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/pub/week38/html/week38-reveal.html b/doc/pub/week38/html/week38-reveal.html index 9ec741115..94ba9db0a 100644 --- a/doc/pub/week38/html/week38-reveal.html +++ b/doc/pub/week38/html/week38-reveal.html @@ -526,14 +526,14 @@ is equivalent to the maximization/minimization of the function itself.
$$
-C(\boldsymbol{\theta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
+C(\boldsymbol{\theta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
$$
which becomes
$$
-C(\boldsymbol{\theta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\theta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
$$
diff --git a/doc/pub/week38/html/week38-solarized.html b/doc/pub/week38/html/week38-solarized.html
index de2ecd7f0..bb7857a3f 100644
--- a/doc/pub/week38/html/week38-solarized.html
+++ b/doc/pub/week38/html/week38-solarized.html
@@ -527,12 +527,12 @@ 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/pub/week38/html/week38.html b/doc/pub/week38/html/week38.html index 366c5f576..fb0c0fad3 100644 --- a/doc/pub/week38/html/week38.html +++ b/doc/pub/week38/html/week38.html @@ -604,12 +604,12 @@ 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/pub/week38/ipynb/ipynb-week38-src.tar.gz b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz index b68a1c64d..ab65f845b 100644 Binary files a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz and b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz differ diff --git a/doc/pub/week38/ipynb/week38.ipynb b/doc/pub/week38/ipynb/week38.ipynb index 544d286d0..471b4dd49 100644 --- a/doc/pub/week38/ipynb/week38.ipynb +++ b/doc/pub/week38/ipynb/week38.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "169923b3", + "id": "799137cd", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "47013ee7", + "id": "f5b17715", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "d1fb5464", + "id": "cc859721", "metadata": { "editable": true }, @@ -47,7 +47,7 @@ }, { "cell_type": "markdown", - "id": "1a34a7ce", + "id": "a3ecb019", "metadata": { "editable": true }, @@ -68,7 +68,7 @@ }, { "cell_type": "markdown", - "id": "c6f56f83", + "id": "f128464d", "metadata": { "editable": true }, @@ -96,7 +96,7 @@ }, { "cell_type": "markdown", - "id": "3ece0c04", + "id": "981db0b8", "metadata": { "editable": true }, @@ -112,7 +112,7 @@ }, { "cell_type": "markdown", - "id": "d36cf6db", + "id": "85cc8db5", "metadata": { "editable": true }, @@ -131,7 +131,7 @@ }, { "cell_type": "markdown", - "id": "5903d2be", + "id": "96a431a6", "metadata": { "editable": true }, @@ -145,7 +145,7 @@ }, { "cell_type": "markdown", - "id": "37f4e199", + "id": "b6bf35de", "metadata": { "editable": true }, @@ -157,7 +157,7 @@ }, { "cell_type": "markdown", - "id": "7a7b084f", + "id": "a4133715", "metadata": { "editable": true }, @@ -168,7 +168,7 @@ }, { "cell_type": "markdown", - "id": "1ec511a1", + "id": "9d8eea64", "metadata": { "editable": true }, @@ -180,7 +180,7 @@ }, { "cell_type": "markdown", - "id": "ffe76935", + "id": "0707109a", "metadata": { "editable": true }, @@ -192,7 +192,7 @@ }, { "cell_type": "markdown", - "id": "e569274a", + "id": "c84ee75e", "metadata": { "editable": true }, @@ -208,7 +208,7 @@ }, { "cell_type": "markdown", - "id": "c4dd2623", + "id": "eceb2fb1", "metadata": { "editable": true }, @@ -219,7 +219,7 @@ }, { "cell_type": "markdown", - "id": "df2f8936", + "id": "571c857b", "metadata": { "editable": true }, @@ -242,7 +242,7 @@ }, { "cell_type": "markdown", - "id": "0a3e5956", + "id": "fa94afa6", "metadata": { "editable": true }, @@ -253,7 +253,7 @@ }, { "cell_type": "markdown", - "id": "973e45a3", + "id": "ae5807fe", "metadata": { "editable": true }, @@ -265,7 +265,7 @@ }, { "cell_type": "markdown", - "id": "ff486d1e", + "id": "9b7dbfc6", "metadata": { "editable": true }, @@ -277,7 +277,7 @@ }, { "cell_type": "markdown", - "id": "e4307815", + "id": "a469ecb5", "metadata": { "editable": true }, @@ -291,7 +291,7 @@ }, { "cell_type": "markdown", - "id": "490b2cbf", + "id": "a22a5899", "metadata": { "editable": true }, @@ -322,7 +322,7 @@ }, { "cell_type": "markdown", - "id": "5d8dd6bc", + "id": "f7b64841", "metadata": { "editable": true }, @@ -344,7 +344,7 @@ }, { "cell_type": "markdown", - "id": "3594078a", + "id": "26d50d5c", "metadata": { "editable": true }, @@ -356,7 +356,7 @@ }, { "cell_type": "markdown", - "id": "43007b7a", + "id": "e2e18a10", "metadata": { "editable": true }, @@ -369,7 +369,7 @@ }, { "cell_type": "markdown", - "id": "3cd4e7da", + "id": "9a97e0bb", "metadata": { "editable": true }, @@ -381,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "5816b21e", + "id": "53cef62d", "metadata": { "editable": true }, @@ -393,7 +393,7 @@ }, { "cell_type": "markdown", - "id": "b58b8607", + "id": "c8ec4ab0", "metadata": { "editable": true }, @@ -405,7 +405,7 @@ }, { "cell_type": "markdown", - "id": "c843db7f", + "id": "1e5e5e07", "metadata": { "editable": true }, @@ -417,7 +417,7 @@ }, { "cell_type": "markdown", - "id": "e81b1c39", + "id": "b1ea4ea7", "metadata": { "editable": true }, @@ -440,7 +440,7 @@ }, { "cell_type": "markdown", - "id": "ea9719e3", + "id": "d9c8dd38", "metadata": { "editable": true }, @@ -452,7 +452,7 @@ }, { "cell_type": "markdown", - "id": "c28b598f", + "id": "7abb690f", "metadata": { "editable": true }, @@ -465,7 +465,7 @@ }, { "cell_type": "markdown", - "id": "88063ed7", + "id": "417c8406", "metadata": { "editable": true }, @@ -477,7 +477,7 @@ }, { "cell_type": "markdown", - "id": "a34e4c28", + "id": "fb01419c", "metadata": { "editable": true }, @@ -489,7 +489,7 @@ }, { "cell_type": "markdown", - "id": "1fc7ae0a", + "id": "dbe14673", "metadata": { "editable": true }, @@ -501,7 +501,7 @@ }, { "cell_type": "markdown", - "id": "30d5a1be", + "id": "a19153fe", "metadata": { "editable": true }, @@ -512,7 +512,7 @@ }, { "cell_type": "markdown", - "id": "1d29fd29", + "id": "017ca4ca", "metadata": { "editable": true }, @@ -524,7 +524,7 @@ }, { "cell_type": "markdown", - "id": "289a116c", + "id": "85c7bc4a", "metadata": { "editable": true }, @@ -535,7 +535,7 @@ }, { "cell_type": "markdown", - "id": "d1cfbb56", + "id": "ad6066d5", "metadata": { "editable": true }, @@ -547,7 +547,7 @@ }, { "cell_type": "markdown", - "id": "e089fc0e", + "id": "7d9872d8", "metadata": { "editable": true }, @@ -557,7 +557,7 @@ }, { "cell_type": "markdown", - "id": "32cf9944", + "id": "e3973752", "metadata": { "editable": true }, @@ -588,7 +588,7 @@ }, { "cell_type": "markdown", - "id": "ee8a9544", + "id": "5adedf8a", "metadata": { "editable": true }, @@ -600,19 +600,19 @@ }, { "cell_type": "markdown", - "id": "4bfeb203", + "id": "23e01c9e", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\theta}=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})},\n", + "C(\\boldsymbol{\\theta})=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\theta})},\n", "$$" ] }, { "cell_type": "markdown", - "id": "256143f9", + "id": "94cc3cc3", "metadata": { "editable": true }, @@ -622,19 +622,19 @@ }, { "cell_type": "markdown", - "id": "60d75bb1", + "id": "0e3f94c9", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\theta}=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta})\\vert\\vert_2^2}{2\\sigma^2}.\n", + "C(\\boldsymbol{\\theta})=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\theta})\\vert\\vert_2^2}{2\\sigma^2}.\n", "$$" ] }, { "cell_type": "markdown", - "id": "7b111014", + "id": "b8dcd25e", "metadata": { "editable": true }, @@ -644,7 +644,7 @@ }, { "cell_type": "markdown", - "id": "0f42a0b5", + "id": "9140542c", "metadata": { "editable": true }, @@ -656,7 +656,7 @@ }, { "cell_type": "markdown", - "id": "39a9276b", + "id": "294a8ce0", "metadata": { "editable": true }, @@ -666,7 +666,7 @@ }, { "cell_type": "markdown", - "id": "84c63927", + "id": "a8c1b097", "metadata": { "editable": true }, @@ -678,7 +678,7 @@ }, { "cell_type": "markdown", - "id": "c087ef22", + "id": "4180c17f", "metadata": { "editable": true }, @@ -688,7 +688,7 @@ }, { "cell_type": "markdown", - "id": "79503987", + "id": "6a48bb05", "metadata": { "editable": true }, @@ -707,7 +707,7 @@ }, { "cell_type": "markdown", - "id": "c165025b", + "id": "d053a5c8", "metadata": { "editable": true }, @@ -735,7 +735,7 @@ }, { "cell_type": "markdown", - "id": "efb63405", + "id": "8cb550a1", "metadata": { "editable": true }, @@ -761,7 +761,7 @@ }, { "cell_type": "markdown", - "id": "88d4bfd8", + "id": "96be5396", "metadata": { "editable": true }, @@ -778,7 +778,7 @@ }, { "cell_type": "markdown", - "id": "6a0795e0", + "id": "f8a288b4", "metadata": { "editable": true }, @@ -798,7 +798,7 @@ }, { "cell_type": "markdown", - "id": "d815fdf3", + "id": "ee8bd2f9", "metadata": { "editable": true }, @@ -827,7 +827,7 @@ }, { "cell_type": "markdown", - "id": "a5b26ed1", + "id": "1037fcf3", "metadata": { "editable": true }, @@ -852,7 +852,7 @@ }, { "cell_type": "markdown", - "id": "e5783b81", + "id": "2653d9e3", "metadata": { "editable": true }, @@ -872,7 +872,7 @@ }, { "cell_type": "markdown", - "id": "9bdfff4f", + "id": "33e4596e", "metadata": { "editable": true }, @@ -884,7 +884,7 @@ }, { "cell_type": "markdown", - "id": "bd1e4a83", + "id": "137d3cd6", "metadata": { "editable": true }, @@ -894,7 +894,7 @@ }, { "cell_type": "markdown", - "id": "66d14a83", + "id": "4c9853b7", "metadata": { "editable": true }, @@ -909,7 +909,7 @@ }, { "cell_type": "markdown", - "id": "ac38d462", + "id": "493028c4", "metadata": { "editable": true }, @@ -922,7 +922,7 @@ }, { "cell_type": "markdown", - "id": "65488a60", + "id": "c819e616", "metadata": { "editable": true }, @@ -935,7 +935,7 @@ }, { "cell_type": "markdown", - "id": "9c8686d8", + "id": "f0385e1a", "metadata": { "editable": true }, @@ -947,7 +947,7 @@ }, { "cell_type": "markdown", - "id": "585dbaff", + "id": "4310a9b4", "metadata": { "editable": true }, @@ -960,7 +960,7 @@ }, { "cell_type": "markdown", - "id": "a8093a3e", + "id": "1e3932be", "metadata": { "editable": true }, @@ -971,7 +971,7 @@ }, { "cell_type": "markdown", - "id": "ec844baa", + "id": "91e64919", "metadata": { "editable": true }, @@ -985,7 +985,7 @@ }, { "cell_type": "markdown", - "id": "7f2b563b", + "id": "c83a8ca5", "metadata": { "editable": true }, @@ -995,7 +995,7 @@ }, { "cell_type": "markdown", - "id": "5a75bbe4", + "id": "16c94c48", "metadata": { "editable": true }, @@ -1009,7 +1009,7 @@ }, { "cell_type": "markdown", - "id": "8d00a9ff", + "id": "63bc9d16", "metadata": { "editable": true }, @@ -1022,7 +1022,7 @@ }, { "cell_type": "markdown", - "id": "cae54a40", + "id": "710fedd5", "metadata": { "editable": true }, @@ -1035,7 +1035,7 @@ }, { "cell_type": "markdown", - "id": "ef87a15a", + "id": "8c47e8f8", "metadata": { "editable": true }, @@ -1045,7 +1045,7 @@ }, { "cell_type": "markdown", - "id": "5bfaef5d", + "id": "c0e43db3", "metadata": { "editable": true }, @@ -1058,7 +1058,7 @@ }, { "cell_type": "markdown", - "id": "0aab5f59", + "id": "e9a40705", "metadata": { "editable": true }, @@ -1068,7 +1068,7 @@ }, { "cell_type": "markdown", - "id": "71269afb", + "id": "de6040d9", "metadata": { "editable": true }, @@ -1081,7 +1081,7 @@ }, { "cell_type": "markdown", - "id": "4d809fab", + "id": "f2907638", "metadata": { "editable": true }, @@ -1093,7 +1093,7 @@ }, { "cell_type": "markdown", - "id": "734f7c5e", + "id": "9e53d173", "metadata": { "editable": true }, @@ -1112,7 +1112,7 @@ }, { "cell_type": "markdown", - "id": "f4ff2861", + "id": "959c77be", "metadata": { "editable": true }, @@ -1125,7 +1125,7 @@ }, { "cell_type": "markdown", - "id": "fd66a47c", + "id": "6470ab77", "metadata": { "editable": true }, @@ -1137,7 +1137,7 @@ }, { "cell_type": "markdown", - "id": "51e5434b", + "id": "720c157a", "metadata": { "editable": true }, @@ -1150,7 +1150,7 @@ }, { "cell_type": "markdown", - "id": "9129f7a5", + "id": "62c153d3", "metadata": { "editable": true }, @@ -1170,7 +1170,7 @@ }, { "cell_type": "markdown", - "id": "e5fa7f9c", + "id": "cfd10bd9", "metadata": { "editable": true }, @@ -1193,7 +1193,7 @@ }, { "cell_type": "markdown", - "id": "f5bbafe6", + "id": "40dc022d", "metadata": { "editable": true }, @@ -1208,7 +1208,7 @@ }, { "cell_type": "markdown", - "id": "0cc93a0c", + "id": "242bfa08", "metadata": { "editable": true }, @@ -1220,7 +1220,7 @@ }, { "cell_type": "markdown", - "id": "8dd4f5e0", + "id": "7dd4616b", "metadata": { "editable": true }, @@ -1240,7 +1240,7 @@ }, { "cell_type": "markdown", - "id": "f51c546c", + "id": "00b509e4", "metadata": { "editable": true }, @@ -1260,7 +1260,7 @@ }, { "cell_type": "markdown", - "id": "e44fcf6d", + "id": "941834ae", "metadata": { "editable": true }, @@ -1284,7 +1284,7 @@ }, { "cell_type": "markdown", - "id": "3bd69373", + "id": "69ba3346", "metadata": { "editable": true }, @@ -1305,7 +1305,7 @@ }, { "cell_type": "markdown", - "id": "e7f867d9", + "id": "99f1499e", "metadata": { "editable": true }, @@ -1335,7 +1335,7 @@ }, { "cell_type": "markdown", - "id": "5c2c3909", + "id": "c817851a", "metadata": { "editable": true }, @@ -1359,7 +1359,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "a32faf6a", + "id": "4b9647f3", "metadata": { "collapsed": false, "editable": true @@ -1398,7 +1398,7 @@ }, { "cell_type": "markdown", - "id": "bc95505d", + "id": "26cf7fd4", "metadata": { "editable": true }, @@ -1408,7 +1408,7 @@ }, { "cell_type": "markdown", - "id": "355f62af", + "id": "b2205188", "metadata": { "editable": true }, @@ -1419,7 +1419,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "39fd1fa8", + "id": "be6f7ced", "metadata": { "collapsed": false, "editable": true @@ -1439,7 +1439,7 @@ }, { "cell_type": "markdown", - "id": "237b4db3", + "id": "69bcb406", "metadata": { "editable": true }, @@ -1457,7 +1457,7 @@ }, { "cell_type": "markdown", - "id": "0c13e5b0", + "id": "ce87dc4f", "metadata": { "editable": true }, @@ -1469,7 +1469,7 @@ }, { "cell_type": "markdown", - "id": "a086aa7e", + "id": "b8d1371c", "metadata": { "editable": true }, @@ -1486,7 +1486,7 @@ }, { "cell_type": "markdown", - "id": "c3837d89", + "id": "c95f3051", "metadata": { "editable": true }, @@ -1498,7 +1498,7 @@ }, { "cell_type": "markdown", - "id": "7c7cd0a7", + "id": "107fab0a", "metadata": { "editable": true }, @@ -1508,7 +1508,7 @@ }, { "cell_type": "markdown", - "id": "b9db0cd5", + "id": "d56b4bd7", "metadata": { "editable": true }, @@ -1520,7 +1520,7 @@ }, { "cell_type": "markdown", - "id": "00482b2d", + "id": "4712d813", "metadata": { "editable": true }, @@ -1537,7 +1537,7 @@ }, { "cell_type": "markdown", - "id": "2e7c7291", + "id": "43a58a59", "metadata": { "editable": true }, @@ -1549,7 +1549,7 @@ }, { "cell_type": "markdown", - "id": "9a8d29b5", + "id": "6333f694", "metadata": { "editable": true }, @@ -1559,7 +1559,7 @@ }, { "cell_type": "markdown", - "id": "9a8e2084", + "id": "24e27c2b", "metadata": { "editable": true }, @@ -1571,7 +1571,7 @@ }, { "cell_type": "markdown", - "id": "4a191c5c", + "id": "0462c197", "metadata": { "editable": true }, @@ -1581,7 +1581,7 @@ }, { "cell_type": "markdown", - "id": "c37713f8", + "id": "965cd453", "metadata": { "editable": true }, @@ -1593,7 +1593,7 @@ }, { "cell_type": "markdown", - "id": "82ca4a7b", + "id": "4426c74e", "metadata": { "editable": true }, @@ -1603,7 +1603,7 @@ }, { "cell_type": "markdown", - "id": "2765a841", + "id": "d68ec470", "metadata": { "editable": true }, @@ -1619,7 +1619,7 @@ }, { "cell_type": "markdown", - "id": "321964c1", + "id": "0198c371", "metadata": { "editable": true }, @@ -1630,7 +1630,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "5942226f", + "id": "af517050", "metadata": { "collapsed": false, "editable": true @@ -1695,7 +1695,7 @@ }, { "cell_type": "markdown", - "id": "cf2af19d", + "id": "2b502d1d", "metadata": { "editable": true }, @@ -1706,7 +1706,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "7b371a0c", + "id": "9a5194fb", "metadata": { "collapsed": false, "editable": true @@ -1763,7 +1763,7 @@ }, { "cell_type": "markdown", - "id": "6f583fcd", + "id": "727c7723", "metadata": { "editable": true }, @@ -1801,7 +1801,7 @@ }, { "cell_type": "markdown", - "id": "37766c51", + "id": "7e90566c", "metadata": { "editable": true }, @@ -1828,7 +1828,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "0eac5ca9", + "id": "7c760f15", "metadata": { "collapsed": false, "editable": true @@ -1890,7 +1890,7 @@ }, { "cell_type": "markdown", - "id": "d698096e", + "id": "2619ab70", "metadata": { "editable": true }, @@ -1915,7 +1915,7 @@ }, { "cell_type": "markdown", - "id": "3e37a4d2", + "id": "3e4d0bdb", "metadata": { "editable": true }, @@ -1943,7 +1943,7 @@ }, { "cell_type": "markdown", - "id": "e7e43cf9", + "id": "65d5f3f5", "metadata": { "editable": true }, @@ -1956,7 +1956,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "7aa6a568", + "id": "66c55986", "metadata": { "collapsed": false, "editable": true @@ -2056,7 +2056,7 @@ }, { "cell_type": "markdown", - "id": "9a90aec7", + "id": "8bd8e7a8", "metadata": { "editable": true }, @@ -2067,7 +2067,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "93b3af24", + "id": "2b363d73", "metadata": { "collapsed": false, "editable": true @@ -2156,7 +2156,7 @@ }, { "cell_type": "markdown", - "id": "90657c6d", + "id": "de30ce89", "metadata": { "editable": true }, @@ -2166,7 +2166,7 @@ }, { "cell_type": "markdown", - "id": "a88b86e7", + "id": "936b8f0f", "metadata": { "editable": true }, @@ -2179,7 +2179,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "89f45188", + "id": "399b09d4", "metadata": { "collapsed": false, "editable": true @@ -2257,7 +2257,7 @@ }, { "cell_type": "markdown", - "id": "75496517", + "id": "ded3c9a0", "metadata": { "editable": true }, diff --git a/doc/src/week38/week38.do.txt b/doc/src/week38/week38.do.txt index a95fd41be..26a521da8 100644 --- a/doc/src/week38/week38.do.txt +++ b/doc/src/week38/week38.do.txt @@ -293,13 +293,13 @@ We could now define a new cost function to minimize, namely the negative logarit !bt \[ -C(\bm{\theta}=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\theta})}, +C(\bm{\theta})=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\theta})}, \] !et which becomes !bt \[ -C(\bm{\theta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\theta})\vert\vert_2^2}{2\sigma^2}. +C(\bm{\theta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\theta})\vert\vert_2^2}{2\sigma^2}. \] !et