From dcb67d32a508a1a51986d74a211f5b2cabf62e5c Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Tue, 17 Sep 2024 06:32:37 +0200
Subject: [PATCH] update

---
 .../_build/.doctrees/environment.pickle       | Bin 338588 -> 338937 bytes
 .../_build/.doctrees/week38.doctree           | Bin 274004 -> 273722 bytes
 .../_build/html/_sources/week38.ipynb         | 364 ++++-----
 doc/LectureNotes/_build/html/searchindex.js   |   2 +-
 doc/LectureNotes/_build/html/week38.html      |  25 +-
 .../_build/jupyter_execute/week38.ipynb       | 364 ++++-----
 .../_build/jupyter_execute/week38.py          |   4 +-
 doc/LectureNotes/week38.ipynb                 | 364 ++++-----
 doc/pub/week38/ipynb/week38.ipynb             | 763 +++++-------------
 9 files changed, 755 insertions(+), 1131 deletions(-)

diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle
index 1801cfa30d4c1c19a419d36d3764034bf73528b8..cec7a4a8b838f53c9e2a69e09997844355c5bdc5 100644
GIT binary patch
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diff --git a/doc/LectureNotes/_build/html/_sources/week38.ipynb b/doc/LectureNotes/_build/html/_sources/week38.ipynb
index ba96b5d66..343d401bc 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": "ab8d23ae",
+   "id": "54608ce4",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
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   {
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-   "id": "080e5293",
+   "id": "702fc25a",
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@@ -27,7 +27,7 @@
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-   "id": "4039a635",
+   "id": "708a3ac3",
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@@ -47,7 +47,7 @@
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-   "id": "25f2dc54",
+   "id": "ca760e72",
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@@ -70,7 +70,7 @@
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@@ -90,17 +90,17 @@
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-   "id": "ee39a15f",
+   "id": "63b2922e",
    "metadata": {
     "editable": true
    },
    "source": [
-    "## Material for lecture Thursday September 21"
+    "## Material for lecture Monday September 16"
    ]
   },
   {
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-   "id": "b079388e",
+   "id": "d5f9f534",
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@@ -122,7 +122,7 @@
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@@ -148,7 +148,7 @@
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@@ -172,7 +172,7 @@
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-   "id": "70bfd4db",
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@@ -197,7 +197,7 @@
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+   "id": "44bcf7a3",
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@@ -209,7 +209,7 @@
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@@ -245,7 +245,7 @@
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@@ -256,7 +256,7 @@
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@@ -376,7 +376,7 @@
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@@ -459,7 +459,7 @@
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@@ -471,7 +471,7 @@
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@@ -559,7 +559,7 @@
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@@ -571,7 +571,7 @@
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@@ -598,7 +598,7 @@
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+   "id": "c72d9c5f",
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@@ -610,7 +610,7 @@
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@@ -627,7 +627,7 @@
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@@ -651,7 +651,7 @@
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@@ -675,7 +675,7 @@
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@@ -687,7 +687,7 @@
   },
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-   "id": "0d5fa113",
+   "id": "d492a29a",
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@@ -698,7 +698,7 @@
   },
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-   "id": "3e145775",
+   "id": "b384d3ea",
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@@ -710,7 +710,7 @@
   },
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-   "id": "0edb76c3",
+   "id": "257c19a6",
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@@ -721,7 +721,7 @@
   },
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    "cell_type": "markdown",
-   "id": "91189e0c",
+   "id": "4fcc7b46",
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@@ -737,7 +737,7 @@
   },
   {
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-   "id": "249b0007",
+   "id": "cccc7482",
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@@ -749,7 +749,7 @@
   },
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    "cell_type": "markdown",
-   "id": "33ab07ad",
+   "id": "ff305cbe",
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@@ -759,7 +759,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8c99503",
+   "id": "ab1aa23e",
    "metadata": {
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@@ -771,7 +771,7 @@
   },
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    "cell_type": "markdown",
-   "id": "bc290dda",
+   "id": "6799086b",
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@@ -786,7 +786,7 @@
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-   "id": "0aa96cf8",
+   "id": "cda3c102",
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@@ -798,7 +798,7 @@
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-   "id": "1708bccc",
+   "id": "b5be8ca2",
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@@ -809,7 +809,7 @@
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-   "id": "80f3c42e",
+   "id": "28868ab9",
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@@ -821,7 +821,7 @@
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-   "id": "b5b70594",
+   "id": "e92418db",
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@@ -833,7 +833,7 @@
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+   "id": "5533c3f5",
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@@ -845,7 +845,7 @@
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    "cell_type": "markdown",
-   "id": "3f981296",
+   "id": "9312b78f",
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@@ -855,7 +855,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab4c25ed",
+   "id": "edbb0614",
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@@ -867,7 +867,7 @@
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   {
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-   "id": "8ad1b13f",
+   "id": "394f6fae",
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@@ -881,7 +881,7 @@
   },
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    "cell_type": "markdown",
-   "id": "cac2084f",
+   "id": "883253c4",
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@@ -893,7 +893,7 @@
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   {
    "cell_type": "markdown",
-   "id": "9fca320f",
+   "id": "7c00e2f2",
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@@ -903,7 +903,7 @@
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+   "id": "deed99f4",
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@@ -925,7 +925,7 @@
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   {
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-   "id": "1c6b584c",
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@@ -937,7 +937,7 @@
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-  },
-  {
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+   "id": "1d6c4caf",
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+   "id": "8e0c1ec4",
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+   "id": "9edb0920",
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-   "id": "8d293124",
+   "id": "bf09a6eb",
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@@ -2689,7 +2679,7 @@
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@@ -2931,7 +2921,7 @@
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diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js
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class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and 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class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization"],titleterms:{"1":[0,15,16,17,18,22,27,28],"16":31,"2":[0,15,16,17,18,27,28,29],"2023":25,"2024":22,"21":[],"23":[],"26":28,"3":[0,15,16,27,28],"34":[15,27],"35":[16,28],"36":[17,29],"37":[18,30],"38":[19,31],"4":[0,28],"5":0,"7":22,"9":30,"case":[8,10,24,28,29,31],"class":31,"do":[1,29,30],"final":[12,28,29],"function":[0,1,6,7,8,10,11,12,13,22,24,27,28,29,30,31],"import":[5,21,27,28,29],"new":[4,29,30],A:[0,1,4,8,9,27,29,30,31],And:[27,28,29,31],For:28,In:25,Ising:6,The:[0,1,2,3,5,6,7,8,9,11,12,17,20,27,28,29,30,31],To:[27,28],With:[4,29],about:[27,28],abov:29,activ:[1,12,29],ad:[0,6,17,22,27,28],adaboost:10,adagrad:13,adam:13,adapt:10,adjust:1,adversari:4,again:[3,9,31],ai:[22,27],aim:[8,9,17,18,19,27],aka:[27,28],algebra:[21,27],algorithm:[9,10,11,12,28],algortithm:[13,31],all:8,an:[0,4,10,27],analys:[5,28],analysi:[0,5,6,11,20,22,24,27,28,29,30],analyt:[0,16,17],ani:[13,31],anoth:[9,29,30],appli:20,approach:[0,8,14,27,30],approxim:12,architectur:1,arrai:[21,27],assist:25,assumpt:[29,30],august:28,autocorrel:24,autograd:[2,13],automat:13,b:[17,22],back:[1,11,12],background:[20,22,30],bag:10,base:[13,30],basic:[0,5,7,9,10,11,21,28,29,30,31],batch:1,bay:[5,29,30],befor:11,beta:[29,30],better:8,bia:[6,22,30],binari:1,bind:27,bird:10,boldsymbol:[28,29,30],boost:10,bootstrap:[6,10,30],boston:0,breast:1,brief:[27,30,31],bring:12,build:[1,3,9],c:[22,27],calcul:28,can:[27,30],cancer:[1,7,9,11,31],cart:9,center:28,central:[13,20,24,30,31],chain:12,challeng:31,chang:10,channel:27,chi:[0,27],choos:1,cifar01:3,classic:11,classif:[1,9,10,31],classifi:[8,31],clip:1,cluster:14,cnn:3,code:[0,1,2,5,9,11,12,13,14,27,28,29,30,31],collect:[1,3],come:31,commun:27,compact:31,compar:[2,10],comparison:29,complet:28,complex:[0,6,22,28],complic:6,compon:11,comput:9,computation:30,computerlab:27,con:9,concept:24,condit:[29,30,31],confid:30,conjug:13,contn:27,convex:[8,13,31],convolut:[3,12],correctli:[29,30],correl:[11,28,31],correspond:31,cost:[1,10,28,29,30,31],cours:[20,26,27],covari:[5,11,24,28],cover:27,cross:[6,22,30,31],cython:27,d:22,data:[0,1,3,6,7,9,11,15,16,20,22,24,27,28,29,31],dataset:[1,3],deadlin:[22,27],decai:2,decis:[9,10],decomposit:[5,11,17,21,28],deep:[1,2,27,31],defin:[1,27],degre:[0,28],deliveri:22,delta:30,dens:[0,27],deriv:[5,12,28,29,30,31],descent:[2,10,13,31],descript:22,design:28,detail:[3,27],develop:1,diagon:11,differ:8,differenti:[2,13],diffus:2,dimension:[2,3,8,22,28],disadvantag:9,discret:24,discuss:31,distribut:[5,24,29,30],distrubut:30,doe:[28,29],domain:24,down:1,dropout:1,e:22,each:31,economi:28,electron:22,element:[0,24,27],elimin:21,energi:27,ensembl:10,entropi:[9,31],environ:[0,15,27],equat:[0,2,12,27,28,29,31],error:[0,10,27,28,30],essenti:27,estim:[29,30],etc:27,euler:2,evalu:1,exampl:[0,1,2,3,4,6,7,8,9,10,27,28,29,30,31],exercis:[0,6,15,16,17,18,19,27,28],expect:[18,24,29,30],expens:30,experi:24,explor:[0,15,16,27],exponenti:2,express:[17,18,28,31],extend:31,extrapol:4,extrem:[10,27],ey:10,f:22,fall:25,famili:[1,27,28],famou:21,fantast:28,featur:[9,21,28],feed:[1,12],find:30,fine:1,first:[4,12,27,28,29,31],fit:[0,10,27,29],fix:28,fold:[30,31],forc:3,forest:10,format:[22,27],forward:[1,2,12],fourier:3,frank:[6,22,28],freedom:[0,28],frequent:28,frequentist:[0,27],fridai:[],from:[5,10,12,28,29,30,31],full:2,further:[3,5,28],g:22,gan:4,gaussian:21,gd:13,gener:[4,9,27],geometr:[11,31],gini:9,good:[0,27],grade:[25,27],gradient:[1,2,10,13,31],grid:31,group:31,growth:2,ha:20,handl:[21,27,28],happen:[29,30],hessian:[28,31],hidden:2,histogram:30,homework:31,hous:0,how:31,hyperparamet:1,hyperplan:8,i:1,id3:9,idea:11,ideal:31,ident:[29,30],identifi:30,ii:27,iid:[29,30],illustr:29,implement:1,implic:[5,28],improv:1,includ:[13,31],increment:11,independ:[29,30],index:9,inform:25,input:2,instal:[20,22,27],instructor:25,intercept:28,interpret:[5,11,27,28,29,30,31],interv:30,introduc:[11,13,28],introduct:[0,6,20,21,22,27],invers:[5,21,29],invert:28,iter:10,its:28,jacobian:28,jax:13,julia:27,jungl:10,k:[30,31],kera:[1,3],kernel:[8,11],lab:[30,31],lagrangian:8,lambda:31,lasso:[5,6,22,28,29,30,31],last:[28,31],later:[5,28],layer:[1,2,3,12],learn:[0,1,2,11,13,14,15,16,20,22,27,28,29,30,31],least:[5,6,18,22,27,28,29],lectur:[27,28,29,30,31],level:10,librari:[20,27],likelihood:[7,29,30,31],limit:[1,13,24,30,31],linear:[0,8,13,21,27,28,29,31],link:[5,11,23,26,28,29,30],literatur:22,logist:[7,27,31],loss:[28,31],lu:21,machin:[0,8,13,20,22,27,31],made:[29,30],main:[24,27],make:[0,9,10,15,16,27,28],mani:[10,12],manipul:28,margin:[29,30],mass:27,materi:[22,23,27,28,29,30,31],math:[5,28],mathemat:[3,5,8,28],matric:[5,21,27,29],matrix:[1,5,11,12,21,27,28,29,31],matter:[0,27],max:28,maximum:[29,30,31],mean:[0,28,29,31],measur:31,meet:[5,10,24,27,28],mercer:8,method:[6,9,10,13,22,27,30,31],midnight:22,min:28,minim:[27,31],ml:27,mle:[29,30],mlp:12,mnist:[3,4],model:[0,1,4,6,12,27],momentum:13,mondai:[28,29,30,31],moon:[8,9],more:[3,6,21,22,27,28,29,30,31],multilay:12,multipl:[1,3],multipli:8,need:[22,27],net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\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/week38.html b/doc/LectureNotes/_build/html/week38.html
index 658747817..c3639e751 100644
--- a/doc/LectureNotes/_build/html/week38.html
+++ b/doc/LectureNotes/_build/html/week38.html
@@ -397,8 +397,8 @@ const thebe_selector_output = ".output, .cell_output"
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-september-21">
-   Material for lecture Thursday September 21
+  <a class="reference internal nav-link" href="#material-for-lecture-monday-september-16">
+   Material for lecture Monday September 16
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
@@ -491,11 +491,6 @@ const thebe_selector_output = ".output, .cell_output"
    More classes
   </a>
  </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#friday-september-23">
-   Friday September 23
-  </a>
- </li>
  <li class="toc-h2 nav-item toc-entry">
   <a class="reference internal nav-link" href="#searching-for-optimal-regularization-parameters-lambda">
    Searching for Optimal Regularization Parameters
@@ -747,8 +742,8 @@ const thebe_selector_output = ".output, .cell_output"
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-september-21">
-   Material for lecture Thursday September 21
+  <a class="reference internal nav-link" href="#material-for-lecture-monday-september-16">
+   Material for lecture Monday September 16
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
@@ -841,11 +836,6 @@ const thebe_selector_output = ".output, .cell_output"
    More classes
   </a>
  </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#friday-september-23">
-   Friday September 23
-  </a>
- </li>
  <li class="toc-h2 nav-item toc-entry">
   <a class="reference internal nav-link" href="#searching-for-optimal-regularization-parameters-lambda">
    Searching for Optimal Regularization Parameters
@@ -1111,8 +1101,8 @@ doconce format html week38.do.txt --no_mako -->
 <li><p>Work on project 1, in particular resampling methods like cross-validation and bootstrap.</p></li>
 </ul>
 </div>
-<div class="section" id="material-for-lecture-thursday-september-21">
-<h2>Material for lecture Thursday September 21<a class="headerlink" href="#material-for-lecture-thursday-september-21" title="Permalink to this headline">¶</a></h2>
+<div class="section" id="material-for-lecture-monday-september-16">
+<h2>Material for lecture Monday September 16<a class="headerlink" href="#material-for-lecture-monday-september-16" title="Permalink to this headline">¶</a></h2>
 </div>
 <div class="section" id="logistic-regression">
 <h2>Logistic Regression<a class="headerlink" href="#logistic-regression" title="Permalink to this headline">¶</a></h2>
@@ -1599,9 +1589,6 @@ descent method.  Newton’s method and gradient descent methods are
 discussed in the material on <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html">optimization
 methods</a>.</p>
 </div>
-<div class="section" id="friday-september-23">
-<h2>Friday September 23<a class="headerlink" href="#friday-september-23" title="Permalink to this headline">¶</a></h2>
-</div>
 <div class="section" id="searching-for-optimal-regularization-parameters-lambda">
 <h2>Searching for Optimal Regularization Parameters <span class="math notranslate nohighlight">\(\lambda\)</span><a class="headerlink" href="#searching-for-optimal-regularization-parameters-lambda" title="Permalink to this headline">¶</a></h2>
 <p>In project 1, when using Ridge and Lasso regression, we end up
diff --git a/doc/LectureNotes/_build/jupyter_execute/week38.ipynb b/doc/LectureNotes/_build/jupyter_execute/week38.ipynb
index ef7f35c0b..bfe58af2b 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": "ab8d23ae",
+   "id": "54608ce4",
    "metadata": {
     "editable": true
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@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "080e5293",
+   "id": "702fc25a",
    "metadata": {
     "editable": true
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@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4039a635",
+   "id": "708a3ac3",
    "metadata": {
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@@ -47,7 +47,7 @@
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   {
    "cell_type": "markdown",
-   "id": "25f2dc54",
+   "id": "ca760e72",
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@@ -70,7 +70,7 @@
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   {
    "cell_type": "markdown",
-   "id": "ce24b7fa",
+   "id": "a9fd5329",
    "metadata": {
     "editable": true
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@@ -90,17 +90,17 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee39a15f",
+   "id": "63b2922e",
    "metadata": {
     "editable": true
    },
    "source": [
-    "## Material for lecture Thursday September 21"
+    "## Material for lecture Monday September 16"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b079388e",
+   "id": "d5f9f534",
    "metadata": {
     "editable": true
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@@ -122,7 +122,7 @@
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   {
    "cell_type": "markdown",
-   "id": "9e80089c",
+   "id": "0143d162",
    "metadata": {
     "editable": true
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@@ -148,7 +148,7 @@
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   {
    "cell_type": "markdown",
-   "id": "30254f9e",
+   "id": "ef85093d",
    "metadata": {
     "editable": true
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@@ -172,7 +172,7 @@
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   {
    "cell_type": "markdown",
-   "id": "70bfd4db",
+   "id": "99320f0f",
    "metadata": {
     "editable": true
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@@ -197,7 +197,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9679b14",
+   "id": "44bcf7a3",
    "metadata": {
     "editable": true
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@@ -209,7 +209,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae7156e0",
+   "id": "403aa0cd",
    "metadata": {
     "editable": true
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@@ -227,7 +227,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "12f49fa9",
+   "id": "7703e42f",
    "metadata": {
     "editable": true
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@@ -245,7 +245,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b02c6f7",
+   "id": "025d7cc2",
    "metadata": {
     "editable": true
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@@ -256,7 +256,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52fdc3bb",
+   "id": "02656176",
    "metadata": {
     "editable": true
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@@ -283,7 +283,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ca51f60",
+   "id": "190a0e98",
    "metadata": {
     "editable": true
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@@ -296,7 +296,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "a5e8c140",
+   "id": "d3aa4736",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -383,7 +383,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "166027fb",
+   "id": "b52054ec",
    "metadata": {
     "editable": true
    },
@@ -396,7 +396,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "cb423fb1",
+   "id": "8c348f42",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -415,7 +415,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba8a95c2",
+   "id": "6df16129",
    "metadata": {
     "editable": true
    },
@@ -426,7 +426,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d59ffea1",
+   "id": "9a89924c",
    "metadata": {
     "editable": true
    },
@@ -438,7 +438,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0abf6dc2",
+   "id": "bf2297a8",
    "metadata": {
     "editable": true
    },
@@ -457,7 +457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88e5e3d0",
+   "id": "a865cd76",
    "metadata": {
     "editable": true
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@@ -479,7 +479,7 @@
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   {
    "cell_type": "markdown",
-   "id": "70bd6cfc",
+   "id": "4137be07",
    "metadata": {
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@@ -491,7 +491,7 @@
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   {
    "cell_type": "markdown",
-   "id": "872532dd",
+   "id": "42c4a103",
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@@ -501,7 +501,7 @@
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   {
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@@ -514,7 +514,7 @@
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@@ -579,7 +579,7 @@
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@@ -591,7 +591,7 @@
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@@ -606,7 +606,7 @@
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@@ -618,7 +618,7 @@
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@@ -630,7 +630,7 @@
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@@ -647,7 +647,7 @@
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@@ -661,7 +661,7 @@
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@@ -671,7 +671,7 @@
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@@ -683,7 +683,7 @@
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@@ -695,7 +695,7 @@
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@@ -707,7 +707,7 @@
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@@ -718,7 +718,7 @@
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@@ -730,7 +730,7 @@
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@@ -741,7 +741,7 @@
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@@ -757,7 +757,7 @@
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@@ -769,7 +769,7 @@
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@@ -779,7 +779,7 @@
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@@ -791,7 +791,7 @@
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@@ -806,7 +806,7 @@
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@@ -818,7 +818,7 @@
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@@ -829,7 +829,7 @@
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@@ -841,7 +841,7 @@
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@@ -853,7 +853,7 @@
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@@ -865,7 +865,7 @@
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@@ -875,7 +875,7 @@
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@@ -887,7 +887,7 @@
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@@ -901,7 +901,7 @@
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@@ -913,7 +913,7 @@
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@@ -923,7 +923,7 @@
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@@ -935,7 +935,7 @@
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@@ -945,7 +945,7 @@
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@@ -957,7 +957,7 @@
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@@ -968,7 +968,7 @@
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@@ -991,7 +991,7 @@
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@@ -1003,7 +1003,7 @@
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@@ -1013,7 +1013,7 @@
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@@ -1025,7 +1025,7 @@
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@@ -1042,17 +1042,7 @@
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@@ -1071,7 +1061,7 @@
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@@ -1126,7 +1116,7 @@
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@@ -1138,7 +1128,7 @@
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@@ -1153,7 +1143,7 @@
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@@ -1206,7 +1196,7 @@
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@@ -1221,7 +1211,7 @@
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@@ -1241,7 +1231,7 @@
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@@ -1295,7 +1285,7 @@
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@@ -1310,7 +1300,7 @@
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@@ -1337,7 +1327,7 @@
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@@ -1351,7 +1341,7 @@
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@@ -1396,7 +1386,7 @@
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@@ -1421,7 +1411,7 @@
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@@ -1433,7 +1423,7 @@
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@@ -1444,7 +1434,7 @@
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@@ -1456,7 +1446,7 @@
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@@ -1469,7 +1459,7 @@
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@@ -1480,7 +1470,7 @@
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@@ -1523,7 +1513,7 @@
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@@ -1544,7 +1534,7 @@
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@@ -1561,7 +1551,7 @@
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@@ -1576,7 +1566,7 @@
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@@ -1586,7 +1576,7 @@
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@@ -1602,7 +1592,7 @@
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@@ -1614,7 +1604,7 @@
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@@ -1625,7 +1615,7 @@
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@@ -1637,7 +1627,7 @@
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@@ -1647,7 +1637,7 @@
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@@ -1661,7 +1651,7 @@
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@@ -1673,7 +1663,7 @@
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@@ -1683,7 +1673,7 @@
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@@ -1695,7 +1685,7 @@
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@@ -1707,7 +1697,7 @@
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@@ -1727,7 +1717,7 @@
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@@ -1743,7 +1733,7 @@
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@@ -1759,7 +1749,7 @@
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@@ -1770,7 +1760,7 @@
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@@ -1782,7 +1772,7 @@
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@@ -1792,7 +1782,7 @@
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@@ -1804,7 +1794,7 @@
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@@ -1814,7 +1804,7 @@
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@@ -1826,7 +1816,7 @@
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@@ -1848,7 +1838,7 @@
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@@ -1861,7 +1851,7 @@
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@@ -1874,7 +1864,7 @@
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@@ -1884,7 +1874,7 @@
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@@ -1902,7 +1892,7 @@
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@@ -1912,7 +1902,7 @@
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@@ -1927,7 +1917,7 @@
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@@ -1937,7 +1927,7 @@
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@@ -1951,7 +1941,7 @@
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@@ -1961,7 +1951,7 @@
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@@ -1975,7 +1965,7 @@
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@@ -1990,7 +1980,7 @@
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@@ -2007,7 +1997,7 @@
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@@ -2019,7 +2009,7 @@
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@@ -2033,7 +2023,7 @@
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@@ -2048,7 +2038,7 @@
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@@ -2060,7 +2050,7 @@
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@@ -2071,7 +2061,7 @@
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@@ -2099,7 +2089,7 @@
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    },
@@ -2121,7 +2111,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ffd59b7",
+   "id": "d8f01f9e",
    "metadata": {
     "editable": true
    },
@@ -2143,7 +2133,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77cf3548",
+   "id": "fc87a9cf",
    "metadata": {
     "editable": true
    },
@@ -2155,7 +2145,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ab40924",
+   "id": "a0b661cc",
    "metadata": {
     "editable": true
    },
@@ -2192,7 +2182,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9bb05d6c",
+   "id": "180f4fbd",
    "metadata": {
     "editable": true
    },
@@ -2220,7 +2210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2f7c61fd",
+   "id": "e1ddb722",
    "metadata": {
     "editable": true
    },
@@ -2250,7 +2240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6086b2fe",
+   "id": "f30489e3",
    "metadata": {
     "editable": true
    },
@@ -2274,7 +2264,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "9f1d5c25",
+   "id": "d8c2af3d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2287,7 +2277,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2f4befe3",
+   "id": "a9356dfb",
    "metadata": {
     "editable": true
    },
@@ -2298,7 +2288,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efea83f9",
+   "id": "1c332ff0",
    "metadata": {
     "editable": true
    },
@@ -2310,7 +2300,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39808e65",
+   "id": "6e4cff1f",
    "metadata": {
     "editable": true
    },
@@ -2320,7 +2310,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "acba99f7",
+   "id": "239b1e2c",
    "metadata": {
     "editable": true
    },
@@ -2332,7 +2322,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3efc01f",
+   "id": "6c8f0818",
    "metadata": {
     "editable": true
    },
@@ -2346,7 +2336,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe149ca8",
+   "id": "3b591ee3",
    "metadata": {
     "editable": true
    },
@@ -2362,7 +2352,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a62c1e4",
+   "id": "4c93f254",
    "metadata": {
     "editable": true
    },
@@ -2372,7 +2362,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "109f30b1",
+   "id": "16996523",
    "metadata": {
     "editable": true
    },
@@ -2384,7 +2374,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3265d97",
+   "id": "3262b60e",
    "metadata": {
     "editable": true
    },
@@ -2394,7 +2384,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9c74aa7",
+   "id": "dfcf41ff",
    "metadata": {
     "editable": true
    },
@@ -2406,7 +2396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22a568b3",
+   "id": "4fbc9b44",
    "metadata": {
     "editable": true
    },
@@ -2420,7 +2410,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "64c20e09",
+   "id": "1972249c",
    "metadata": {
     "editable": true
    },
@@ -2430,7 +2420,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6bbac8da",
+   "id": "7e4e1d18",
    "metadata": {
     "editable": true
    },
@@ -2441,7 +2431,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62959d3b",
+   "id": "64c801f1",
    "metadata": {
     "editable": true
    },
@@ -2456,7 +2446,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a06a5b7e",
+   "id": "16f76226",
    "metadata": {
     "editable": true
    },
@@ -2466,7 +2456,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d72f9402",
+   "id": "51aca262",
    "metadata": {
     "editable": true
    },
@@ -2478,7 +2468,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb94a4a9",
+   "id": "3e7e9594",
    "metadata": {
     "editable": true
    },
@@ -2490,7 +2480,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbbed685",
+   "id": "31584669",
    "metadata": {
     "editable": true
    },
@@ -2505,7 +2495,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2ecccf4",
+   "id": "850d7725",
    "metadata": {
     "editable": true
    },
@@ -2518,7 +2508,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "b40baa2e",
+   "id": "20e6fb89",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2575,7 +2565,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "35c94947",
+   "id": "36c762c7",
    "metadata": {
     "editable": true
    },
@@ -2586,7 +2576,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "5e6057cb",
+   "id": "1ba65efc",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2613,7 +2603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3eb169b8",
+   "id": "845acf36",
    "metadata": {
     "editable": true
    },
@@ -2625,7 +2615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a37fc8af",
+   "id": "ae354b8b",
    "metadata": {
     "editable": true
    },
@@ -2637,7 +2627,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44eba894",
+   "id": "a6349642",
    "metadata": {
     "editable": true
    },
@@ -2647,7 +2637,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0caf10a2",
+   "id": "d4a4a710",
    "metadata": {
     "editable": true
    },
@@ -2661,7 +2651,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ee0ca77",
+   "id": "3a8c4b43",
    "metadata": {
     "editable": true
    },
@@ -2671,7 +2661,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec5ce9e6",
+   "id": "a4efb50c",
    "metadata": {
     "editable": true
    },
@@ -2683,7 +2673,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b6826ef",
+   "id": "d180548c",
    "metadata": {
     "editable": true
    },
@@ -2694,7 +2684,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9010e7b8",
+   "id": "87acd12f",
    "metadata": {
     "editable": true
    },
@@ -2709,7 +2699,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d667b28e",
+   "id": "869f478b",
    "metadata": {
     "editable": true
    },
@@ -2723,7 +2713,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60399cca",
+   "id": "9035cf3a",
    "metadata": {
     "editable": true
    },
@@ -2734,7 +2724,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "80369e14",
+   "id": "10e7bb54",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2795,7 +2785,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aee627f0",
+   "id": "4a349d39",
    "metadata": {
     "editable": true
    },
@@ -2817,7 +2807,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abb67183",
+   "id": "33424a86",
    "metadata": {
     "editable": true
    },
@@ -2829,7 +2819,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6adadded",
+   "id": "facda6dc",
    "metadata": {
     "editable": true
    },
@@ -2839,7 +2829,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1aeddf5f",
+   "id": "71006b8a",
    "metadata": {
     "editable": true
    },
@@ -2864,7 +2854,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25afc3fa",
+   "id": "8a7b6bd2",
    "metadata": {
     "editable": true
    },
@@ -2880,7 +2870,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcbe01f2",
+   "id": "01381fbd",
    "metadata": {
     "editable": true
    },
@@ -2896,7 +2886,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90c19306",
+   "id": "db6812a1",
    "metadata": {
     "editable": true
    },
@@ -2910,7 +2900,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ef5b23c",
+   "id": "e98af5ba",
    "metadata": {
     "editable": true
    },
@@ -2938,7 +2928,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8be821b",
+   "id": "e3fb483e",
    "metadata": {
     "editable": true
    },
@@ -2951,7 +2941,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "6edbc166",
+   "id": "b78643de",
    "metadata": {
     "collapsed": false,
     "editable": true
diff --git a/doc/LectureNotes/_build/jupyter_execute/week38.py b/doc/LectureNotes/_build/jupyter_execute/week38.py
index 63868e0b2..42b468135 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week38.py
+++ b/doc/LectureNotes/_build/jupyter_execute/week38.py
@@ -49,7 +49,7 @@
 # 
 #   * Work on project 1, in particular resampling methods like cross-validation and bootstrap.
 
-# ## Material for lecture Thursday September 21
+# ## Material for lecture Monday September 16
 
 # ## Logistic Regression
 # 
@@ -512,8 +512,6 @@ plt.show()
 # discussed in the material on [optimization
 # methods](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html).
 
-# ## Friday September 23
-
 # ## Searching for Optimal Regularization Parameters $\lambda$
 # 
 # In project 1, when using Ridge and Lasso regression, we end up
diff --git a/doc/LectureNotes/week38.ipynb b/doc/LectureNotes/week38.ipynb
index ba96b5d66..343d401bc 100644
--- a/doc/LectureNotes/week38.ipynb
+++ b/doc/LectureNotes/week38.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "ab8d23ae",
+   "id": "54608ce4",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "080e5293",
+   "id": "702fc25a",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4039a635",
+   "id": "708a3ac3",
    "metadata": {
     "editable": true
    },
@@ -47,7 +47,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25f2dc54",
+   "id": "ca760e72",
    "metadata": {
     "editable": true
    },
@@ -70,7 +70,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce24b7fa",
+   "id": "a9fd5329",
    "metadata": {
     "editable": true
    },
@@ -90,17 +90,17 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee39a15f",
+   "id": "63b2922e",
    "metadata": {
     "editable": true
    },
    "source": [
-    "## Material for lecture Thursday September 21"
+    "## Material for lecture Monday September 16"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b079388e",
+   "id": "d5f9f534",
    "metadata": {
     "editable": true
    },
@@ -122,7 +122,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e80089c",
+   "id": "0143d162",
    "metadata": {
     "editable": true
    },
@@ -148,7 +148,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30254f9e",
+   "id": "ef85093d",
    "metadata": {
     "editable": true
    },
@@ -172,7 +172,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70bfd4db",
+   "id": "99320f0f",
    "metadata": {
     "editable": true
    },
@@ -197,7 +197,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9679b14",
+   "id": "44bcf7a3",
    "metadata": {
     "editable": true
    },
@@ -209,7 +209,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae7156e0",
+   "id": "403aa0cd",
    "metadata": {
     "editable": true
    },
@@ -227,7 +227,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "12f49fa9",
+   "id": "7703e42f",
    "metadata": {
     "editable": true
    },
@@ -245,7 +245,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b02c6f7",
+   "id": "025d7cc2",
    "metadata": {
     "editable": true
    },
@@ -256,7 +256,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52fdc3bb",
+   "id": "02656176",
    "metadata": {
     "editable": true
    },
@@ -283,7 +283,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ca51f60",
+   "id": "190a0e98",
    "metadata": {
     "editable": true
    },
@@ -296,7 +296,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "a5e8c140",
+   "id": "d3aa4736",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -363,7 +363,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "166027fb",
+   "id": "b52054ec",
    "metadata": {
     "editable": true
    },
@@ -376,7 +376,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "cb423fb1",
+   "id": "8c348f42",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -395,7 +395,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba8a95c2",
+   "id": "6df16129",
    "metadata": {
     "editable": true
    },
@@ -406,7 +406,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d59ffea1",
+   "id": "9a89924c",
    "metadata": {
     "editable": true
    },
@@ -418,7 +418,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0abf6dc2",
+   "id": "bf2297a8",
    "metadata": {
     "editable": true
    },
@@ -437,7 +437,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88e5e3d0",
+   "id": "a865cd76",
    "metadata": {
     "editable": true
    },
@@ -459,7 +459,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70bd6cfc",
+   "id": "4137be07",
    "metadata": {
     "editable": true
    },
@@ -471,7 +471,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "872532dd",
+   "id": "42c4a103",
    "metadata": {
     "editable": true
    },
@@ -481,7 +481,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52bd04cb",
+   "id": "9b193f51",
    "metadata": {
     "editable": true
    },
@@ -494,7 +494,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "37944dba",
+   "id": "02f9e114",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -559,7 +559,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1e349be",
+   "id": "cf81cc5c",
    "metadata": {
     "editable": true
    },
@@ -571,7 +571,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3813b51d",
+   "id": "905fc981",
    "metadata": {
     "editable": true
    },
@@ -586,7 +586,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6277d3c8",
+   "id": "2c734796",
    "metadata": {
     "editable": true
    },
@@ -598,7 +598,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e47e2dc",
+   "id": "c72d9c5f",
    "metadata": {
     "editable": true
    },
@@ -610,7 +610,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eafc0787",
+   "id": "bc0af9ee",
    "metadata": {
     "editable": true
    },
@@ -627,7 +627,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "21feec2b",
+   "id": "7362c186",
    "metadata": {
     "editable": true
    },
@@ -641,7 +641,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "54a1ab90",
+   "id": "553b6180",
    "metadata": {
     "editable": true
    },
@@ -651,7 +651,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "343cf5e0",
+   "id": "4a4286b1",
    "metadata": {
     "editable": true
    },
@@ -663,7 +663,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92c13cec",
+   "id": "5873ef6a",
    "metadata": {
     "editable": true
    },
@@ -675,7 +675,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ce0539f",
+   "id": "97f8406f",
    "metadata": {
     "editable": true
    },
@@ -687,7 +687,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0d5fa113",
+   "id": "d492a29a",
    "metadata": {
     "editable": true
    },
@@ -698,7 +698,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e145775",
+   "id": "b384d3ea",
    "metadata": {
     "editable": true
    },
@@ -710,7 +710,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0edb76c3",
+   "id": "257c19a6",
    "metadata": {
     "editable": true
    },
@@ -721,7 +721,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91189e0c",
+   "id": "4fcc7b46",
    "metadata": {
     "editable": true
    },
@@ -737,7 +737,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "249b0007",
+   "id": "cccc7482",
    "metadata": {
     "editable": true
    },
@@ -749,7 +749,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33ab07ad",
+   "id": "ff305cbe",
    "metadata": {
     "editable": true
    },
@@ -759,7 +759,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8c99503",
+   "id": "ab1aa23e",
    "metadata": {
     "editable": true
    },
@@ -771,7 +771,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc290dda",
+   "id": "6799086b",
    "metadata": {
     "editable": true
    },
@@ -786,7 +786,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0aa96cf8",
+   "id": "cda3c102",
    "metadata": {
     "editable": true
    },
@@ -798,7 +798,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1708bccc",
+   "id": "b5be8ca2",
    "metadata": {
     "editable": true
    },
@@ -809,7 +809,7 @@
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@@ -821,7 +821,7 @@
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@@ -833,7 +833,7 @@
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@@ -845,7 +845,7 @@
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@@ -855,7 +855,7 @@
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@@ -867,7 +867,7 @@
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@@ -881,7 +881,7 @@
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@@ -893,7 +893,7 @@
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@@ -903,7 +903,7 @@
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@@ -915,7 +915,7 @@
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@@ -925,7 +925,7 @@
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@@ -937,7 +937,7 @@
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@@ -948,7 +948,7 @@
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@@ -971,7 +971,7 @@
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@@ -983,7 +983,7 @@
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@@ -993,7 +993,7 @@
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@@ -1005,7 +1005,7 @@
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@@ -1022,17 +1022,7 @@
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-   "metadata": {
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-   "source": [
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-  },
-  {
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@@ -1051,7 +1041,7 @@
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@@ -1106,7 +1096,7 @@
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@@ -1118,7 +1108,7 @@
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@@ -1133,7 +1123,7 @@
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@@ -1186,7 +1176,7 @@
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@@ -1201,7 +1191,7 @@
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@@ -1221,7 +1211,7 @@
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@@ -1275,7 +1265,7 @@
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@@ -1290,7 +1280,7 @@
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@@ -1317,7 +1307,7 @@
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@@ -1331,7 +1321,7 @@
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@@ -1376,7 +1366,7 @@
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@@ -1401,7 +1391,7 @@
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@@ -1413,7 +1403,7 @@
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@@ -1424,7 +1414,7 @@
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@@ -1436,7 +1426,7 @@
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@@ -1449,7 +1439,7 @@
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@@ -1460,7 +1450,7 @@
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@@ -1503,7 +1493,7 @@
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@@ -1524,7 +1514,7 @@
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@@ -1541,7 +1531,7 @@
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@@ -1556,7 +1546,7 @@
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@@ -1566,7 +1556,7 @@
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@@ -1582,7 +1572,7 @@
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@@ -1594,7 +1584,7 @@
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@@ -1605,7 +1595,7 @@
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@@ -1617,7 +1607,7 @@
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@@ -1627,7 +1617,7 @@
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@@ -1641,7 +1631,7 @@
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@@ -1653,7 +1643,7 @@
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@@ -1663,7 +1653,7 @@
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@@ -1675,7 +1665,7 @@
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@@ -1687,7 +1677,7 @@
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@@ -1707,7 +1697,7 @@
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@@ -1723,7 +1713,7 @@
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@@ -1739,7 +1729,7 @@
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@@ -1750,7 +1740,7 @@
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@@ -1762,7 +1752,7 @@
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@@ -1772,7 +1762,7 @@
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@@ -1784,7 +1774,7 @@
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@@ -1794,7 +1784,7 @@
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@@ -1806,7 +1796,7 @@
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@@ -1828,7 +1818,7 @@
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@@ -1841,7 +1831,7 @@
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@@ -1854,7 +1844,7 @@
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@@ -1864,7 +1854,7 @@
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@@ -1882,7 +1872,7 @@
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@@ -1892,7 +1882,7 @@
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@@ -1907,7 +1897,7 @@
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@@ -1917,7 +1907,7 @@
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@@ -1931,7 +1921,7 @@
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@@ -1941,7 +1931,7 @@
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@@ -1955,7 +1945,7 @@
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@@ -1970,7 +1960,7 @@
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@@ -1987,7 +1977,7 @@
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@@ -1999,7 +1989,7 @@
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@@ -2013,7 +2003,7 @@
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@@ -2028,7 +2018,7 @@
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@@ -2040,7 +2030,7 @@
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@@ -2051,7 +2041,7 @@
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@@ -2079,7 +2069,7 @@
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@@ -2101,7 +2091,7 @@
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@@ -2123,7 +2113,7 @@
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@@ -2135,7 +2125,7 @@
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@@ -2172,7 +2162,7 @@
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@@ -2200,7 +2190,7 @@
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@@ -2230,7 +2220,7 @@
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@@ -2254,7 +2244,7 @@
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@@ -2267,7 +2257,7 @@
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@@ -2278,7 +2268,7 @@
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@@ -2290,7 +2280,7 @@
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@@ -2300,7 +2290,7 @@
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@@ -2312,7 +2302,7 @@
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@@ -2326,7 +2316,7 @@
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@@ -2342,7 +2332,7 @@
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@@ -2352,7 +2342,7 @@
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@@ -2364,7 +2354,7 @@
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@@ -2374,7 +2364,7 @@
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@@ -2386,7 +2376,7 @@
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@@ -2400,7 +2390,7 @@
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@@ -2410,7 +2400,7 @@
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@@ -2421,7 +2411,7 @@
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@@ -2436,7 +2426,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a06a5b7e",
+   "id": "16f76226",
    "metadata": {
     "editable": true
    },
@@ -2446,7 +2436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d72f9402",
+   "id": "51aca262",
    "metadata": {
     "editable": true
    },
@@ -2458,7 +2448,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb94a4a9",
+   "id": "3e7e9594",
    "metadata": {
     "editable": true
    },
@@ -2470,7 +2460,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbbed685",
+   "id": "31584669",
    "metadata": {
     "editable": true
    },
@@ -2485,7 +2475,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2ecccf4",
+   "id": "850d7725",
    "metadata": {
     "editable": true
    },
@@ -2498,7 +2488,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "b40baa2e",
+   "id": "20e6fb89",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2555,7 +2545,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "35c94947",
+   "id": "36c762c7",
    "metadata": {
     "editable": true
    },
@@ -2566,7 +2556,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "5e6057cb",
+   "id": "1ba65efc",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2593,7 +2583,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3eb169b8",
+   "id": "845acf36",
    "metadata": {
     "editable": true
    },
@@ -2605,7 +2595,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a37fc8af",
+   "id": "ae354b8b",
    "metadata": {
     "editable": true
    },
@@ -2617,7 +2607,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44eba894",
+   "id": "a6349642",
    "metadata": {
     "editable": true
    },
@@ -2627,7 +2617,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0caf10a2",
+   "id": "d4a4a710",
    "metadata": {
     "editable": true
    },
@@ -2641,7 +2631,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ee0ca77",
+   "id": "3a8c4b43",
    "metadata": {
     "editable": true
    },
@@ -2651,7 +2641,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec5ce9e6",
+   "id": "a4efb50c",
    "metadata": {
     "editable": true
    },
@@ -2663,7 +2653,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b6826ef",
+   "id": "d180548c",
    "metadata": {
     "editable": true
    },
@@ -2674,7 +2664,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9010e7b8",
+   "id": "87acd12f",
    "metadata": {
     "editable": true
    },
@@ -2689,7 +2679,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d667b28e",
+   "id": "869f478b",
    "metadata": {
     "editable": true
    },
@@ -2703,7 +2693,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60399cca",
+   "id": "9035cf3a",
    "metadata": {
     "editable": true
    },
@@ -2714,7 +2704,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "80369e14",
+   "id": "10e7bb54",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2775,7 +2765,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aee627f0",
+   "id": "4a349d39",
    "metadata": {
     "editable": true
    },
@@ -2797,7 +2787,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abb67183",
+   "id": "33424a86",
    "metadata": {
     "editable": true
    },
@@ -2809,7 +2799,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6adadded",
+   "id": "facda6dc",
    "metadata": {
     "editable": true
    },
@@ -2819,7 +2809,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1aeddf5f",
+   "id": "71006b8a",
    "metadata": {
     "editable": true
    },
@@ -2844,7 +2834,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25afc3fa",
+   "id": "8a7b6bd2",
    "metadata": {
     "editable": true
    },
@@ -2860,7 +2850,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcbe01f2",
+   "id": "01381fbd",
    "metadata": {
     "editable": true
    },
@@ -2876,7 +2866,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90c19306",
+   "id": "db6812a1",
    "metadata": {
     "editable": true
    },
@@ -2890,7 +2880,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ef5b23c",
+   "id": "e98af5ba",
    "metadata": {
     "editable": true
    },
@@ -2918,7 +2908,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8be821b",
+   "id": "e3fb483e",
    "metadata": {
     "editable": true
    },
@@ -2931,7 +2921,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "6edbc166",
+   "id": "b78643de",
    "metadata": {
     "collapsed": false,
     "editable": true
diff --git a/doc/pub/week38/ipynb/week38.ipynb b/doc/pub/week38/ipynb/week38.ipynb
index 343d401bc..a01340aed 100644
--- a/doc/pub/week38/ipynb/week38.ipynb
+++ b/doc/pub/week38/ipynb/week38.ipynb
@@ -3,9 +3,7 @@
   {
    "cell_type": "markdown",
    "id": "54608ce4",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
     "doconce format html week38.do.txt --no_mako -->\n",
@@ -15,9 +13,7 @@
   {
    "cell_type": "markdown",
    "id": "702fc25a",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "# Week 38: Logistic Regression and Optimization\n",
     "**Morten Hjorth-Jensen**, Department of Physics and Center for Computing in Science Education, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
@@ -28,9 +24,7 @@
   {
    "cell_type": "markdown",
    "id": "708a3ac3",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Plans for week 38, lecture Monday September 16\n",
     "\n",
@@ -48,9 +42,7 @@
   {
    "cell_type": "markdown",
    "id": "ca760e72",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Suggested reading and videos\n",
     "  * Readings and Videos:\n",
@@ -71,9 +63,7 @@
   {
    "cell_type": "markdown",
    "id": "a9fd5329",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Plans for the lab sessions\n",
     "\n",
@@ -91,9 +81,7 @@
   {
    "cell_type": "markdown",
    "id": "63b2922e",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Material for lecture Monday September 16"
    ]
@@ -101,9 +89,7 @@
   {
    "cell_type": "markdown",
    "id": "d5f9f534",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Logistic Regression\n",
     "\n",
@@ -123,9 +109,7 @@
   {
    "cell_type": "markdown",
    "id": "0143d162",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Classification problems\n",
     "\n",
@@ -149,9 +133,7 @@
   {
    "cell_type": "markdown",
    "id": "ef85093d",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Optimization and Deep learning\n",
     "\n",
@@ -173,9 +155,7 @@
   {
    "cell_type": "markdown",
    "id": "99320f0f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Basics\n",
     "\n",
@@ -198,9 +178,7 @@
   {
    "cell_type": "markdown",
    "id": "44bcf7a3",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "y_i = \\begin{bmatrix} 0 & \\mathrm{no}\\\\  1 & \\mathrm{yes} \\end{bmatrix}.\n",
@@ -210,9 +188,7 @@
   {
    "cell_type": "markdown",
    "id": "403aa0cd",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Linear classifier\n",
     "\n",
@@ -228,9 +204,7 @@
   {
    "cell_type": "markdown",
    "id": "7703e42f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto1\"></div>\n",
@@ -246,9 +220,7 @@
   {
    "cell_type": "markdown",
    "id": "025d7cc2",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "where $\\boldsymbol{y}$ is a vector representing the possible outcomes, $\\boldsymbol{X}$ is our\n",
     "$n\\times p$ design matrix and $\\boldsymbol{\\beta}$ represents our estimators/predictors."
@@ -257,9 +229,7 @@
   {
    "cell_type": "markdown",
    "id": "02656176",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Some selected properties\n",
     "\n",
@@ -284,9 +254,7 @@
   {
    "cell_type": "markdown",
    "id": "190a0e98",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Simple example\n",
     "\n",
@@ -297,10 +265,7 @@
    "cell_type": "code",
    "execution_count": 1,
    "id": "d3aa4736",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "%matplotlib inline\n",
@@ -364,9 +329,7 @@
   {
    "cell_type": "markdown",
    "id": "b52054ec",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Plotting the mean value for each group\n",
     "\n",
@@ -377,10 +340,7 @@
    "cell_type": "code",
    "execution_count": 2,
    "id": "8c348f42",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "agegroupmean = np.array([0.1, 0.133, 0.250, 0.333, 0.462, 0.625, 0.765, 0.800])\n",
@@ -396,9 +356,7 @@
   {
    "cell_type": "markdown",
    "id": "6df16129",
-   "metadata": {
-    "editable": true
-   },
+   "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"
@@ -407,9 +365,7 @@
   {
    "cell_type": "markdown",
    "id": "9a89924c",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "f(y_i\\vert x_i)=\\beta_0+\\beta_1 x_i.\n",
@@ -419,9 +375,7 @@
   {
    "cell_type": "markdown",
    "id": "bf2297a8",
-   "metadata": {
-    "editable": true
-   },
+   "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",
@@ -438,9 +392,7 @@
   {
    "cell_type": "markdown",
    "id": "a865cd76",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The logistic function\n",
     "\n",
@@ -460,9 +412,7 @@
   {
    "cell_type": "markdown",
    "id": "4137be07",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "p(t) = \\frac{1}{1+\\mathrm \\exp{-t}}=\\frac{\\exp{t}}{1+\\mathrm \\exp{t}}.\n",
@@ -472,9 +422,7 @@
   {
    "cell_type": "markdown",
    "id": "42c4a103",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "Note that $1-p(t)= p(-t)$."
    ]
@@ -482,9 +430,7 @@
   {
    "cell_type": "markdown",
    "id": "9b193f51",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Examples of likelihood functions used in logistic regression and nueral networks\n",
     "\n",
@@ -495,10 +441,7 @@
    "cell_type": "code",
    "execution_count": 3,
    "id": "02f9e114",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "\"\"\"The sigmoid function (or the logistic curve) is a\n",
@@ -560,9 +503,7 @@
   {
    "cell_type": "markdown",
    "id": "cf81cc5c",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Two parameters\n",
     "\n",
@@ -572,9 +513,7 @@
   {
    "cell_type": "markdown",
    "id": "905fc981",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -587,9 +526,7 @@
   {
    "cell_type": "markdown",
    "id": "2c734796",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$. \n",
     "\n",
@@ -599,9 +536,7 @@
   {
    "cell_type": "markdown",
    "id": "c72d9c5f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "p(y_i=0\\vert x_i, \\boldsymbol{\\beta}) = 1-p(y_i=1\\vert x_i, \\boldsymbol{\\beta}).\n",
@@ -611,9 +546,7 @@
   {
    "cell_type": "markdown",
    "id": "bc0af9ee",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Maximum likelihood\n",
     "\n",
@@ -628,9 +561,7 @@
   {
    "cell_type": "markdown",
    "id": "7362c186",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -642,9 +573,7 @@
   {
    "cell_type": "markdown",
    "id": "553b6180",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "from which we obtain the log-likelihood and our **cost/loss** function"
    ]
@@ -652,9 +581,7 @@
   {
    "cell_type": "markdown",
    "id": "4a4286b1",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\beta}) = \\sum_{i=1}^n \\left( y_i\\log{p(y_i=1|x_i,\\boldsymbol{\\beta})} + (1-y_i)\\log\\left[1-p(y_i=1|x_i,\\boldsymbol{\\beta}))\\right]\\right).\n",
@@ -664,9 +591,7 @@
   {
    "cell_type": "markdown",
    "id": "5873ef6a",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The cost function rewritten\n",
     "\n",
@@ -676,9 +601,7 @@
   {
    "cell_type": "markdown",
    "id": "97f8406f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\beta}) = \\sum_{i=1}^n  \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n",
@@ -688,9 +611,7 @@
   {
    "cell_type": "markdown",
    "id": "d492a29a",
-   "metadata": {
-    "editable": true
-   },
+   "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"
@@ -699,9 +620,7 @@
   {
    "cell_type": "markdown",
    "id": "b384d3ea",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\beta})=-\\sum_{i=1}^n  \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n",
@@ -711,9 +630,7 @@
   {
    "cell_type": "markdown",
    "id": "257c19a6",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "This equation is known in statistics as the **cross entropy**. Finally, we note that just as in linear regression, \n",
     "in practice we often supplement the cross-entropy with additional regularization terms, usually $L_1$ and $L_2$ regularization as we did for Ridge and Lasso regression."
@@ -722,9 +639,7 @@
   {
    "cell_type": "markdown",
    "id": "4fcc7b46",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Minimizing the cross entropy\n",
     "\n",
@@ -738,9 +653,7 @@
   {
    "cell_type": "markdown",
    "id": "cccc7482",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\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",
@@ -750,9 +663,7 @@
   {
    "cell_type": "markdown",
    "id": "ff305cbe",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "and"
    ]
@@ -760,9 +671,7 @@
   {
    "cell_type": "markdown",
    "id": "ab1aa23e",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\beta_1} = -\\sum_{i=1}^n  \\left(y_ix_i -x_i\\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}}\\right).\n",
@@ -772,9 +681,7 @@
   {
    "cell_type": "markdown",
    "id": "6799086b",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## A more compact expression\n",
     "\n",
@@ -787,9 +694,7 @@
   {
    "cell_type": "markdown",
    "id": "cda3c102",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
@@ -799,9 +704,7 @@
   {
    "cell_type": "markdown",
    "id": "b5be8ca2",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
     "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
@@ -810,9 +713,7 @@
   {
    "cell_type": "markdown",
    "id": "28868ab9",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
@@ -822,9 +723,7 @@
   {
    "cell_type": "markdown",
    "id": "e92418db",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Extending to more predictors\n",
     "\n",
@@ -834,9 +733,7 @@
   {
    "cell_type": "markdown",
    "id": "5533c3f5",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\log{ \\frac{p(\\boldsymbol{\\beta}\\boldsymbol{x})}{1-p(\\boldsymbol{\\beta}\\boldsymbol{x})}} = \\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p.\n",
@@ -846,9 +743,7 @@
   {
    "cell_type": "markdown",
    "id": "9312b78f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "Here we defined $\\boldsymbol{x}=[1,x_1,x_2,\\dots,x_p]$ and $\\boldsymbol{\\beta}=[\\beta_0, \\beta_1, \\dots, \\beta_p]$ leading to"
    ]
@@ -856,9 +751,7 @@
   {
    "cell_type": "markdown",
    "id": "edbb0614",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "p(\\boldsymbol{\\beta}\\boldsymbol{x})=\\frac{ \\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}{1+\\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}.\n",
@@ -868,9 +761,7 @@
   {
    "cell_type": "markdown",
    "id": "394f6fae",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Including more classes\n",
     "\n",
@@ -882,9 +773,7 @@
   {
    "cell_type": "markdown",
    "id": "883253c4",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\log{\\frac{p(C=1\\vert x)}{p(K\\vert x)}} = \\beta_{10}+\\beta_{11}x_1,\n",
@@ -894,9 +783,7 @@
   {
    "cell_type": "markdown",
    "id": "7c00e2f2",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "and"
    ]
@@ -904,9 +791,7 @@
   {
    "cell_type": "markdown",
    "id": "6a4795d0",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\log{\\frac{p(C=2\\vert x)}{p(K\\vert x)}} = \\beta_{20}+\\beta_{21}x_1,\n",
@@ -916,9 +801,7 @@
   {
    "cell_type": "markdown",
    "id": "deed99f4",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "and so on till the class $C=K-1$ class"
    ]
@@ -926,9 +809,7 @@
   {
    "cell_type": "markdown",
    "id": "3ca93d73",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\log{\\frac{p(C=K-1\\vert x)}{p(K\\vert x)}} = \\beta_{(K-1)0}+\\beta_{(K-1)1}x_1,\n",
@@ -938,9 +819,7 @@
   {
    "cell_type": "markdown",
    "id": "89672774",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "and the model is specified in term of $K-1$ so-called log-odds or\n",
     "**logit** transformations."
@@ -949,9 +828,7 @@
   {
    "cell_type": "markdown",
    "id": "8a75d099",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## More classes\n",
     "\n",
@@ -972,9 +849,7 @@
   {
    "cell_type": "markdown",
    "id": "780a498d",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "p(C=k\\vert \\mathbf {x} )=\\frac{\\exp{(\\beta_{k0}+\\beta_{k1}x_1)}}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}}.\n",
@@ -984,9 +859,7 @@
   {
    "cell_type": "markdown",
    "id": "f19ad43b",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "It is easy to extend to more predictors. The final class is"
    ]
@@ -994,9 +867,7 @@
   {
    "cell_type": "markdown",
    "id": "25956ba0",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "p(C=K\\vert \\mathbf {x} )=\\frac{1}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}},\n",
@@ -1006,9 +877,7 @@
   {
    "cell_type": "markdown",
    "id": "4cb5ea2b",
-   "metadata": {
-    "editable": true
-   },
+   "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",
@@ -1023,9 +892,7 @@
   {
    "cell_type": "markdown",
    "id": "1d6c4caf",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Searching for Optimal Regularization Parameters $\\lambda$\n",
     "\n",
@@ -1042,10 +909,7 @@
    "cell_type": "code",
    "execution_count": 4,
    "id": "2cc35ceb",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -1097,9 +961,7 @@
   {
    "cell_type": "markdown",
    "id": "d5c16758",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "Here we have performed a rather data greedy calculation as function of the regularization parameter $\\lambda$. There is no resampling here. The latter can easily be added by employing the function **RidgeCV** instead of just calling the **Ridge** function. For **RidgeCV** we need to pass the array of $\\lambda$ values.\n",
     "By inspecting the figure we can in turn determine which is the optimal regularization parameter.\n",
@@ -1109,9 +971,7 @@
   {
    "cell_type": "markdown",
    "id": "67640d94",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Grid Search\n",
     "\n",
@@ -1124,10 +984,7 @@
    "cell_type": "code",
    "execution_count": 5,
    "id": "6aee13c4",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -1177,9 +1034,7 @@
   {
    "cell_type": "markdown",
    "id": "fbf16323",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "By default the grid search function includes cross validation with\n",
     "five folds. The [Scikit-Learn\n",
@@ -1192,9 +1047,7 @@
   {
    "cell_type": "markdown",
    "id": "b32612ca",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Randomized Grid Search\n",
     "\n",
@@ -1212,10 +1065,7 @@
    "cell_type": "code",
    "execution_count": 6,
    "id": "ec7749b1",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -1266,9 +1116,7 @@
   {
    "cell_type": "markdown",
    "id": "8e0c1ec4",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Wisconsin Cancer Data\n",
     "\n",
@@ -1281,10 +1129,7 @@
    "cell_type": "code",
    "execution_count": 7,
    "id": "9edb0920",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
@@ -1308,9 +1153,7 @@
   {
    "cell_type": "markdown",
    "id": "72beef44",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Using the correlation matrix\n",
     "\n",
@@ -1322,10 +1165,7 @@
    "cell_type": "code",
    "execution_count": 8,
    "id": "bf09a6eb",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
@@ -1367,9 +1207,7 @@
   {
    "cell_type": "markdown",
    "id": "2d081372",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Discussing the correlation data\n",
     "\n",
@@ -1392,10 +1230,7 @@
    "cell_type": "code",
    "execution_count": 9,
    "id": "cd0fad75",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)"
@@ -1404,9 +1239,7 @@
   {
    "cell_type": "markdown",
    "id": "0cf534b2",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "and then"
    ]
@@ -1415,10 +1248,7 @@
    "cell_type": "code",
    "execution_count": 10,
    "id": "6429451b",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "correlation_matrix = cancerpd.corr().round(1)"
@@ -1427,9 +1257,7 @@
   {
    "cell_type": "markdown",
    "id": "ed0138cc",
-   "metadata": {
-    "editable": true
-   },
+   "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",
@@ -1440,9 +1268,7 @@
   {
    "cell_type": "markdown",
    "id": "9b32814b",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Other measures in classification studies: Cancer Data  again"
    ]
@@ -1451,10 +1277,7 @@
    "cell_type": "code",
    "execution_count": 11,
    "id": "bfe200b0",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
@@ -1494,9 +1317,7 @@
   {
    "cell_type": "markdown",
    "id": "13691108",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Optimization, the central part of any Machine Learning algortithm\n",
     "\n",
@@ -1515,9 +1336,7 @@
   {
    "cell_type": "markdown",
    "id": "9622bff1",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Revisiting our Logistic Regression case\n",
     "\n",
@@ -1532,9 +1351,7 @@
   {
    "cell_type": "markdown",
    "id": "bffe481f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -1547,9 +1364,7 @@
   {
    "cell_type": "markdown",
    "id": "f967b579",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$."
    ]
@@ -1557,9 +1372,7 @@
   {
    "cell_type": "markdown",
    "id": "929b2860",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The equations to solve\n",
     "\n",
@@ -1573,9 +1386,7 @@
   {
    "cell_type": "markdown",
    "id": "4d50befc",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
@@ -1585,9 +1396,7 @@
   {
    "cell_type": "markdown",
    "id": "0c55b82a",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
     "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
@@ -1596,9 +1405,7 @@
   {
    "cell_type": "markdown",
    "id": "69de59e3",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
@@ -1608,9 +1415,7 @@
   {
    "cell_type": "markdown",
    "id": "5615f25a",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "This defines what is called  the Hessian matrix."
    ]
@@ -1618,9 +1423,7 @@
   {
    "cell_type": "markdown",
    "id": "48df73cf",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Solving using Newton-Raphson's method\n",
     "\n",
@@ -1632,9 +1435,7 @@
   {
    "cell_type": "markdown",
    "id": "cb6d2d95",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n",
@@ -1644,9 +1445,7 @@
   {
    "cell_type": "markdown",
    "id": "7f1e6122",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "or in matrix form as"
    ]
@@ -1654,9 +1453,7 @@
   {
    "cell_type": "markdown",
    "id": "830f7b44",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n",
@@ -1666,9 +1463,7 @@
   {
    "cell_type": "markdown",
    "id": "1860e409",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "The right-hand side is computed with the old values of $\\beta$. \n",
     "\n",
@@ -1678,9 +1473,7 @@
   {
    "cell_type": "markdown",
    "id": "49bb5265",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Brief reminder on Newton-Raphson's method\n",
     "\n",
@@ -1698,9 +1491,7 @@
   {
    "cell_type": "markdown",
    "id": "9142c2ca",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The equations\n",
     "\n",
@@ -1714,9 +1505,7 @@
   {
    "cell_type": "markdown",
    "id": "d98a052f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"eq:taylornr\"></div>\n",
@@ -1730,9 +1519,7 @@
   {
    "cell_type": "markdown",
    "id": "3d013035",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "For small enough values of the function and for well-behaved\n",
     "functions, the terms beyond linear are unimportant, hence we obtain"
@@ -1741,9 +1528,7 @@
   {
    "cell_type": "markdown",
    "id": "67e37396",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "f(x)+(s-x)f'(x)\\approx 0,\n",
@@ -1753,9 +1538,7 @@
   {
    "cell_type": "markdown",
    "id": "aaad3cb4",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "yielding"
    ]
@@ -1763,9 +1546,7 @@
   {
    "cell_type": "markdown",
    "id": "1c4c599d",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "s\\approx x-\\frac{f(x)}{f'(x)}.\n",
@@ -1775,9 +1556,7 @@
   {
    "cell_type": "markdown",
    "id": "947ebe9a",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "Having in mind an iterative procedure, it is natural to start iterating with"
    ]
@@ -1785,9 +1564,7 @@
   {
    "cell_type": "markdown",
    "id": "f7a44bbf",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n",
@@ -1797,9 +1574,7 @@
   {
    "cell_type": "markdown",
    "id": "6db59422",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Simple geometric interpretation\n",
     "\n",
@@ -1819,9 +1594,7 @@
   {
    "cell_type": "markdown",
    "id": "d8287387",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Extending to more than one variable\n",
     "\n",
@@ -1832,9 +1605,7 @@
   {
    "cell_type": "markdown",
    "id": "80c8b46c",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n",
@@ -1845,9 +1616,7 @@
   {
    "cell_type": "markdown",
    "id": "49a9d35c",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "which we Taylor expand to obtain"
    ]
@@ -1855,9 +1624,7 @@
   {
    "cell_type": "markdown",
    "id": "78a67613",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n",
@@ -1873,9 +1640,7 @@
   {
    "cell_type": "markdown",
    "id": "5eb2659a",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have"
    ]
@@ -1883,9 +1648,7 @@
   {
    "cell_type": "markdown",
    "id": "8a8fe9da",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n",
@@ -1898,9 +1661,7 @@
   {
    "cell_type": "markdown",
    "id": "71b1c4c8",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "we can rephrase Newton's method as"
    ]
@@ -1908,9 +1669,7 @@
   {
    "cell_type": "markdown",
    "id": "881e1a96",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n",
@@ -1922,9 +1681,7 @@
   {
    "cell_type": "markdown",
    "id": "6551a36e",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "where we have defined"
    ]
@@ -1932,9 +1689,7 @@
   {
    "cell_type": "markdown",
    "id": "c0e75b50",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n",
@@ -1946,9 +1701,7 @@
   {
    "cell_type": "markdown",
    "id": "ac897f51",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "We need thus to compute the inverse of the Jacobian matrix and it\n",
     "is to understand that difficulties  may\n",
@@ -1961,9 +1714,7 @@
   {
    "cell_type": "markdown",
    "id": "8c19a119",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Steepest descent\n",
     "\n",
@@ -1978,9 +1729,7 @@
   {
    "cell_type": "markdown",
    "id": "782860fa",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n",
@@ -1990,9 +1739,7 @@
   {
    "cell_type": "markdown",
    "id": "5ec3bde0",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "with $\\gamma_k > 0$.\n",
     "\n",
@@ -2004,9 +1751,7 @@
   {
    "cell_type": "markdown",
    "id": "ddb67ab3",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## More on Steepest descent\n",
     "\n",
@@ -2019,9 +1764,7 @@
   {
    "cell_type": "markdown",
    "id": "5a8be57f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n",
@@ -2031,9 +1774,7 @@
   {
    "cell_type": "markdown",
    "id": "4a60b86d",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "The parameter $\\gamma_k$ is often referred to as the step length or\n",
     "the learning rate within the context of Machine Learning."
@@ -2042,9 +1783,7 @@
   {
    "cell_type": "markdown",
    "id": "9ff0c7db",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The ideal\n",
     "\n",
@@ -2070,9 +1809,7 @@
   {
    "cell_type": "markdown",
    "id": "0c9c1201",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The sensitiveness of the gradient descent\n",
     "\n",
@@ -2092,9 +1829,7 @@
   {
    "cell_type": "markdown",
    "id": "d8f01f9e",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Convex functions\n",
     "\n",
@@ -2114,9 +1849,7 @@
   {
    "cell_type": "markdown",
    "id": "fc87a9cf",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Convex function\n",
     "\n",
@@ -2126,9 +1859,7 @@
   {
    "cell_type": "markdown",
    "id": "a0b661cc",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Conditions on convex functions\n",
     "\n",
@@ -2163,9 +1894,7 @@
   {
    "cell_type": "markdown",
    "id": "180f4fbd",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## More on convex functions\n",
     "\n",
@@ -2191,9 +1920,7 @@
   {
    "cell_type": "markdown",
    "id": "e1ddb722",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Some simple problems\n",
     "\n",
@@ -2221,9 +1948,7 @@
   {
    "cell_type": "markdown",
    "id": "f30489e3",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Revisiting our first homework\n",
     "\n",
@@ -2245,10 +1970,7 @@
    "cell_type": "code",
    "execution_count": 12,
    "id": "d8c2af3d",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "x = 2*np.random.rand(m,1)\n",
@@ -2258,9 +1980,7 @@
   {
    "cell_type": "markdown",
    "id": "a9356dfb",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n",
     "The linear regression model is given by"
@@ -2269,9 +1989,7 @@
   {
    "cell_type": "markdown",
    "id": "1c332ff0",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n",
@@ -2281,9 +1999,7 @@
   {
    "cell_type": "markdown",
    "id": "6e4cff1f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "such that"
    ]
@@ -2291,9 +2007,7 @@
   {
    "cell_type": "markdown",
    "id": "239b1e2c",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n",
@@ -2303,9 +2017,7 @@
   {
    "cell_type": "markdown",
    "id": "6c8f0818",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Gradient descent example\n",
     "\n",
@@ -2317,9 +2029,7 @@
   {
    "cell_type": "markdown",
    "id": "3b591ee3",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "X \\equiv \\begin{bmatrix}\n",
@@ -2333,9 +2043,7 @@
   {
    "cell_type": "markdown",
    "id": "4c93f254",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "The cost/loss/risk function is given by ("
    ]
@@ -2343,9 +2051,7 @@
   {
    "cell_type": "markdown",
    "id": "16996523",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n",
@@ -2355,9 +2061,7 @@
   {
    "cell_type": "markdown",
    "id": "3262b60e",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "and we want to find $\\beta$ such that $C(\\beta)$ is minimized."
    ]
@@ -2365,9 +2069,7 @@
   {
    "cell_type": "markdown",
    "id": "dfcf41ff",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The derivative of the cost/loss function\n",
     "\n",
@@ -2377,9 +2079,7 @@
   {
    "cell_type": "markdown",
    "id": "4fbc9b44",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n",
@@ -2391,9 +2091,7 @@
   {
    "cell_type": "markdown",
    "id": "1972249c",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "where $X$ is the design matrix defined above."
    ]
@@ -2401,9 +2099,7 @@
   {
    "cell_type": "markdown",
    "id": "7e4e1d18",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The Hessian matrix\n",
     "The Hessian matrix of $C(\\beta)$ is given by"
@@ -2412,9 +2108,7 @@
   {
    "cell_type": "markdown",
    "id": "64c801f1",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n",
@@ -2427,9 +2121,7 @@
   {
    "cell_type": "markdown",
    "id": "16f76226",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite."
    ]
@@ -2437,9 +2129,7 @@
   {
    "cell_type": "markdown",
    "id": "51aca262",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Simple program\n",
     "\n",
@@ -2449,9 +2139,7 @@
   {
    "cell_type": "markdown",
    "id": "3e7e9594",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n",
@@ -2461,9 +2149,7 @@
   {
    "cell_type": "markdown",
    "id": "31584669",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "We can use the expression we computed for the gradient and let use a\n",
     "$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n",
@@ -2476,9 +2162,7 @@
   {
    "cell_type": "markdown",
    "id": "850d7725",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Gradient Descent Example\n",
     "\n",
@@ -2489,10 +2173,7 @@
    "cell_type": "code",
    "execution_count": 13,
    "id": "20e6fb89",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "\n",
@@ -2546,9 +2227,7 @@
   {
    "cell_type": "markdown",
    "id": "36c762c7",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## And a corresponding example using **scikit-learn**"
    ]
@@ -2557,10 +2236,7 @@
    "cell_type": "code",
    "execution_count": 14,
    "id": "1ba65efc",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# Importing various packages\n",
@@ -2584,9 +2260,7 @@
   {
    "cell_type": "markdown",
    "id": "845acf36",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Gradient descent and Ridge\n",
     "\n",
@@ -2596,9 +2270,7 @@
   {
    "cell_type": "markdown",
    "id": "ae354b8b",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n",
@@ -2608,9 +2280,7 @@
   {
    "cell_type": "markdown",
    "id": "a6349642",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we adjust the gradient as follows"
    ]
@@ -2618,9 +2288,7 @@
   {
    "cell_type": "markdown",
    "id": "d4a4a710",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\nabla_\\beta C_{\\text{ridge}}(\\beta)  = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n",
@@ -2632,9 +2300,7 @@
   {
    "cell_type": "markdown",
    "id": "3a8c4b43",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by"
    ]
@@ -2642,9 +2308,7 @@
   {
    "cell_type": "markdown",
    "id": "a4efb50c",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\beta_{\\text{ridge}} = \\left(X^T X + n\\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n",
@@ -2654,9 +2318,7 @@
   {
    "cell_type": "markdown",
    "id": "d180548c",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## The Hessian matrix for Ridge Regression\n",
     "The Hessian matrix of Ridge Regression for our simple example  is given by"
@@ -2665,9 +2327,7 @@
   {
    "cell_type": "markdown",
    "id": "87acd12f",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n",
@@ -2680,9 +2340,7 @@
   {
    "cell_type": "markdown",
    "id": "869f478b",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "This implies that the Hessian matrix  is positive definite, hence the stationary point is a\n",
     "minimum.\n",
@@ -2694,9 +2352,7 @@
   {
    "cell_type": "markdown",
    "id": "9035cf3a",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Program example for gradient descent with Ridge Regression"
    ]
@@ -2705,10 +2361,7 @@
    "cell_type": "code",
    "execution_count": 15,
    "id": "10e7bb54",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from random import random, seed\n",
@@ -2766,9 +2419,7 @@
   {
    "cell_type": "markdown",
    "id": "4a349d39",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Using gradient descent methods, limitations\n",
     "\n",
@@ -2788,9 +2439,7 @@
   {
    "cell_type": "markdown",
    "id": "33424a86",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Challenge yourself the coming weekend\n",
     "\n",
@@ -2800,9 +2449,7 @@
   {
    "cell_type": "markdown",
    "id": "facda6dc",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Lab session: Material from last week and relevant for the first project"
    ]
@@ -2810,9 +2457,7 @@
   {
    "cell_type": "markdown",
    "id": "71006b8a",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Various steps in cross-validation\n",
     "\n",
@@ -2835,9 +2480,7 @@
   {
    "cell_type": "markdown",
    "id": "8a7b6bd2",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## How to set up the cross-validation for Ridge and/or Lasso\n",
     "\n",
@@ -2851,9 +2494,7 @@
   {
    "cell_type": "markdown",
    "id": "01381fbd",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -2867,9 +2508,7 @@
   {
    "cell_type": "markdown",
    "id": "db6812a1",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "* Evaluate the prediction performance of these models on the test set by $C[y_i, \\boldsymbol{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]$. 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",
@@ -2881,9 +2520,7 @@
   {
    "cell_type": "markdown",
    "id": "e98af5ba",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Cross-validation in brief\n",
     "\n",
@@ -2909,9 +2546,7 @@
   {
    "cell_type": "markdown",
    "id": "e3fb483e",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "## Code Example for Cross-validation and $k$-fold Cross-validation\n",
     "\n",
@@ -2920,13 +2555,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 1,
    "id": "b78643de",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
@@ -3018,9 +2661,35 @@
     "\n",
     "plt.show()"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f03f3f0d",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
- "metadata": {},
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.18"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 5
 }