ols_inv(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n", - " return scl.inv(x.T @ x) @ (x.T @ y)\n", - "beta = ols_inv(X_train_own, y_train)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Singular Value decomposition\n", - "\n", - "Doing the inversion directly turns out to be a bad idea since the matrix\n", - "$\\boldsymbol{X}^T\\boldsymbol{X}$ is singular. An alternative approach is to use the **singular\n", - "value decomposition**. Using the definition of the Moore-Penrose\n", - "pseudoinverse we can write the equation for $\\boldsymbol{\\beta}$ as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\boldsymbol{\\beta} = \\boldsymbol{X}^{+}\\boldsymbol{y},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where the pseudoinverse of $\\boldsymbol{X}$ is given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\boldsymbol{X}^{+} = \\frac{\\boldsymbol{X}^T}{\\boldsymbol{X}^T\\boldsymbol{X}}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Using singular value decomposition we can decompose the matrix $\\boldsymbol{X} = \\boldsymbol{U}\\boldsymbol{\\Sigma} \\boldsymbol{V}^T$,\n", - "where $\\boldsymbol{U}$ and $\\boldsymbol{V}$ are orthogonal(unitary) matrices and $\\boldsymbol{\\Sigma}$ contains the singular values (more details below).\n", - "where $X^{+} = V\\Sigma^{+} U^T$. This reduces the equation for\n", - "$\\omega$ to" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " \\boldsymbol{\\beta} = \\boldsymbol{V}\\boldsymbol{\\Sigma}^{+} \\boldsymbol{U}^T \\boldsymbol{y}.\n", - "\\label{_auto6} \\tag{6}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that solving this equation by actually doing the pseudoinverse\n", - "(which is what we will do) is not a good idea as this operation scales\n", - "as $\\mathcal{O}(n^3)$, where $n$ is the number of elements in a\n", - "general matrix. Instead, doing $QR$-factorization and solving the\n", - "linear system as an equation would reduce this down to\n", - "$\\mathcal{O}(n^2)$ operations." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "def ols_svd(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n", - " u, s, v = scl.svd(x)\n", - " return v.T @ scl.pinv(scl.diagsvd(s, u.shape[0], v.shape[0])) @ u.T @ y" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "beta = ols_svd(X_train_own,y_train)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "When extracting the $J$-matrix we need to make sure that we remove the intercept, as is done here" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "J = beta[1:].reshape(L, L)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A way of looking at the coefficients in $J$ is to plot the matrices as images." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "fig = plt.figure(figsize=(20, 14))\n", - "im = plt.imshow(J, **cmap_args)\n", - "plt.title(\"OLS\", fontsize=18)\n", - "plt.xticks(fontsize=18)\n", - "plt.yticks(fontsize=18)\n", - "cb = fig.colorbar(im)\n", - "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is interesting to note that OLS\n", - "considers both $J_{j, j + 1} = -0.5$ and $J_{j, j - 1} = -0.5$ as\n", - "valid matrix elements for $J$.\n", - "In our discussion below on hyperparameters and Ridge and Lasso regression we will see that\n", - "this problem can be removed, partly and only with Lasso regression. \n", - "\n", - "In this case our matrix inversion was actually possible. The obvious question now is what is the mathematics behind the SVD?\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## The one-dimensional Ising model\n", - "\n", - "Let us bring back the Ising model again, but now with an additional\n", - "focus on Ridge and Lasso regression as well. We repeat some of the\n", - "basic parts of the Ising model and the setup of the training and test\n", - "data. The one-dimensional Ising model with nearest neighbor\n", - "interaction, no external field and a constant coupling constant $J$ is\n", - "given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " H = -J \\sum_{k}^L s_k s_{k + 1},\n", - "\\label{_auto7} \\tag{7}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins in the system is determined by $L$. For the one-dimensional system there is no phase transition.\n", - "\n", - "We will look at a system of $L = 40$ spins with a coupling constant of $J = 1$. To get enough training data we will generate 10000 states with their respective energies." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", - "import seaborn as sns\n", - "import scipy.linalg as scl\n", - "from sklearn.model_selection import train_test_split\n", - "import sklearn.linear_model as skl\n", - "import tqdm\n", - "sns.set(color_codes=True)\n", - "cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n", - "\n", - "L = 40\n", - "n = int(1e4)\n", - "\n", - "spins = np.random.choice([-1, 1], size=(n, L))\n", - "J = 1.0\n", - "\n", - "energies = np.zeros(n)\n", - "\n", - "for i in range(n):\n", - " energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A more general form for the one-dimensional Ising model is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n", - "\\label{_auto8} \\tag{8}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we allow for interactions beyond the nearest neighbors and a more\n", - "adaptive coupling matrix. This latter expression can be formulated as\n", - "a matrix-product on the form" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " H = X J,\n", - "\\label{_auto9} \\tag{9}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $X_{jk} = s_j s_k$ and $J$ is the matrix consisting of the\n", - "elements $-J_{jk}$. This form of writing the energy fits perfectly\n", - "with the form utilized in linear regression, viz." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon}.\n", - "\\label{_auto10} \\tag{10}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We organize the data as we did above" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [], - "source": [ - "X = np.zeros((n, L ** 2))\n", - "for i in range(n):\n", - " X[i] = np.outer(spins[i], spins[i]).ravel()\n", - "y = energies\n", - "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.96)\n", - "\n", - "X_train_own = np.concatenate(\n", - " (np.ones(len(X_train))[:, np.newaxis], X_train),\n", - " axis=1\n", - ")\n", - "\n", - "X_test_own = np.concatenate(\n", - " (np.ones(len(X_test))[:, np.newaxis], X_test),\n", - " axis=1\n", - ")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We will do all fitting with **Scikit-Learn**," - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [], - "source": [ - "clf = skl.LinearRegression().fit(X_train, y_train)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "When extracting the $J$-matrix we make sure to remove the intercept" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "J_sk = clf.coef_.reshape(L, L)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And then we plot the results" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "fig = plt.figure(figsize=(20, 14))\n", - "im = plt.imshow(J_sk, **cmap_args)\n", - "plt.title(\"LinearRegression from Scikit-learn\", fontsize=18)\n", - "plt.xticks(fontsize=18)\n", - "plt.yticks(fontsize=18)\n", - "cb = fig.colorbar(im)\n", - "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The results perfectly with our previous discussion where we used our own code.\n", - "\n", - "## Ridge regression\n", - "\n", - "Having explored the ordinary least squares we move on to ridge\n", - "regression. In ridge regression we include a **regularizer**. This\n", - "involves a new cost function which leads to a new estimate for the\n", - "weights $\\boldsymbol{\\beta}$. This results in a penalized regression problem. The\n", - "cost function is given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\n", - "2\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "M\n", - "A\n", - "T\n", - "H\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [], - "source": [ - "_lambda = 0.1\n", - "clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)\n", - "J_ridge_sk = clf_ridge.coef_.reshape(L, L)\n", - "fig = plt.figure(figsize=(20, 14))\n", - "im = plt.imshow(J_ridge_sk, **cmap_args)\n", - "plt.title(\"Ridge from Scikit-learn\", fontsize=18)\n", - "plt.xticks(fontsize=18)\n", - "plt.yticks(fontsize=18)\n", - "cb = fig.colorbar(im)\n", - "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## LASSO regression\n", - "\n", - "In the **Least Absolute Shrinkage and Selection Operator** (LASSO)-method we get a third cost function." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - " C(\\boldsymbol{X}, \\boldsymbol{\\beta}; \\lambda) = (\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y}) + \\lambda \\sqrt{\\boldsymbol{\\beta}^T\\boldsymbol{\\beta}}.\n", - "\\label{_auto12} \\tag{12}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finding the extremal point of this cost function is not so straight-forward as in least squares and ridge. We will therefore rely solely on the function ``Lasso`` from **Scikit-Learn**." - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [], - "source": [ - "clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n", - "J_lasso_sk = clf_lasso.coef_.reshape(L, L)\n", - "fig = plt.figure(figsize=(20, 14))\n", - "im = plt.imshow(J_lasso_sk, **cmap_args)\n", - "plt.title(\"Lasso from Scikit-learn\", fontsize=18)\n", - "plt.xticks(fontsize=18)\n", - "plt.yticks(fontsize=18)\n", - "cb = fig.colorbar(im)\n", - "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is quite striking how LASSO breaks the symmetry of the coupling\n", - "constant as opposed to ridge and OLS. We get a sparse solution with\n", - "$J_{j, j + 1} = -1$.\n", - "\n", - "\n", - "\n", - "## Performance as function of the regularization parameter\n", - "\n", - "We see how the different models perform for a different set of values for $\\lambda$." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [], - "source": [ - "lambdas = np.logspace(-4, 5, 10)\n", - "\n", - "train_errors = {\n", - " \"ols_sk\": np.zeros(lambdas.size),\n", - " \"ridge_sk\": np.zeros(lambdas.size),\n", - " \"lasso_sk\": np.zeros(lambdas.size)\n", - "}\n", - "\n", - "test_errors = {\n", - " \"ols_sk\": np.zeros(lambdas.size),\n", - " \"ridge_sk\": np.zeros(lambdas.size),\n", - " \"lasso_sk\": np.zeros(lambdas.size)\n", - "}\n", - "\n", - "plot_counter = 1\n", - "\n", - "fig = plt.figure(figsize=(32, 54))\n", - "\n", - "for i, _lambda in enumerate(tqdm.tqdm(lambdas)):\n", - " for key, method in zip(\n", - " [\"ols_sk\", \"ridge_sk\", \"lasso_sk\"],\n", - " [skl.LinearRegression(), skl.Ridge(alpha=_lambda), skl.Lasso(alpha=_lambda)]\n", - " ):\n", - " method = method.fit(X_train, y_train)\n", - "\n", - " train_errors[key][i] = method.score(X_train, y_train)\n", - " test_errors[key][i] = method.score(X_test, y_test)\n", - "\n", - " omega = method.coef_.reshape(L, L)\n", - "\n", - " plt.subplot(10, 5, plot_counter)\n", - " plt.imshow(omega, **cmap_args)\n", - " plt.title(r\"%s, $\\lambda = %.4f$\" % (key, _lambda))\n", - " plot_counter += 1\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We see that LASSO reaches a good solution for low\n", - "values of $\\lambda$, but will \"wither\" when we increase $\\lambda$ too\n", - "much. Ridge is more stable over a larger range of values for\n", - "$\\lambda$, but eventually also fades away.\n", - "\n", - "## Finding the optimal value of $\\lambda$\n", - "\n", - "To determine which value of $\\lambda$ is best we plot the accuracy of\n", - "the models when predicting the training and the testing set. We expect\n", - "the accuracy of the training set to be quite good, but if the accuracy\n", - "of the testing set is much lower this tells us that we might be\n", - "subject to an overfit model. The ideal scenario is an accuracy on the\n", - "testing set that is close to the accuracy of the training set." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [], - "source": [ - "fig = plt.figure(figsize=(20, 14))\n", - "\n", - "colors = {\n", - " \"ols_sk\": \"r\",\n", - " \"ridge_sk\": \"y\",\n", - " \"lasso_sk\": \"c\"\n", - "}\n", - "\n", - "for key in train_errors:\n", - " plt.semilogx(\n", - " lambdas,\n", - " train_errors[key],\n", - " colors[key],\n", - " label=\"Train {0}\".format(key),\n", - " linewidth=4.0\n", - " )\n", - "\n", - "for key in test_errors:\n", - " plt.semilogx(\n", - " lambdas,\n", - " test_errors[key],\n", - " colors[key] + \"--\",\n", - " label=\"Test {0}\".format(key),\n", - " linewidth=4.0\n", - " )\n", - "plt.legend(loc=\"best\", fontsize=18)\n", - "plt.xlabel(r\"$\\lambda$\", fontsize=18)\n", - "plt.ylabel(r\"$R^2$\", fontsize=18)\n", - "plt.tick_params(labelsize=18)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "From the above figure we can see that LASSO with $\\lambda = 10^{-2}$\n", - "achieves a very good accuracy on the test set. This by far surpasses the\n", - "other models for all values of $\\lambda$.\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Friday September 18: Intro to Logistic Regression\n", - "\n", - "[Video of Lecture](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureSeptember18.mp4?vrtx=view-as-webpage) and [link to handwritten notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesSeptember18.pdf).\n", - "\n", - "\n", ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - "\n", - "\n", - "## Logistic Regression\n", - "\n", - "In linear regression our main interest was centered on learning the\n", - "coefficients of a functional fit (say a polynomial) in order to be\n", - "able to predict the response of a continuous variable on some unseen\n", - "data. The fit to the continuous variable $y_i$ is based on some\n", - "independent variables $\\hat{x}_i$. Linear regression resulted in\n", - "analytical expressions for standard ordinary Least Squares or Ridge\n", - "regression (in terms of matrices to invert) for several quantities,\n", - "ranging from the variance and thereby the confidence intervals of the\n", - "parameters $\\hat{\\beta}$ to the mean squared error. If we can invert\n", - "the product of the design matrices, linear regression gives then a\n", - "simple recipe for fitting our data.\n", - "\n", - "\n", - "## Classification problems\n", - "\n", - "\n", - "Classification problems, however, are concerned with outcomes taking\n", - "the form of discrete variables (i.e. categories). We may for example,\n", - "on the basis of DNA sequencing for a number of patients, like to find\n", - "out which mutations are important for a certain disease; or based on\n", - "scans of various patients' brains, figure out if there is a tumor or\n", - "not; or given a specific physical system, we'd like to identify its\n", - "state, say whether it is an ordered or disordered system (typical\n", - "situation in solid state physics); or classify the status of a\n", - "patient, whether she/he has a stroke or not and many other similar\n", - "situations.\n", - "\n", - "The most common situation we encounter when we apply logistic\n", - "regression is that of two possible outcomes, normally denoted as a\n", - "binary outcome, true or false, positive or negative, success or\n", - "failure etc.\n", - "\n", - "## Optimization and Deep learning\n", - "\n", - "Logistic regression will also serve as our stepping stone towards\n", - "neural network algorithms and supervised deep learning. For logistic\n", - "learning, the minimization of the cost function leads to a non-linear\n", - "equation in the parameters $\\hat{\\beta}$. The optimization of the\n", - "problem calls therefore for minimization algorithms. This forms the\n", - "bottle neck of all machine learning algorithms, namely how to find\n", - "reliable minima of a multi-variable function. This leads us to the\n", - "family of gradient descent methods. The latter are the working horses\n", - "of basically all modern machine learning algorithms.\n", - "\n", - "We note also that many of the topics discussed here on logistic \n", - "regression are also commonly used in modern supervised Deep Learning\n", - "models, as we will see later.\n", - "\n", - "\n", - "\n", - "## Basics\n", - "\n", - "We consider the case where the dependent variables, also called the\n", - "responses or the outcomes, $y_i$ are discrete and only take values\n", - "from $k=0,\\dots,K-1$ (i.e. $K$ classes).\n", - "\n", - "The goal is to predict the\n", - "output classes from the design matrix $\\hat{X}\\in\\mathbb{R}^{n\\times p}$\n", - "made of $n$ samples, each of which carries $p$ features or predictors. The\n", - "primary goal is to identify the classes to which new unseen samples\n", - "belong.\n", - "\n", - "Let us specialize to the case of two classes only, with outputs\n", - "$y_i=0$ and $y_i=1$. Our outcomes could represent the status of a\n", - "credit card user that could default or not on her/his credit card\n", - "debt. That is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "y_i = \\begin{bmatrix} 0 & \\mathrm{no}\\\\ 1 & \\mathrm{yes} \\end{bmatrix}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Linear classifier\n", - "\n", - "Before moving to the logistic model, let us try to use our linear\n", - "regression model to classify these two outcomes. We could for example\n", - "fit a linear model to the default case if $y_i > 0.5$ and the no\n", - "default case $y_i \\leq 0.5$.\n", - "\n", - "We would then have our \n", - "weighted linear combination, namely" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", -<<<<<<< HEAD - "
    \n", -======= - "
    \n", ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - "\n", - "$$\n", - "\\begin{equation}\n", - "\\hat{y} = \\hat{X}^T\\hat{\\beta} + \\hat{\\epsilon},\n", -<<<<<<< HEAD - "\\label{_auto1} \\tag{1}\n", -======= - "\\label{_auto13} \\tag{13}\n", ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $\\hat{y}$ is a vector representing the possible outcomes, $\\hat{X}$ is our\n", - "$n\\times p$ design matrix and $\\hat{\\beta}$ represents our estimators/predictors.\n", - "\n", - "## Some selected properties\n", - "\n", - "The main problem with our function is that it takes values on the\n", - "entire real axis. In the case of logistic regression, however, the\n", - "labels $y_i$ are discrete variables. A typical example is the credit\n", - "card data discussed below here, where we can set the state of\n", - "defaulting the debt to $y_i=1$ and not to $y_i=0$ for one the persons\n", - "in the data set (see the full example below).\n", - "\n", - "One simple way to get a discrete output is to have sign\n", - "functions that map the output of a linear regressor to values $\\{0,1\\}$,\n", - "$f(s_i)=sign(s_i)=1$ if $s_i\\ge 0$ and 0 if otherwise. \n", -<<<<<<< HEAD - "We will encounter this model in our first demonstration of neural networks. Historically it is called the \"perceptron\" model in the machine learning\n", -======= - "We will encounter this model in our first demonstration of neural networks. Historically it is called the ``perceptron\" model in the machine learning\n", ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - "literature. This model is extremely simple. However, in many cases it is more\n", - "favorable to use a ``soft\" classifier that outputs\n", - "the probability of a given category. This leads us to the logistic function.\n", - "\n", -<<<<<<< HEAD - "\n", - "## The logistic function\n", - "\n", - "The perceptron is an example of a ``hard classification\" model. We\n", - "will encounter this model when we discuss neural networks as\n", - "well. Each datapoint is deterministically assigned to a category (i.e\n", - "$y_i=0$ or $y_i=1$). In many cases, it is favorable to have a \"soft\"\n", -======= - "## Simple example\n", - "\n", - "The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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\n", 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    " - ] - }, - "metadata": {}, - "output_type": "display_data" + "id": "2b363d73", + "metadata": { + "collapsed": false, + "editable": true, + "jupyter": { + "outputs_hidden": false } - ], + }, + "outputs": [], "source": [ "# Common imports\n", "import os\n", @@ -1730,10 +2104,122 @@ "from sklearn.model_selection import train_test_split\n", "from sklearn.utils import resample\n", "from sklearn.metrics import mean_squared_error\n", - "from IPython.display import display\n", - "from pylab import plt, mpl\n", - "plt.style.use('seaborn')\n", - "mpl.rcParams['font.family'] = 'serif'\n", + "# Where to save the figures and data files\n", + "PROJECT_ROOT_DIR = \"Results\"\n", + "FIGURE_ID = \"Results/FigureFiles\"\n", + "DATA_ID = \"DataFiles/\"\n", + "\n", + "if not os.path.exists(PROJECT_ROOT_DIR):\n", + " os.mkdir(PROJECT_ROOT_DIR)\n", + "\n", + "if not os.path.exists(FIGURE_ID):\n", + " os.makedirs(FIGURE_ID)\n", + "\n", + "if not os.path.exists(DATA_ID):\n", + " os.makedirs(DATA_ID)\n", + "\n", + "def image_path(fig_id):\n", + " return os.path.join(FIGURE_ID, fig_id)\n", + "\n", + "def data_path(dat_id):\n", + " return os.path.join(DATA_ID, dat_id)\n", + "\n", + "def save_fig(fig_id):\n", + " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", + "\n", + "infile = open(data_path(\"EoS.csv\"),'r')\n", + "\n", + "# Read the EoS data as csv file and organize the data into two arrays with density and energies\n", + "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n", + "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n", + "EoS = EoS.dropna()\n", + "Energies = EoS['Energy']\n", + "Density = EoS['Density']\n", + "# The design matrix now as function of various polytrops\n", + "\n", + "Maxpolydegree = 30\n", + "X = np.zeros((len(Density),Maxpolydegree))\n", + "X[:,0] = 1.0\n", + "testerror = np.zeros(Maxpolydegree)\n", + "trainingerror = np.zeros(Maxpolydegree)\n", + "polynomial = np.zeros(Maxpolydegree)\n", + "\n", + "trials = 100\n", + "for polydegree in range(1, Maxpolydegree):\n", + " polynomial[polydegree] = polydegree\n", + " for degree in range(polydegree):\n", + " X[:,degree] = Density**(degree/3.0)\n", + "\n", + "# loop over trials in order to estimate the expectation value of the MSE\n", + " testerror[polydegree] = 0.0\n", + " trainingerror[polydegree] = 0.0\n", + " for samples in range(trials):\n", + " x_train, x_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2)\n", + " model = LinearRegression(fit_intercept=False).fit(x_train, y_train)\n", + " ypred = model.predict(x_train)\n", + " ytilde = model.predict(x_test)\n", + " testerror[polydegree] += mean_squared_error(y_test, ytilde)\n", + " trainingerror[polydegree] += mean_squared_error(y_train, ypred) \n", + "\n", + " testerror[polydegree] /= trials\n", + " trainingerror[polydegree] /= trials\n", + " print(\"Degree of polynomial: %3d\"% polynomial[polydegree])\n", + " print(\"Mean squared error on training data: %.8f\" % trainingerror[polydegree])\n", + " print(\"Mean squared error on test data: %.8f\" % testerror[polydegree])\n", + "\n", + "plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n", + "plt.plot(polynomial, np.log10(testerror), label='Test Error')\n", + "plt.xlabel('Polynomial degree')\n", + "plt.ylabel('log10[MSE]')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "de30ce89", + "metadata": { + "editable": true + }, + "source": [ + "Note that we kept the intercept column in the fitting here. This means that we need to set the **intercept** in the call to the **Scikit-Learn** function as **False**. Alternatively, we could have set up the design matrix $X$ without the first column of ones." + ] + }, + { + "cell_type": "markdown", + "id": "936b8f0f", + "metadata": { + "editable": true + }, + "source": [ + "## The same example but now with cross-validation\n", + "\n", + "In this example we keep the intercept column again but add cross-validation in order to estimate the best possible value of the means squared error." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "399b09d4", + "metadata": { + "collapsed": false, + "editable": true, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [], + "source": [ + "# Common imports\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.metrics import mean_squared_error\n", + "from sklearn.model_selection import KFold\n", + "from sklearn.model_selection import cross_val_score\n", + "\n", "\n", "# Where to save the figures and data files\n", "PROJECT_ROOT_DIR = \"Results\"\n", @@ -1758,994 +2244,64 @@ "def save_fig(fig_id):\n", " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", "\n", - "infile = open(data_path(\"chddata.csv\"),'r')\n", + "infile = open(data_path(\"EoS.csv\"),'r')\n", "\n", - "# Read the chd data as csv file and organize the data into arrays with age group, age, and chd\n", - "chd = pd.read_csv(infile, names=('ID', 'Age', 'Agegroup', 'CHD'))\n", - "chd.columns = ['ID', 'Age', 'Agegroup', 'CHD']\n", - "output = chd['CHD']\n", - "age = chd['Age']\n", - "agegroup = chd['Agegroup']\n", - "numberID = chd['ID'] \n", - "display(chd)\n", + "# Read the EoS data as csv file and organize the data into two arrays with density and energies\n", + "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n", + "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n", + "EoS = EoS.dropna()\n", + "Energies = EoS['Energy']\n", + "Density = EoS['Density']\n", + "# The design matrix now as function of various polytrops\n", "\n", - "plt.scatter(age, output, marker='o')\n", - "plt.axis([18,70.0,-0.1, 1.2])\n", - "plt.xlabel(r'Age')\n", - "plt.ylabel(r'CHD')\n", - "plt.title(r'Age distribution and Coronary heart disease')\n", + "Maxpolydegree = 30\n", + "X = np.zeros((len(Density),Maxpolydegree))\n", + "X[:,0] = 1.0\n", + "estimated_mse_sklearn = np.zeros(Maxpolydegree)\n", + "polynomial = np.zeros(Maxpolydegree)\n", + "k =5\n", + "kfold = KFold(n_splits = k)\n", + "\n", + "for polydegree in range(1, Maxpolydegree):\n", + " polynomial[polydegree] = polydegree\n", + " for degree in range(polydegree):\n", + " X[:,degree] = Density**(degree/3.0)\n", + " OLS = LinearRegression(fit_intercept=False)\n", + "# loop over trials in order to estimate the expectation value of the MSE\n", + " estimated_mse_folds = cross_val_score(OLS, X, Energies, scoring='neg_mean_squared_error', cv=kfold)\n", + "#[:, np.newaxis]\n", + " estimated_mse_sklearn[polydegree] = np.mean(-estimated_mse_folds)\n", + "\n", + "plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n", + "plt.xlabel('Polynomial degree')\n", + "plt.ylabel('log10[MSE]')\n", + "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "ded3c9a0", + "metadata": { + "editable": true + }, "source": [ - "## Plotting the mean value for each group\n", + "## Material for the lab sessions\n", "\n", - "What we could attempt however is to plot the mean value for each group." + "This week we will discuss during the first hour of each lab session\n", + "some technicalities related to the project and methods for updating\n", + "the learning like ADAgrad, RMSprop and ADAM. As teaching material, see\n", + "the jupyter-notebook from week 37 (September 12-16).\n", + "\n", + "For the lab session, the following video on cross validation (from 2024), could be helpful, see \n", + "\n", + "See also video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at " ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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    " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "agegroupmean = np.array([0.1, 0.133, 0.250, 0.333, 0.462, 0.625, 0.765, 0.800])\n", - "group = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n", - "plt.plot(group, agegroupmean, \"r-\")\n", - "plt.axis([0,9,0, 1.0])\n", - "plt.xlabel(r'Age group')\n", - "plt.ylabel(r'CHD mean values')\n", - "plt.title(r'Mean values for each age group')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We are now trying to find a function $f(y\\vert x)$, that is a function which gives us an expected value for the output $y$ with a given input $x$.\n", - "In standard linear regression with a linear dependence on $x$, we would write this in terms of our model" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "f(y_i\\vert x_i)=\\beta_0+\\beta_1 x_i.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This expression implies however that $f(y_i\\vert x_i)$ could take any\n", - "value from minus infinity to plus infinity. If we however let\n", - "$f(y\\vert y)$ be represented by the mean value, the above example\n", - "shows us that we can constrain the function to take values between\n", - "zero and one, that is we have $0 \\le f(y_i\\vert x_i) \\le 1$. Looking\n", - "at our last curve we see also that it has an S-shaped form. This leads\n", - "us to a very popular model for the function $f$, namely the so-called\n", - "Sigmoid function or logistic model. We will consider this function as\n", - "representing the probability for finding a value of $y_i$ with a given\n", - "$x_i$.\n", - "\n", - "## The logistic function\n", - "\n", - "Another widely studied model, is the so-called \n", - "perceptron model, which is an example of a \"hard classification\" model. We\n", - "will encounter this model when we discuss neural networks as\n", - "well. Each datapoint is deterministically assigned to a category (i.e\n", - "$y_i=0$ or $y_i=1$). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a \"soft\"\n", ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - "classifier that outputs the probability of a given category rather\n", - "than a single value. For example, given $x_i$, the classifier\n", - "outputs the probability of being in a category $k$. Logistic regression\n", - "is the most common example of a so-called soft classifier. In logistic\n", - "regression, the probability that a data point $x_i$\n", - "belongs to a category $y_i=\\{0,1\\}$ is given by the so-called logit function (or Sigmoid) which is meant to represent the likelihood for a given event," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(t) = \\frac{1}{1+\\mathrm \\exp{-t}}=\\frac{\\exp{t}}{1+\\mathrm \\exp{t}}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that $1-p(t)= p(-t)$.\n", - "\n", - "## Examples of likelihood functions used in logistic regression and nueral networks\n", - "\n", - "\n", - "The following code plots the logistic function, the step function and other functions we will encounter from here and on." - ] - }, - { - "cell_type": "code", -<<<<<<< HEAD - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "\n", -======= - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - 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\n", 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\n", 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\n", 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    " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - "\"\"\"The sigmoid function (or the logistic curve) is a\n", - "function that takes any real number, z, and outputs a number (0,1).\n", - "It is useful in neural networks for assigning weights on a relative scale.\n", - "The value z is the weighted sum of parameters involved in the learning algorithm.\"\"\"\n", - "\n", - "import numpy\n", - "import matplotlib.pyplot as plt\n", - "import math as mt\n", - "\n", - "z = numpy.arange(-5, 5, .1)\n", - "sigma_fn = numpy.vectorize(lambda z: 1/(1+numpy.exp(-z)))\n", - "sigma = sigma_fn(z)\n", - "\n", - "fig = plt.figure()\n", - "ax = fig.add_subplot(111)\n", - "ax.plot(z, sigma)\n", - "ax.set_ylim([-0.1, 1.1])\n", - "ax.set_xlim([-5,5])\n", - "ax.grid(True)\n", - "ax.set_xlabel('z')\n", - "ax.set_title('sigmoid function')\n", - "\n", - "plt.show()\n", - "\n", - "\"\"\"Step Function\"\"\"\n", - "z = numpy.arange(-5, 5, .02)\n", - "step_fn = numpy.vectorize(lambda z: 1.0 if z >= 0.0 else 0.0)\n", - "step = step_fn(z)\n", - "\n", - "fig = plt.figure()\n", - "ax = fig.add_subplot(111)\n", - "ax.plot(z, step)\n", - "ax.set_ylim([-0.5, 1.5])\n", - "ax.set_xlim([-5,5])\n", - "ax.grid(True)\n", - "ax.set_xlabel('z')\n", - "ax.set_title('step function')\n", - "\n", - "plt.show()\n", - "\n", - "\"\"\"tanh Function\"\"\"\n", - "z = numpy.arange(-2*mt.pi, 2*mt.pi, 0.1)\n", - "t = numpy.tanh(z)\n", - "\n", - "fig = plt.figure()\n", - "ax = fig.add_subplot(111)\n", - "ax.plot(z, t)\n", - "ax.set_ylim([-1.0, 1.0])\n", - "ax.set_xlim([-2*mt.pi,2*mt.pi])\n", - "ax.grid(True)\n", - "ax.set_xlabel('z')\n", - "ax.set_title('tanh function')\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Two parameters\n", - "\n", - "We assume now that we have two classes with $y_i$ either $0$ or $1$. Furthermore we assume also that we have only two parameters $\\beta$ in our fitting of the Sigmoid function, that is we define probabilities" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "p(y_i=1|x_i,\\hat{\\beta}) &= \\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}},\\nonumber\\\\\n", - "p(y_i=0|x_i,\\hat{\\beta}) &= 1 - p(y_i=1|x_i,\\hat{\\beta}),\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $\\hat{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$. \n", - "\n", - "Note that we used" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(y_i=0\\vert x_i, \\hat{\\beta}) = 1-p(y_i=1\\vert x_i, \\hat{\\beta}).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "## Maximum likelihood\n", - "\n", - "In order to define the total likelihood for all possible outcomes from a \n", - "dataset $\\mathcal{D}=\\{(y_i,x_i)\\}$, with the binary labels\n", - "$y_i\\in\\{0,1\\}$ and where the data points are drawn independently, we use the so-called [Maximum Likelihood Estimation](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) (MLE) principle. \n", - "We aim thus at maximizing \n", - "the probability of seeing the observed data. We can then approximate the \n", - "likelihood in terms of the product of the individual probabilities of a specific outcome $y_i$, that is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "P(\\mathcal{D}|\\hat{\\beta})& = \\prod_{i=1}^n \\left[p(y_i=1|x_i,\\hat{\\beta})\\right]^{y_i}\\left[1-p(y_i=1|x_i,\\hat{\\beta}))\\right]^{1-y_i}\\nonumber \\\\\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "from which we obtain the log-likelihood and our **cost/loss** function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathcal{C}(\\hat{\\beta}) = \\sum_{i=1}^n \\left( y_i\\log{p(y_i=1|x_i,\\hat{\\beta})} + (1-y_i)\\log\\left[1-p(y_i=1|x_i,\\hat{\\beta}))\\right]\\right).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The cost function rewritten\n", - "\n", - "Reordering the logarithms, we can rewrite the **cost/loss** function as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathcal{C}(\\hat{\\beta}) = \\sum_{i=1}^n \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The maximum likelihood estimator is defined as the set of parameters that maximize the log-likelihood where we maximize with respect to $\\beta$.\n", - "Since the cost (error) function is just the negative log-likelihood, for logistic regression we have that" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathcal{C}(\\hat{\\beta})=-\\sum_{i=1}^n \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This equation is known in statistics as the **cross entropy**. Finally, we note that just as in linear regression, \n", - "in practice we often supplement the cross-entropy with additional regularization terms, usually $L_1$ and $L_2$ regularization as we did for Ridge and Lasso regression.\n", - "\n", - "## Minimizing the cross entropy\n", - "\n", - "The cross entropy is a convex function of the weights $\\hat{\\beta}$ and,\n", - "therefore, any local minimizer is a global minimizer. \n", - "\n", - "\n", - "Minimizing this\n", - "cost function with respect to the two parameters $\\beta_0$ and $\\beta_1$ we obtain" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial \\mathcal{C}(\\hat{\\beta})}{\\partial \\beta_0} = -\\sum_{i=1}^n \\left(y_i -\\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}}\\right),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial \\mathcal{C}(\\hat{\\beta})}{\\partial \\beta_1} = -\\sum_{i=1}^n \\left(y_ix_i -x_i\\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}}\\right).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## A more compact expression\n", - "\n", - "Let us now define a vector $\\hat{y}$ with $n$ elements $y_i$, an\n", - "$n\\times p$ matrix $\\hat{X}$ which contains the $x_i$ values and a\n", - "vector $\\hat{p}$ of fitted probabilities $p(y_i\\vert x_i,\\hat{\\beta})$. We can rewrite in a more compact form the first\n", - "derivative of cost function as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial \\mathcal{C}(\\hat{\\beta})}{\\partial \\hat{\\beta}} = -\\hat{X}^T\\left(\\hat{y}-\\hat{p}\\right).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If we in addition define a diagonal matrix $\\hat{W}$ with elements \n", - "$p(y_i\\vert x_i,\\hat{\\beta})(1-p(y_i\\vert x_i,\\hat{\\beta})$, we can obtain a compact expression of the second derivative as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial^2 \\mathcal{C}(\\hat{\\beta})}{\\partial \\hat{\\beta}\\partial \\hat{\\beta}^T} = \\hat{X}^T\\hat{W}\\hat{X}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Extending to more predictors\n", - "\n", - "Within a binary classification problem, we can easily expand our model to include multiple predictors. Our ratio between likelihoods is then with $p$ predictors" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\log{ \\frac{p(\\hat{\\beta}\\hat{x})}{1-p(\\hat{\\beta}\\hat{x})}} = \\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we defined $\\hat{x}=[1,x_1,x_2,\\dots,x_p]$ and $\\hat{\\beta}=[\\beta_0, \\beta_1, \\dots, \\beta_p]$ leading to" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(\\hat{\\beta}\\hat{x})=\\frac{ \\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}{1+\\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Including more classes\n", - "\n", - "Till now we have mainly focused on two classes, the so-called binary\n", - "system. Suppose we wish to extend to $K$ classes. Let us for the sake\n", -<<<<<<< HEAD - "of simplicity assume we have only two predictors. We have then\n", - "following model" -======= - "of simplicity assume we have only two predictors. We have then following model" ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ -<<<<<<< HEAD - "1\n", - "5\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "M\n", - "A\n", - "T\n", - "H\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K" -======= - "$$\n", - "\\log{\\frac{p(C=1\\vert x)}{p(K\\vert x)}} = \\beta_{10}+\\beta_{11}x_1,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and" ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\log{\\frac{p(C=2\\vert x)}{p(K\\vert x)}} = \\beta_{20}+\\beta_{21}x_1,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and so on till the class $C=K-1$ class" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\log{\\frac{p(C=K-1\\vert x)}{p(K\\vert x)}} = \\beta_{(K-1)0}+\\beta_{(K-1)1}x_1,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and the model is specified in term of $K-1$ so-called log-odds or\n", - "**logit** transformations.\n", - "\n", - "\n", - "## More classes\n", - "\n", - "In our discussion of neural networks we will encounter the above again\n", - "in terms of a slightly modified function, the so-called **Softmax** function.\n", - "\n", - "The softmax function is used in various multiclass classification\n", - "methods, such as multinomial logistic regression (also known as\n", - "softmax regression), multiclass linear discriminant analysis, naive\n", - "Bayes classifiers, and artificial neural networks. Specifically, in\n", - "multinomial logistic regression and linear discriminant analysis, the\n", - "input to the function is the result of $K$ distinct linear functions,\n", - "and the predicted probability for the $k$-th class given a sample\n", - "vector $\\hat{x}$ and a weighting vector $\\hat{\\beta}$ is (with two\n", - "predictors):" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(C=k\\vert \\mathbf {x} )=\\frac{\\exp{(\\beta_{k0}+\\beta_{k1}x_1)}}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is easy to extend to more predictors. The final class is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(C=K\\vert \\mathbf {x} )=\\frac{1}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and they sum to one. Our earlier discussions were all specialized to\n", - "the case with two classes only. It is easy to see from the above that\n", - "what we derived earlier is compatible with these equations.\n", - "\n", - "To find the optimal parameters we would typically use a gradient\n", - "descent method. Newton's method and gradient descent methods are\n", - "discussed in the material on [optimization\n", - "methods](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html).\n", - "\n", -<<<<<<< HEAD - "\n", - "\n", - "\n", - "## A simple classification problem" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from sklearn import datasets, linear_model\n", - "import matplotlib.pyplot as plt\n", - "\n", - "\n", - "def generate_data():\n", - " np.random.seed(0)\n", - " X, y = datasets.make_moons(200, noise=0.20)\n", - " return X, y\n", - "\n", - "\n", - "def visualize(X, y, clf):\n", - " plot_decision_boundary(lambda x: clf.predict(x), X, y)\n", - "\n", - "def plot_decision_boundary(pred_func, X, y):\n", - " # Set min and max values and give it some padding\n", - " x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n", - " y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n", - " h = 0.01\n", - " # Generate a grid of points with distance h between them\n", - " xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n", - " # Predict the function value for the whole gid\n", - " Z = pred_func(np.c_[xx.ravel(), yy.ravel()])\n", - " Z = Z.reshape(xx.shape)\n", - " # Plot the contour and training examples\n", - " plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)\n", - " plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)\n", - " plt.show()\n", - "\n", - "\n", - "def classify(X, y):\n", - " clf = linear_model.LogisticRegressionCV()\n", - " clf.fit(X, y)\n", - " return clf\n", - "\n", - "\n", - "def main():\n", - " X, y = generate_data()\n", - " # visualize(X, y)\n", - " clf = classify(X, y)\n", - " visualize(X, y, clf)\n", - "\n", - "if __name__ == \"__main__\":\n", - " main()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Cancer Data again now with Decision Trees and other Methods" -======= - "This will be discussed next week. Before we develop our own codes for logistic regression, we end this lecture by studying the functionality that **Scikit-learn** offers. \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Wisconsin Cancer Data\n", - "\n", - "We show here how we can use a simple regression case on the breast\n", - "cancer data using Logistic regression as our algorithm for\n", - "classification." ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - ] - }, - { - "cell_type": "code", -<<<<<<< HEAD - "execution_count": 3, - "metadata": {}, - "outputs": [], -======= - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(426, 30)\n", - "(143, 30)\n", - "Test set accuracy with Logistic Regression: 0.95\n", - "Test set accuracy Logistic Regression with scaled data: 0.96\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:762: ConvergenceWarning: lbfgs failed to converge (status=1):\n", - "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n", - "\n", - "Increase the number of iterations (max_iter) or scale the data as shown in:\n", - " https://scikit-learn.org/stable/modules/preprocessing.html\n", - "Please also refer to the documentation for alternative solver options:\n", - " https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n", - " n_iter_i = _check_optimize_result(\n" - ] - } - ], ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - "source": [ - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "from sklearn.model_selection import train_test_split \n", - "from sklearn.datasets import load_breast_cancer\n", - "from sklearn.linear_model import LogisticRegression\n", - "\n", - "# Load the data\n", - "cancer = load_breast_cancer()\n", - "\n", - "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n", - "print(X_train.shape)\n", - "print(X_test.shape)\n", - "# Logistic Regression\n", - "logreg = LogisticRegression(solver='lbfgs')\n", - "logreg.fit(X_train, y_train)\n", - "print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n", - "#now scale the data\n", - "from sklearn.preprocessing import StandardScaler\n", - "scaler = StandardScaler()\n", - "scaler.fit(X_train)\n", - "X_train_scaled = scaler.transform(X_train)\n", - "X_test_scaled = scaler.transform(X_test)\n", - "# Logistic Regression\n", - "logreg.fit(X_train_scaled, y_train)\n", - "print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ -<<<<<<< HEAD - "## Other measures in classification studies: Cancer Data again" -======= - "## Using the correlation matrix\n", - "\n", - "In addition to the above scores, we could also study the covariance (and the correlation matrix).\n", - "We use **Pandas** to compute the correlation matrix." ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - ] - }, - { - "cell_type": "code", -<<<<<<< HEAD - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ -======= - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", - "text/plain": [ - "
    " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "from sklearn.model_selection import train_test_split \n", - "from sklearn.datasets import load_breast_cancer\n", - "from sklearn.linear_model import LogisticRegression\n", - "cancer = load_breast_cancer()\n", - "import pandas as pd\n", - "# Making a data frame\n", - "cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n", - "\n", - "fig, axes = plt.subplots(15,2,figsize=(10,20))\n", - "malignant = cancer.data[cancer.target == 0]\n", - "benign = cancer.data[cancer.target == 1]\n", - "ax = axes.ravel()\n", - "\n", - "for i in range(30):\n", - " _, bins = np.histogram(cancer.data[:,i], bins =50)\n", - " ax[i].hist(malignant[:,i], bins = bins, alpha = 0.5)\n", - " ax[i].hist(benign[:,i], bins = bins, alpha = 0.5)\n", - " ax[i].set_title(cancer.feature_names[i])\n", - " ax[i].set_yticks(())\n", - "ax[0].set_xlabel(\"Feature magnitude\")\n", - "ax[0].set_ylabel(\"Frequency\")\n", - "ax[0].legend([\"Malignant\", \"Benign\"], loc =\"best\")\n", - "fig.tight_layout()\n", - "plt.show()\n", - "\n", - "import seaborn as sns\n", - "correlation_matrix = cancerpd.corr().round(1)\n", - "# use the heatmap function from seaborn to plot the correlation matrix\n", - "# annot = True to print the values inside the square\n", - "plt.figure(figsize=(15,8))\n", - "sns.heatmap(data=correlation_matrix, annot=True)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Discussing the correlation data\n", - "\n", - "In the above example we note two things. In the first plot we display\n", - "the overlap of benign and malignant tumors as functions of the various\n", - "features in the Wisconsing breast cancer data set. We see that for\n", - "some of the features we can distinguish clearly the benign and\n", - "malignant cases while for other features we cannot. This can point to\n", - "us which features may be of greater interest when we wish to classify\n", - "a benign or not benign tumour.\n", - "\n", - "In the second figure we have computed the so-called correlation\n", - "matrix, which in our case with thirty features becomes a $30\\times 30$\n", - "matrix.\n", - "\n", - "We constructed this matrix using **pandas** via the statements" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [], - "source": [ - "cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and then" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [], - "source": [ - "correlation_matrix = cancerpd.corr().round(1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Diagonalizing this matrix we can in turn say something about which\n", - "features are of relevance and which are not. This leads us to\n", - "the classical Principal Component Analysis (PCA) theorem with\n", - "applications. This will be discussed later this semester ([week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html)).\n", - "\n", - "\n", - "\n", - "## Other measures in classification studies: Cancer Data again" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(426, 30)\n", - "(143, 30)\n", - "Test set accuracy with Logistic Regression: 0.95\n", - "Test set accuracy Logistic Regression with scaled data: 0.96\n", - "[1. 1. 1. 1. 1. 1.\n", - " 1. 1. 0.92857143 0.92857143]\n", - "Test set accuracy with Logistic Regression and scaled data: 0.96\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:762: ConvergenceWarning: lbfgs failed to converge (status=1):\n", - "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n", - "\n", - "Increase the number of iterations (max_iter) or scale the data as shown in:\n", - " https://scikit-learn.org/stable/modules/preprocessing.html\n", - "Please also refer to the documentation for alternative solver options:\n", - " https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n", - " n_iter_i = _check_optimize_result(\n" - ] - }, - { - "ename": "ModuleNotFoundError", - "evalue": "No module named 'scikitplot'", - "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 34\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 35\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 36\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mscikitplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mskplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 37\u001b[0m \u001b[0my_pred\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlogreg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_test_scaled\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 38\u001b[0m \u001b[0mskplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmetrics\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot_confusion_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_pred\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnormalize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'scikitplot'" - ] - } - ], - "source": [ ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "from sklearn.model_selection import train_test_split \n", - "from sklearn.datasets import load_breast_cancer\n", - "from sklearn.linear_model import LogisticRegression\n", - "\n", - "# Load the data\n", - "cancer = load_breast_cancer()\n", - "\n", - "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n", - "print(X_train.shape)\n", - "print(X_test.shape)\n", - "# Logistic Regression\n", - "logreg = LogisticRegression(solver='lbfgs')\n", - "logreg.fit(X_train, y_train)\n", - "print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n", - "#now scale the data\n", - "from sklearn.preprocessing import StandardScaler\n", - "scaler = StandardScaler()\n", - "scaler.fit(X_train)\n", - "X_train_scaled = scaler.transform(X_train)\n", - "X_test_scaled = scaler.transform(X_test)\n", - "# Logistic Regression\n", - "logreg.fit(X_train_scaled, y_train)\n", - "print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n", - "\n", - "\n", - "from sklearn.preprocessing import LabelEncoder\n", - "from sklearn.model_selection import cross_validate\n", - "#Cross validation\n", - "accuracy = cross_validate(logreg,X_test_scaled,y_test,cv=10)['test_score']\n", - "print(accuracy)\n", - "print(\"Test set accuracy with Logistic Regression and scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n", - "\n", - "\n", - "import scikitplot as skplt\n", - "y_pred = logreg.predict(X_test_scaled)\n", - "skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n", - "plt.show()\n", - "y_probas = logreg.predict_proba(X_test_scaled)\n", - "skplt.metrics.plot_roc(y_test, y_probas)\n", - "plt.show()\n", - "skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n", - "plt.show()" - ] -<<<<<<< HEAD -======= - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 } ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -2759,13 +2315,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", -<<<<<<< HEAD - "version": "3.6.8" -======= - "version": "3.8.3" ->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252 + "version": "3.9.15" } }, "nbformat": 4, - "nbformat_minor": 2 + "nbformat_minor": 5 } diff --git a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz index ab65f845bc67e1706df34d5d432b21c1e02ae262..99906213f2606093f500fa8fa4282242a746ea9d 100644 GIT binary patch delta 63 zcmWN_ISqh7002S$J$?m*1R>{*Vhe%<+Oq%}kOfmtdSZGa>lw0Rdv_$4LQ1KmmPY;z P(n=@23^K}eGcVT%EG!Rs delta 63 zcmWN_IT3&`002S$3xr1jgOiBD0mW5Fpp6BvfGyZ^^ON$E*v?Sw@jZ}IDygNBRyz4J PNH2p#8D*0BW?8QfBDoJr diff --git a/doc/pub/week38/ipynb/week38.ipynb b/doc/pub/week38/ipynb/week38.ipynb index 471b4dd49..1d25f9941 100644 --- a/doc/pub/week38/ipynb/week38.ipynb +++ b/doc/pub/week38/ipynb/week38.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "799137cd", + "id": "8f27372d", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "f5b17715", + "id": "fff8ca30", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "cc859721", + "id": "7ee7e714", "metadata": { "editable": true }, @@ -41,13 +41,15 @@ "2. Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff\n", "\n", "3. The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at \n", - "\n", - "" + "\n", + "4. [Video of Lecture](https://youtu.be/4Fo7ITVA7V4)\n", + "\n", + "5. [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek38.pdf)" ] }, { "cell_type": "markdown", - "id": "a3ecb019", + "id": "3b5ac440", "metadata": { "editable": true }, @@ -68,7 +70,7 @@ }, { "cell_type": "markdown", - "id": "f128464d", + "id": "6d5dba52", "metadata": { "editable": true }, @@ -96,7 +98,7 @@ }, { "cell_type": "markdown", - "id": "981db0b8", + "id": "bfc2983a", "metadata": { "editable": true }, @@ -112,7 +114,7 @@ }, { "cell_type": "markdown", - "id": "85cc8db5", + "id": "2b5f5980", "metadata": { "editable": true }, @@ -131,7 +133,7 @@ }, { "cell_type": "markdown", - "id": "96a431a6", + "id": "3464c7e8", "metadata": { "editable": true }, @@ -145,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "b6bf35de", + "id": "ed0fd2df", "metadata": { "editable": true }, @@ -157,7 +159,7 @@ }, { "cell_type": "markdown", - "id": "a4133715", + "id": "feb9d4c2", "metadata": { "editable": true }, @@ -168,7 +170,7 @@ }, { "cell_type": "markdown", - "id": "9d8eea64", + "id": "eb6d71f8", "metadata": { "editable": true }, @@ -180,7 +182,7 @@ }, { "cell_type": "markdown", - "id": "0707109a", + "id": "566399f6", "metadata": { "editable": true }, @@ -192,7 +194,7 @@ }, { "cell_type": "markdown", - "id": "c84ee75e", + "id": "6b33f497", "metadata": { "editable": true }, @@ -208,7 +210,7 @@ }, { "cell_type": "markdown", - "id": "eceb2fb1", + "id": "5f2f79f2", "metadata": { "editable": true }, @@ -219,7 +221,7 @@ }, { "cell_type": "markdown", - "id": "571c857b", + "id": "199121b0", "metadata": { "editable": true }, @@ -242,7 +244,7 @@ }, { "cell_type": "markdown", - "id": "fa94afa6", + "id": "9a1cc529", "metadata": { "editable": true }, @@ -253,7 +255,7 @@ }, { "cell_type": "markdown", - "id": "ae5807fe", + "id": "149e63be", "metadata": { "editable": true }, @@ -265,7 +267,7 @@ }, { "cell_type": "markdown", - "id": "9b7dbfc6", + "id": "6a6fb04a", "metadata": { "editable": true }, @@ -277,7 +279,7 @@ }, { "cell_type": "markdown", - "id": "a469ecb5", + "id": "79420d06", "metadata": { "editable": true }, @@ -291,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "a22a5899", + "id": "0e3de992", "metadata": { "editable": true }, @@ -322,7 +324,7 @@ }, { "cell_type": "markdown", - "id": "f7b64841", + "id": "d3ea2897", "metadata": { "editable": true }, @@ -344,7 +346,7 @@ }, { "cell_type": "markdown", - "id": "26d50d5c", + "id": "da5e3927", "metadata": { "editable": true }, @@ -356,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "e2e18a10", + "id": "7ab5488b", "metadata": { "editable": true }, @@ -369,7 +371,7 @@ }, { "cell_type": "markdown", - "id": "9a97e0bb", + "id": "f904a739", "metadata": { "editable": true }, @@ -381,7 +383,7 @@ }, { "cell_type": "markdown", - "id": "53cef62d", + "id": "10fd648b", "metadata": { "editable": true }, @@ -393,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "c8ec4ab0", + "id": "4812c2a4", "metadata": { "editable": true }, @@ -405,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "1e5e5e07", + "id": "199d8531", "metadata": { "editable": true }, @@ -417,7 +419,7 @@ }, { "cell_type": "markdown", - "id": "b1ea4ea7", + "id": "96c16676", "metadata": { "editable": true }, @@ -440,7 +442,7 @@ }, { "cell_type": "markdown", - "id": "d9c8dd38", + "id": "a2a1a004", "metadata": { "editable": true }, @@ -452,7 +454,7 @@ }, { "cell_type": "markdown", - "id": "7abb690f", + "id": "5aad445b", "metadata": { "editable": true }, @@ -465,7 +467,7 @@ }, { "cell_type": "markdown", - "id": "417c8406", + "id": "d197c8bb", "metadata": { "editable": true }, @@ -477,7 +479,7 @@ }, { "cell_type": "markdown", - "id": "fb01419c", + "id": "e2e7462f", "metadata": { "editable": true }, @@ -489,7 +491,7 @@ }, { "cell_type": "markdown", - "id": "dbe14673", + "id": "eb635d3d", "metadata": { "editable": true }, @@ -501,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "a19153fe", + "id": "445ed13e", "metadata": { "editable": true }, @@ -512,7 +514,7 @@ }, { "cell_type": "markdown", - "id": "017ca4ca", + "id": "319bfc6c", "metadata": { "editable": true }, @@ -524,7 +526,7 @@ }, { "cell_type": "markdown", - "id": "85c7bc4a", + "id": "90abf35a", "metadata": { "editable": true }, @@ -535,7 +537,7 @@ }, { "cell_type": "markdown", - "id": "ad6066d5", + "id": "04b66fbd", "metadata": { "editable": true }, @@ -547,7 +549,7 @@ }, { "cell_type": "markdown", - "id": "7d9872d8", + "id": "4a27b5a7", "metadata": { "editable": true }, @@ -557,7 +559,7 @@ }, { "cell_type": "markdown", - "id": "e3973752", + "id": "8d12543f", "metadata": { "editable": true }, @@ -588,7 +590,7 @@ }, { "cell_type": "markdown", - "id": "5adedf8a", + "id": "2e5cd118", "metadata": { "editable": true }, @@ -600,7 +602,7 @@ }, { "cell_type": "markdown", - "id": "23e01c9e", + "id": "c71a5edf", "metadata": { "editable": true }, @@ -612,7 +614,7 @@ }, { "cell_type": "markdown", - "id": "94cc3cc3", + "id": "e663bf2e", "metadata": { "editable": true }, @@ -622,7 +624,7 @@ }, { "cell_type": "markdown", - "id": "0e3f94c9", + "id": "c4bc4873", "metadata": { "editable": true }, @@ -634,7 +636,7 @@ }, { "cell_type": "markdown", - "id": "b8dcd25e", + "id": "f5bc59b8", "metadata": { "editable": true }, @@ -644,7 +646,7 @@ }, { "cell_type": "markdown", - "id": "9140542c", + "id": "4f6ddf4a", "metadata": { "editable": true }, @@ -656,7 +658,7 @@ }, { "cell_type": "markdown", - "id": "294a8ce0", + "id": "afda0a6b", "metadata": { "editable": true }, @@ -666,7 +668,7 @@ }, { "cell_type": "markdown", - "id": "a8c1b097", + "id": "b5335dc0", "metadata": { "editable": true }, @@ -678,7 +680,7 @@ }, { "cell_type": "markdown", - "id": "4180c17f", + "id": "4f86a52d", "metadata": { "editable": true }, @@ -688,7 +690,7 @@ }, { "cell_type": "markdown", - "id": "6a48bb05", + "id": "5cdb1767", "metadata": { "editable": true }, @@ -707,7 +709,7 @@ }, { "cell_type": "markdown", - "id": "d053a5c8", + "id": "69435d77", "metadata": { "editable": true }, @@ -735,7 +737,7 @@ }, { "cell_type": "markdown", - "id": "8cb550a1", + "id": "cefbb559", "metadata": { "editable": true }, @@ -761,7 +763,7 @@ }, { "cell_type": "markdown", - "id": "96be5396", + "id": "2659401a", "metadata": { "editable": true }, @@ -778,7 +780,7 @@ }, { "cell_type": "markdown", - "id": "f8a288b4", + "id": "4d5d7748", "metadata": { "editable": true }, @@ -798,7 +800,7 @@ }, { "cell_type": "markdown", - "id": "ee8bd2f9", + "id": "54df92b3", "metadata": { "editable": true }, @@ -827,7 +829,7 @@ }, { "cell_type": "markdown", - "id": "1037fcf3", + "id": "5b1a1390", "metadata": { "editable": true }, @@ -852,7 +854,7 @@ }, { "cell_type": "markdown", - "id": "2653d9e3", + "id": "39f233e4", "metadata": { "editable": true }, @@ -872,7 +874,7 @@ }, { "cell_type": "markdown", - "id": "33e4596e", + "id": "361320d8", "metadata": { "editable": true }, @@ -884,7 +886,7 @@ }, { "cell_type": "markdown", - "id": "137d3cd6", + "id": "a363db1e", "metadata": { "editable": true }, @@ -894,7 +896,7 @@ }, { "cell_type": "markdown", - "id": "4c9853b7", + "id": "92967efc", "metadata": { "editable": true }, @@ -909,7 +911,7 @@ }, { "cell_type": "markdown", - "id": "493028c4", + "id": "1bffca97", "metadata": { "editable": true }, @@ -922,7 +924,7 @@ }, { "cell_type": "markdown", - "id": "c819e616", + "id": "0dacb6fc", "metadata": { "editable": true }, @@ -935,7 +937,7 @@ }, { "cell_type": "markdown", - "id": "f0385e1a", + "id": "baeedf81", "metadata": { "editable": true }, @@ -947,7 +949,7 @@ }, { "cell_type": "markdown", - "id": "4310a9b4", + "id": "20cc7770", "metadata": { "editable": true }, @@ -960,7 +962,7 @@ }, { "cell_type": "markdown", - "id": "1e3932be", + "id": "f67d3b94", "metadata": { "editable": true }, @@ -971,7 +973,7 @@ }, { "cell_type": "markdown", - "id": "91e64919", + "id": "17f59fb6", "metadata": { "editable": true }, @@ -985,7 +987,7 @@ }, { "cell_type": "markdown", - "id": "c83a8ca5", + "id": "5f899fbe", "metadata": { "editable": true }, @@ -995,7 +997,7 @@ }, { "cell_type": "markdown", - "id": "16c94c48", + "id": "19a1f5bb", "metadata": { "editable": true }, @@ -1009,7 +1011,7 @@ }, { "cell_type": "markdown", - "id": "63bc9d16", + "id": "1db8fcf2", "metadata": { "editable": true }, @@ -1022,7 +1024,7 @@ }, { "cell_type": "markdown", - "id": "710fedd5", + "id": "bfadf7e5", "metadata": { "editable": true }, @@ -1035,7 +1037,7 @@ }, { "cell_type": "markdown", - "id": "8c47e8f8", + "id": "7c65ce24", "metadata": { "editable": true }, @@ -1045,7 +1047,7 @@ }, { "cell_type": "markdown", - "id": "c0e43db3", + "id": "8cd5650a", "metadata": { "editable": true }, @@ -1058,7 +1060,7 @@ }, { "cell_type": "markdown", - "id": "e9a40705", + "id": "11fdc936", "metadata": { "editable": true }, @@ -1068,7 +1070,7 @@ }, { "cell_type": "markdown", - "id": "de6040d9", + "id": "ed88642e", "metadata": { "editable": true }, @@ -1081,7 +1083,7 @@ }, { "cell_type": "markdown", - "id": "f2907638", + "id": "82c61b81", "metadata": { "editable": true }, @@ -1093,7 +1095,7 @@ }, { "cell_type": "markdown", - "id": "9e53d173", + "id": "bc43db46", "metadata": { "editable": true }, @@ -1112,7 +1114,7 @@ }, { "cell_type": "markdown", - "id": "959c77be", + "id": "25418113", "metadata": { "editable": true }, @@ -1125,7 +1127,7 @@ }, { "cell_type": "markdown", - "id": "6470ab77", + "id": "e5d3c3eb", "metadata": { "editable": true }, @@ -1137,7 +1139,7 @@ }, { "cell_type": "markdown", - "id": "720c157a", + "id": "c504cba4", "metadata": { "editable": true }, @@ -1150,7 +1152,7 @@ }, { "cell_type": "markdown", - "id": "62c153d3", + "id": "079ded2a", "metadata": { "editable": true }, @@ -1170,7 +1172,7 @@ }, { "cell_type": "markdown", - "id": "cfd10bd9", + "id": "e8534a50", "metadata": { "editable": true }, @@ -1193,7 +1195,7 @@ }, { "cell_type": "markdown", - "id": "40dc022d", + "id": "2fc73431", "metadata": { "editable": true }, @@ -1208,7 +1210,7 @@ }, { "cell_type": "markdown", - "id": "242bfa08", + "id": "0f8b0845", "metadata": { "editable": true }, @@ -1220,7 +1222,7 @@ }, { "cell_type": "markdown", - "id": "7dd4616b", + "id": "25105753", "metadata": { "editable": true }, @@ -1240,7 +1242,7 @@ }, { "cell_type": "markdown", - "id": "00b509e4", + "id": "89be6eea", "metadata": { "editable": true }, @@ -1260,7 +1262,7 @@ }, { "cell_type": "markdown", - "id": "941834ae", + "id": "6c240b38", "metadata": { "editable": true }, @@ -1284,7 +1286,7 @@ }, { "cell_type": "markdown", - "id": "69ba3346", + "id": "fbd95a5c", "metadata": { "editable": true }, @@ -1305,7 +1307,7 @@ }, { "cell_type": "markdown", - "id": "99f1499e", + "id": "dc50d43a", "metadata": { "editable": true }, @@ -1335,7 +1337,7 @@ }, { "cell_type": "markdown", - "id": "c817851a", + "id": "283068cc", "metadata": { "editable": true }, @@ -1359,7 +1361,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "4b9647f3", + "id": "ff4790ba", "metadata": { "collapsed": false, "editable": true @@ -1398,7 +1400,7 @@ }, { "cell_type": "markdown", - "id": "26cf7fd4", + "id": "3e6adc2f", "metadata": { "editable": true }, @@ -1408,7 +1410,7 @@ }, { "cell_type": "markdown", - "id": "b2205188", + "id": "6ec8223c", "metadata": { "editable": true }, @@ -1419,7 +1421,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "be6f7ced", + "id": "3cf4144d", "metadata": { "collapsed": false, "editable": true @@ -1439,7 +1441,7 @@ }, { "cell_type": "markdown", - "id": "69bcb406", + "id": "db5a8f91", "metadata": { "editable": true }, @@ -1457,7 +1459,7 @@ }, { "cell_type": "markdown", - "id": "ce87dc4f", + "id": "327bce6a", "metadata": { "editable": true }, @@ -1469,7 +1471,7 @@ }, { "cell_type": "markdown", - "id": "b8d1371c", + "id": "1c671d4e", "metadata": { "editable": true }, @@ -1486,7 +1488,7 @@ }, { "cell_type": "markdown", - "id": "c95f3051", + "id": "6e05fc43", "metadata": { "editable": true }, @@ -1498,7 +1500,7 @@ }, { "cell_type": "markdown", - "id": "107fab0a", + "id": "c45e0752", "metadata": { "editable": true }, @@ -1508,7 +1510,7 @@ }, { "cell_type": "markdown", - "id": "d56b4bd7", + "id": "bafa4ab6", "metadata": { "editable": true }, @@ -1520,7 +1522,7 @@ }, { "cell_type": "markdown", - "id": "4712d813", + "id": "ea0bc471", "metadata": { "editable": true }, @@ -1537,7 +1539,7 @@ }, { "cell_type": "markdown", - "id": "43a58a59", + "id": "08b603f3", "metadata": { "editable": true }, @@ -1549,7 +1551,7 @@ }, { "cell_type": "markdown", - "id": "6333f694", + "id": "4114d10e", "metadata": { "editable": true }, @@ -1559,7 +1561,7 @@ }, { "cell_type": "markdown", - "id": "24e27c2b", + "id": "8890c666", "metadata": { "editable": true }, @@ -1571,7 +1573,7 @@ }, { "cell_type": "markdown", - "id": "0462c197", + "id": "7d5b7ce4", "metadata": { "editable": true }, @@ -1581,7 +1583,7 @@ }, { "cell_type": "markdown", - "id": "965cd453", + "id": "3913c5b9", "metadata": { "editable": true }, @@ -1593,7 +1595,7 @@ }, { "cell_type": "markdown", - "id": "4426c74e", + "id": "5e0067b1", "metadata": { "editable": true }, @@ -1603,7 +1605,7 @@ }, { "cell_type": "markdown", - "id": "d68ec470", + "id": "326bc8f1", "metadata": { "editable": true }, @@ -1619,7 +1621,7 @@ }, { "cell_type": "markdown", - "id": "0198c371", + "id": "d3713eca", "metadata": { "editable": true }, @@ -1630,7 +1632,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "af517050", + "id": "01c3b507", "metadata": { "collapsed": false, "editable": true @@ -1695,7 +1697,7 @@ }, { "cell_type": "markdown", - "id": "2b502d1d", + "id": "949e3a5e", "metadata": { "editable": true }, @@ -1706,7 +1708,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "9a5194fb", + "id": "7e7f4926", "metadata": { "collapsed": false, "editable": true @@ -1763,7 +1765,7 @@ }, { "cell_type": "markdown", - "id": "727c7723", + "id": "33c5cae5", "metadata": { "editable": true }, @@ -1801,7 +1803,7 @@ }, { "cell_type": "markdown", - "id": "7e90566c", + "id": "f931f0f2", "metadata": { "editable": true }, @@ -1828,7 +1830,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "7c760f15", + "id": "58daa28d", "metadata": { "collapsed": false, "editable": true @@ -1890,7 +1892,7 @@ }, { "cell_type": "markdown", - "id": "2619ab70", + "id": "3bbcf741", "metadata": { "editable": true }, @@ -1915,7 +1917,7 @@ }, { "cell_type": "markdown", - "id": "3e4d0bdb", + "id": "4b0ffe06", "metadata": { "editable": true }, @@ -1943,7 +1945,7 @@ }, { "cell_type": "markdown", - "id": "65d5f3f5", + "id": "b11baed6", "metadata": { "editable": true }, @@ -1956,7 +1958,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "66c55986", + "id": "39e76d49", "metadata": { "collapsed": false, "editable": true @@ -2056,7 +2058,7 @@ }, { "cell_type": "markdown", - "id": "8bd8e7a8", + "id": "e7d12ef0", "metadata": { "editable": true }, @@ -2067,7 +2069,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "2b363d73", + "id": "47f6ae18", "metadata": { "collapsed": false, "editable": true @@ -2156,7 +2158,7 @@ }, { "cell_type": "markdown", - "id": "de30ce89", + "id": "9c1d4754", "metadata": { "editable": true }, @@ -2166,7 +2168,7 @@ }, { "cell_type": "markdown", - "id": "936b8f0f", + "id": "b698ac66", "metadata": { "editable": true }, @@ -2179,7 +2181,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "399b09d4", + "id": "0a2409b0", "metadata": { "collapsed": false, "editable": true @@ -2257,7 +2259,7 @@ }, { "cell_type": "markdown", - "id": "ded3c9a0", + "id": "56f130b5", "metadata": { "editable": true }, diff --git a/doc/src/week38/week38.do.txt b/doc/src/week38/week38.do.txt index 26a521da8..18367d6b9 100644 --- a/doc/src/week38/week38.do.txt +++ b/doc/src/week38/week38.do.txt @@ -11,8 +11,8 @@ DATE: September 15-19, 2025 o Statistical interpretation of OLS and various expectation values o Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff o The material we did not cover last week, that is on more advanced methods for updating the learning rate, are covered by its own video. We will briefly discuss these topics at the beginning of the lecture and during the lab sessions. See video on ADAgrad, RMSprop and ADAM (material from last week not covered during lecture) at URL:"https://youtu.be/J_41Hld6tTU" -# * "Video of Lecture":"https://youtu.be/omLmp_kkie0" -# * "Whiteboard notes":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember9.pdf" +o "Video of Lecture":"https://youtu.be/4Fo7ITVA7V4" +o "Whiteboard notes":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek38.pdf" !eblock