small typos

Author: mhjensen

doc/LectureNotes/_build/.doctrees/environment.pickle

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "b0268cb1",
+   "id": "9b0bb122",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "700a1d0b",
+   "id": "48cf6ad1",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbe5809a",
+   "id": "3765446f",
    "metadata": {
     "editable": true
    },
@@ -46,7 +46,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac99e9c0",
+   "id": "82ccb1c9",
    "metadata": {
     "editable": true
    },
@@ -58,19 +58,19 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d71a32d",
+   "id": "2d9c0494",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\f(x)= 2-x+5x^2,\n",
+    "f(x)= 2-x+5x^2,\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c6496768",
+   "id": "df88ac02",
    "metadata": {
     "editable": true
    },
@@ -83,7 +83,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "24678181",
+   "id": "ce2e4a69",
    "metadata": {
     "editable": true
    },
@@ -99,7 +99,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b1bd90a",
+   "id": "294f41ac",
    "metadata": {
     "editable": true
    },
@@ -120,7 +120,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "5e751a16",
+   "id": "9c98b0d9",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -140,7 +140,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50a68a52",
+   "id": "802cf96b",
    "metadata": {
     "editable": true
    },
@@ -156,7 +156,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "db74a970",
+   "id": "90164acc",
    "metadata": {
     "editable": true
    },
@@ -168,7 +168,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8feaa49",
+   "id": "55d1c701",
    "metadata": {
     "editable": true
    },
@@ -179,7 +179,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "e6eca7a7",
+   "id": "22b80fe2",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -200,21 +200,21 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2dff0cf",
+   "id": "a0a8a8ec",
    "metadata": {
     "editable": true
    },
    "source": [
     "This computes the Ridge and OLS regression coefficients directly. The identity\n",
-    "matrix $I$ has the same size as $X^T X$. It adds $\\lambda$ to the diagonal of $X^T X for Ridge regression. We\n",
+    "matrix $I$ has the same size as $X^T X$. It adds $\\lambda$ to the diagonal of $X^T X$ for Ridge regression. We\n",
     "then invert this matrix and multiply by $X^T y$. The result\n",
     "for $\\boldsymbol{\\theta}$  is a NumPy array of shape (n$\\_$features,) containing the\n",
-    "fitted parameters $\\boldsymbol{\\theta}$.."
+    "fitted parameters $\\boldsymbol{\\theta}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "d7542c3e",
+   "id": "8e317939",
    "metadata": {
     "editable": true
    },
@@ -226,7 +226,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b922fd54",
+   "id": "7b52e9af",
    "metadata": {
     "editable": true
    },
@@ -238,7 +238,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92268a9a",
+   "id": "ba0b5a80",
    "metadata": {
     "editable": true
    },
@@ -258,7 +258,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "81660fa3",
+   "id": "e29c2842",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -301,7 +301,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "95149551",
+   "id": "9dc52b0e",
    "metadata": {
     "editable": true
    },
@@ -313,7 +313,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09b5400e",
+   "id": "4584ce15",
    "metadata": {
     "editable": true
    },
@@ -325,7 +325,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c635ca9e",
+   "id": "2f9f5861",
    "metadata": {
     "editable": true
    },
@@ -351,7 +351,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "4ca4ce05",
+   "id": "9e336d9b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -380,7 +380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af39d8bc",
+   "id": "5afbeef2",
    "metadata": {
     "editable": true
    },
@@ -394,7 +394,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d35d3438",
+   "id": "28beeaf3",
    "metadata": {
     "editable": true
    },
@@ -406,7 +406,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b28bf122",
+   "id": "36ba38c1",
    "metadata": {
     "editable": true
    },

doc/LectureNotes/_build/.doctrees/exercisesweek37.doctree

@@ -427,7 +427,7 @@ <h2>Simple one-dimensional second-order polynomial<a class="headerlink" href="#s
 <p>We start with a very simple function</p>
 <div class="math notranslate nohighlight">
 \[
-\f(x)= 2-x+5x^2,
+f(x)= 2-x+5x^2,
 \]</div>
 <p>defined for <span class="math notranslate nohighlight">\(x\in [-2,2]\)</span>. You can add noise if you wish.</p>
 <p>We are going to fit this function with a polynomial ansatz. The easiest thing is to set up a second-order polynomial and see if you can fit the above function.
@@ -496,10 +496,10 @@ <h2>Exercise 3, use the analytical formulae for OLS and Ridge regression to find
 </div>
 </div>
 <p>This computes the Ridge and OLS regression coefficients directly. The identity
-matrix <span class="math notranslate nohighlight">\(I\)</span> has the same size as <span class="math notranslate nohighlight">\(X^T X\)</span>. It adds <span class="math notranslate nohighlight">\(\lambda\)</span> to the diagonal of <span class="math notranslate nohighlight">\(X^T X for Ridge regression. We
-then invert this matrix and multiply by \)</span>X^T y<span class="math notranslate nohighlight">\(. The result
-for \)</span>\boldsymbol{\theta}<span class="math notranslate nohighlight">\(  is a NumPy array of shape (n\)</span>_<span class="math notranslate nohighlight">\(features,) containing the
-fitted parameters \)</span>\boldsymbol{\theta}$..</p>
+matrix <span class="math notranslate nohighlight">\(I\)</span> has the same size as <span class="math notranslate nohighlight">\(X^T X\)</span>. It adds <span class="math notranslate nohighlight">\(\lambda\)</span> to the diagonal of <span class="math notranslate nohighlight">\(X^T X\)</span> for Ridge regression. We
+then invert this matrix and multiply by <span class="math notranslate nohighlight">\(X^T y\)</span>. The result
+for <span class="math notranslate nohighlight">\(\boldsymbol{\theta}\)</span>  is a NumPy array of shape (n<span class="math notranslate nohighlight">\(\_\)</span>features,) containing the
+fitted parameters <span class="math notranslate nohighlight">\(\boldsymbol{\theta}\)</span>.</p>
 <section id="id1">
 <h3>3a)<a class="headerlink" href="#id1" title="Link to this heading">#</a></h3>
 <p>Finalize, in the above code, the OLS and Ridge regression determination of the optimal parameters <span class="math notranslate nohighlight">\(\boldsymbol{\theta}\)</span>.</p>