diff --git a/doc/pub/week35/html/._week35-bs000.html b/doc/pub/week35/html/._week35-bs000.html index f6f977e68..e6f5e6ee0 100644 --- a/doc/pub/week35/html/._week35-bs000.html +++ b/doc/pub/week35/html/._week35-bs000.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
  • Plans for week 35, August 30 -September 3
    • -
  • Thursday September 2
    • +
  • Plans for week 35
    • +
  • Thursday September 1
  • Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
  • Regression analysis, overarching aims
  • Regression analysis, overarching aims II
    • @@ -339,7 +336,7 @@ MathJax.Hub.Config({
  • Economy-size SVD
  • Codes for the SVD
  • Note about SVD Calculations
    • -
  • Friday September 3
    • +
  • Friday September 2
  • Mathematics of the SVD and implications
  • Example Matrix
  • Setting up the Matrix to be inverted
    • @@ -393,7 +390,7 @@ MathJax.Hub.Config({
    -

    Nov 3, 2021

    +

    Aug 23, 2022


    @@ -432,7 +429,7 @@ MathJax.Hub.Config({ -->
    - © 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license + © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
    diff --git a/doc/pub/week35/html/._week35-bs001.html b/doc/pub/week35/html/._week35-bs001.html index 2af7c186e..fdade8102 100644 --- a/doc/pub/week35/html/._week35-bs001.html +++ b/doc/pub/week35/html/._week35-bs001.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
  • Plans for week 35, August 30 -September 3
    • -
  • Thursday September 2
    • +
  • Plans for week 35
    • +
  • Thursday September 1
  • Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
  • Regression analysis, overarching aims
  • Regression analysis, overarching aims II
    • @@ -339,7 +336,7 @@ MathJax.Hub.Config({
  • Economy-size SVD
  • Codes for the SVD
  • Note about SVD Calculations
    • -
  • Friday September 3
    • +
  • Friday September 2
  • Mathematics of the SVD and implications
  • Example Matrix
  • Setting up the Matrix to be inverted
    • @@ -375,13 +372,11 @@ MathJax.Hub.Config({

     

     

     

    -

    Plans for week 35, August 30 -September 3

    +

    Plans for week 35

    diff --git a/doc/pub/week35/html/._week35-bs002.html b/doc/pub/week35/html/._week35-bs002.html index af1a23a8d..6b87b5921 100644 --- a/doc/pub/week35/html/._week35-bs002.html +++ b/doc/pub/week35/html/._week35-bs002.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d

  • Plans for week 35, August 30 -September 3
    • -
  • Thursday September 2
    • +
  • Plans for week 35
    • +
  • Thursday September 1
  • Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
  • Regression analysis, overarching aims
  • Regression analysis, overarching aims II
    • @@ -339,7 +336,7 @@ MathJax.Hub.Config({
  • Economy-size SVD
  • Codes for the SVD
  • Note about SVD Calculations
    • -
  • Friday September 3
    • +
  • Friday September 2
  • Mathematics of the SVD and implications
  • Example Matrix
  • Setting up the Matrix to be inverted
    • @@ -375,7 +372,7 @@ MathJax.Hub.Config({

     

     

     

    -

    Thursday September 2

    +

    Thursday September 1

    The main topics on Thursday are:

      diff --git a/doc/pub/week35/html/._week35-bs003.html b/doc/pub/week35/html/._week35-bs003.html index a80d2fd80..2bb3b019f 100644 --- a/doc/pub/week35/html/._week35-bs003.html +++ b/doc/pub/week35/html/._week35-bs003.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    1. Plans for week 35, August 30 -September 3
      2. -
    2. Thursday September 2
      3. +
    3. Plans for week 35
      4. +
    4. Thursday September 1
    5. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    6. Regression analysis, overarching aims
    7. Regression analysis, overarching aims II
      8. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    8. Economy-size SVD
    9. Codes for the SVD
    10. Note about SVD Calculations
      11. -
    11. Friday September 3
      12. +
    12. Friday September 2
    13. Mathematics of the SVD and implications
    14. Example Matrix
    15. Setting up the Matrix to be inverted
      16. diff --git a/doc/pub/week35/html/._week35-bs004.html b/doc/pub/week35/html/._week35-bs004.html index ca6eaffaa..c6bf0658a 100644 --- a/doc/pub/week35/html/._week35-bs004.html +++ b/doc/pub/week35/html/._week35-bs004.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    16. Plans for week 35, August 30 -September 3
      17. -
    17. Thursday September 2
      18. +
    18. Plans for week 35
      19. +
    19. Thursday September 1
    20. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    21. Regression analysis, overarching aims
    22. Regression analysis, overarching aims II
      23. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    23. Economy-size SVD
    24. Codes for the SVD
    25. Note about SVD Calculations
      26. -
    26. Friday September 3
      27. +
    27. Friday September 2
    28. Mathematics of the SVD and implications
    29. Example Matrix
    30. Setting up the Matrix to be inverted
      31. diff --git a/doc/pub/week35/html/._week35-bs005.html b/doc/pub/week35/html/._week35-bs005.html index a9948d15a..b048db462 100644 --- a/doc/pub/week35/html/._week35-bs005.html +++ b/doc/pub/week35/html/._week35-bs005.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    31. Plans for week 35, August 30 -September 3
      32. -
    32. Thursday September 2
      33. +
    33. Plans for week 35
      34. +
    34. Thursday September 1
    35. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    36. Regression analysis, overarching aims
    37. Regression analysis, overarching aims II
      38. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    38. Economy-size SVD
    39. Codes for the SVD
    40. Note about SVD Calculations
      41. -
    41. Friday September 3
      42. +
    42. Friday September 2
    43. Mathematics of the SVD and implications
    44. Example Matrix
    45. Setting up the Matrix to be inverted
      46. diff --git a/doc/pub/week35/html/._week35-bs006.html b/doc/pub/week35/html/._week35-bs006.html index 97bbb235c..9f1d3b7c2 100644 --- a/doc/pub/week35/html/._week35-bs006.html +++ b/doc/pub/week35/html/._week35-bs006.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    46. Plans for week 35, August 30 -September 3
      47. -
    47. Thursday September 2
      48. +
    48. Plans for week 35
      49. +
    49. Thursday September 1
    50. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    51. Regression analysis, overarching aims
    52. Regression analysis, overarching aims II
      53. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    53. Economy-size SVD
    54. Codes for the SVD
    55. Note about SVD Calculations
      56. -
    56. Friday September 3
      57. +
    57. Friday September 2
    58. Mathematics of the SVD and implications
    59. Example Matrix
    60. Setting up the Matrix to be inverted
      61. diff --git a/doc/pub/week35/html/._week35-bs007.html b/doc/pub/week35/html/._week35-bs007.html index a74a0c4d0..975d994ae 100644 --- a/doc/pub/week35/html/._week35-bs007.html +++ b/doc/pub/week35/html/._week35-bs007.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    61. Plans for week 35, August 30 -September 3
      62. -
    62. Thursday September 2
      63. +
    63. Plans for week 35
      64. +
    64. Thursday September 1
    65. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    66. Regression analysis, overarching aims
    67. Regression analysis, overarching aims II
      68. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    68. Economy-size SVD
    69. Codes for the SVD
    70. Note about SVD Calculations
      71. -
    71. Friday September 3
      72. +
    72. Friday September 2
    73. Mathematics of the SVD and implications
    74. Example Matrix
    75. Setting up the Matrix to be inverted
      76. diff --git a/doc/pub/week35/html/._week35-bs008.html b/doc/pub/week35/html/._week35-bs008.html index 3ae96ab97..4465bf8c9 100644 --- a/doc/pub/week35/html/._week35-bs008.html +++ b/doc/pub/week35/html/._week35-bs008.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    76. Plans for week 35, August 30 -September 3
      77. -
    77. Thursday September 2
      78. +
    78. Plans for week 35
      79. +
    79. Thursday September 1
    80. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    81. Regression analysis, overarching aims
    82. Regression analysis, overarching aims II
      83. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    83. Economy-size SVD
    84. Codes for the SVD
    85. Note about SVD Calculations
      86. -
    86. Friday September 3
      87. +
    87. Friday September 2
    88. Mathematics of the SVD and implications
    89. Example Matrix
    90. Setting up the Matrix to be inverted
      91. diff --git a/doc/pub/week35/html/._week35-bs009.html b/doc/pub/week35/html/._week35-bs009.html index a2327d1af..9e2bf8b71 100644 --- a/doc/pub/week35/html/._week35-bs009.html +++ b/doc/pub/week35/html/._week35-bs009.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    91. Plans for week 35, August 30 -September 3
      92. -
    92. Thursday September 2
      93. +
    93. Plans for week 35
      94. +
    94. Thursday September 1
    95. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    96. Regression analysis, overarching aims
    97. Regression analysis, overarching aims II
      98. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    98. Economy-size SVD
    99. Codes for the SVD
    100. Note about SVD Calculations
      101. -
    101. Friday September 3
      102. +
    102. Friday September 2
    103. Mathematics of the SVD and implications
    104. Example Matrix
    105. Setting up the Matrix to be inverted
      106. diff --git a/doc/pub/week35/html/._week35-bs010.html b/doc/pub/week35/html/._week35-bs010.html index 7a91e79b7..2ef90c645 100644 --- a/doc/pub/week35/html/._week35-bs010.html +++ b/doc/pub/week35/html/._week35-bs010.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    106. Plans for week 35, August 30 -September 3
      107. -
    107. Thursday September 2
      108. +
    108. Plans for week 35
      109. +
    109. Thursday September 1
    110. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    111. Regression analysis, overarching aims
    112. Regression analysis, overarching aims II
      113. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    113. Economy-size SVD
    114. Codes for the SVD
    115. Note about SVD Calculations
      116. -
    116. Friday September 3
      117. +
    117. Friday September 2
    118. Mathematics of the SVD and implications
    119. Example Matrix
    120. Setting up the Matrix to be inverted
      121. diff --git a/doc/pub/week35/html/._week35-bs011.html b/doc/pub/week35/html/._week35-bs011.html index 20dd4910e..a3becfa7b 100644 --- a/doc/pub/week35/html/._week35-bs011.html +++ b/doc/pub/week35/html/._week35-bs011.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    121. Plans for week 35, August 30 -September 3
      122. -
    122. Thursday September 2
      123. +
    123. Plans for week 35
      124. +
    124. Thursday September 1
    125. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    126. Regression analysis, overarching aims
    127. Regression analysis, overarching aims II
      128. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    128. Economy-size SVD
    129. Codes for the SVD
    130. Note about SVD Calculations
      131. -
    131. Friday September 3
      132. +
    132. Friday September 2
    133. Mathematics of the SVD and implications
    134. Example Matrix
    135. Setting up the Matrix to be inverted
      136. diff --git a/doc/pub/week35/html/._week35-bs012.html b/doc/pub/week35/html/._week35-bs012.html index e70f9e3bf..485669976 100644 --- a/doc/pub/week35/html/._week35-bs012.html +++ b/doc/pub/week35/html/._week35-bs012.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    136. Plans for week 35, August 30 -September 3
      137. -
    137. Thursday September 2
      138. +
    138. Plans for week 35
      139. +
    139. Thursday September 1
    140. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    141. Regression analysis, overarching aims
    142. Regression analysis, overarching aims II
      143. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    143. Economy-size SVD
    144. Codes for the SVD
    145. Note about SVD Calculations
      146. -
    146. Friday September 3
      147. +
    147. Friday September 2
    148. Mathematics of the SVD and implications
    149. Example Matrix
    150. Setting up the Matrix to be inverted
      151. diff --git a/doc/pub/week35/html/._week35-bs013.html b/doc/pub/week35/html/._week35-bs013.html index f377b4488..f7eff7056 100644 --- a/doc/pub/week35/html/._week35-bs013.html +++ b/doc/pub/week35/html/._week35-bs013.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    151. Plans for week 35, August 30 -September 3
      152. -
    152. Thursday September 2
      153. +
    153. Plans for week 35
      154. +
    154. Thursday September 1
    155. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    156. Regression analysis, overarching aims
    157. Regression analysis, overarching aims II
      158. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    158. Economy-size SVD
    159. Codes for the SVD
    160. Note about SVD Calculations
      161. -
    161. Friday September 3
      162. +
    162. Friday September 2
    163. Mathematics of the SVD and implications
    164. Example Matrix
    165. Setting up the Matrix to be inverted
      166. diff --git a/doc/pub/week35/html/._week35-bs014.html b/doc/pub/week35/html/._week35-bs014.html index 4dc2b9b3b..f1deb9698 100644 --- a/doc/pub/week35/html/._week35-bs014.html +++ b/doc/pub/week35/html/._week35-bs014.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    166. Plans for week 35, August 30 -September 3
      167. -
    167. Thursday September 2
      168. +
    168. Plans for week 35
      169. +
    169. Thursday September 1
    170. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    171. Regression analysis, overarching aims
    172. Regression analysis, overarching aims II
      173. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    173. Economy-size SVD
    174. Codes for the SVD
    175. Note about SVD Calculations
      176. -
    176. Friday September 3
      177. +
    177. Friday September 2
    178. Mathematics of the SVD and implications
    179. Example Matrix
    180. Setting up the Matrix to be inverted
      181. diff --git a/doc/pub/week35/html/._week35-bs015.html b/doc/pub/week35/html/._week35-bs015.html index d770d9588..e4c339929 100644 --- a/doc/pub/week35/html/._week35-bs015.html +++ b/doc/pub/week35/html/._week35-bs015.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    181. Plans for week 35, August 30 -September 3
      182. -
    182. Thursday September 2
      183. +
    183. Plans for week 35
      184. +
    184. Thursday September 1
    185. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    186. Regression analysis, overarching aims
    187. Regression analysis, overarching aims II
      188. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    188. Economy-size SVD
    189. Codes for the SVD
    190. Note about SVD Calculations
      191. -
    191. Friday September 3
      192. +
    192. Friday September 2
    193. Mathematics of the SVD and implications
    194. Example Matrix
    195. Setting up the Matrix to be inverted
      196. diff --git a/doc/pub/week35/html/._week35-bs016.html b/doc/pub/week35/html/._week35-bs016.html index 505ca8579..afb3294e3 100644 --- a/doc/pub/week35/html/._week35-bs016.html +++ b/doc/pub/week35/html/._week35-bs016.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    196. Plans for week 35, August 30 -September 3
      197. -
    197. Thursday September 2
      198. +
    198. Plans for week 35
      199. +
    199. Thursday September 1
    200. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    201. Regression analysis, overarching aims
    202. Regression analysis, overarching aims II
      203. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    203. Economy-size SVD
    204. Codes for the SVD
    205. Note about SVD Calculations
      206. -
    206. Friday September 3
      207. +
    207. Friday September 2
    208. Mathematics of the SVD and implications
    209. Example Matrix
    210. Setting up the Matrix to be inverted
      211. diff --git a/doc/pub/week35/html/._week35-bs017.html b/doc/pub/week35/html/._week35-bs017.html index 814c190eb..fa7cb048e 100644 --- a/doc/pub/week35/html/._week35-bs017.html +++ b/doc/pub/week35/html/._week35-bs017.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    211. Plans for week 35, August 30 -September 3
      212. -
    212. Thursday September 2
      213. +
    213. Plans for week 35
      214. +
    214. Thursday September 1
    215. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    216. Regression analysis, overarching aims
    217. Regression analysis, overarching aims II
      218. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    218. Economy-size SVD
    219. Codes for the SVD
    220. Note about SVD Calculations
      221. -
    221. Friday September 3
      222. +
    222. Friday September 2
    223. Mathematics of the SVD and implications
    224. Example Matrix
    225. Setting up the Matrix to be inverted
      226. diff --git a/doc/pub/week35/html/._week35-bs018.html b/doc/pub/week35/html/._week35-bs018.html index 3001a47e8..630965756 100644 --- a/doc/pub/week35/html/._week35-bs018.html +++ b/doc/pub/week35/html/._week35-bs018.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    226. Plans for week 35, August 30 -September 3
      227. -
    227. Thursday September 2
      228. +
    228. Plans for week 35
      229. +
    229. Thursday September 1
    230. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    231. Regression analysis, overarching aims
    232. Regression analysis, overarching aims II
      233. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    233. Economy-size SVD
    234. Codes for the SVD
    235. Note about SVD Calculations
      236. -
    236. Friday September 3
      237. +
    237. Friday September 2
    238. Mathematics of the SVD and implications
    239. Example Matrix
    240. Setting up the Matrix to be inverted
      241. diff --git a/doc/pub/week35/html/._week35-bs019.html b/doc/pub/week35/html/._week35-bs019.html index 097daf45c..2dc388d53 100644 --- a/doc/pub/week35/html/._week35-bs019.html +++ b/doc/pub/week35/html/._week35-bs019.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    241. Plans for week 35, August 30 -September 3
      242. -
    242. Thursday September 2
      243. +
    243. Plans for week 35
      244. +
    244. Thursday September 1
    245. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    246. Regression analysis, overarching aims
    247. Regression analysis, overarching aims II
      248. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    248. Economy-size SVD
    249. Codes for the SVD
    250. Note about SVD Calculations
      251. -
    251. Friday September 3
      252. +
    252. Friday September 2
    253. Mathematics of the SVD and implications
    254. Example Matrix
    255. Setting up the Matrix to be inverted
      256. diff --git a/doc/pub/week35/html/._week35-bs020.html b/doc/pub/week35/html/._week35-bs020.html index 96b4ecaf7..2a16db91e 100644 --- a/doc/pub/week35/html/._week35-bs020.html +++ b/doc/pub/week35/html/._week35-bs020.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    256. Plans for week 35, August 30 -September 3
      257. -
    257. Thursday September 2
      258. +
    258. Plans for week 35
      259. +
    259. Thursday September 1
    260. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    261. Regression analysis, overarching aims
    262. Regression analysis, overarching aims II
      263. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    263. Economy-size SVD
    264. Codes for the SVD
    265. Note about SVD Calculations
      266. -
    266. Friday September 3
      267. +
    267. Friday September 2
    268. Mathematics of the SVD and implications
    269. Example Matrix
    270. Setting up the Matrix to be inverted
      271. diff --git a/doc/pub/week35/html/._week35-bs021.html b/doc/pub/week35/html/._week35-bs021.html index 62f43b27b..3789d951d 100644 --- a/doc/pub/week35/html/._week35-bs021.html +++ b/doc/pub/week35/html/._week35-bs021.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    271. Plans for week 35, August 30 -September 3
      272. -
    272. Thursday September 2
      273. +
    273. Plans for week 35
      274. +
    274. Thursday September 1
    275. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    276. Regression analysis, overarching aims
    277. Regression analysis, overarching aims II
      278. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    278. Economy-size SVD
    279. Codes for the SVD
    280. Note about SVD Calculations
      281. -
    281. Friday September 3
      282. +
    282. Friday September 2
    283. Mathematics of the SVD and implications
    284. Example Matrix
    285. Setting up the Matrix to be inverted
      286. diff --git a/doc/pub/week35/html/._week35-bs022.html b/doc/pub/week35/html/._week35-bs022.html index 1d3d493bb..6fa90006a 100644 --- a/doc/pub/week35/html/._week35-bs022.html +++ b/doc/pub/week35/html/._week35-bs022.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    286. Plans for week 35, August 30 -September 3
      287. -
    287. Thursday September 2
      288. +
    288. Plans for week 35
      289. +
    289. Thursday September 1
    290. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    291. Regression analysis, overarching aims
    292. Regression analysis, overarching aims II
      293. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    293. Economy-size SVD
    294. Codes for the SVD
    295. Note about SVD Calculations
      296. -
    296. Friday September 3
      297. +
    297. Friday September 2
    298. Mathematics of the SVD and implications
    299. Example Matrix
    300. Setting up the Matrix to be inverted
      301. diff --git a/doc/pub/week35/html/._week35-bs023.html b/doc/pub/week35/html/._week35-bs023.html index f40ad4122..afd88ef47 100644 --- a/doc/pub/week35/html/._week35-bs023.html +++ b/doc/pub/week35/html/._week35-bs023.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    301. Plans for week 35, August 30 -September 3
      302. -
    302. Thursday September 2
      303. +
    303. Plans for week 35
      304. +
    304. Thursday September 1
    305. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    306. Regression analysis, overarching aims
    307. Regression analysis, overarching aims II
      308. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    308. Economy-size SVD
    309. Codes for the SVD
    310. Note about SVD Calculations
      311. -
    311. Friday September 3
      312. +
    312. Friday September 2
    313. Mathematics of the SVD and implications
    314. Example Matrix
    315. Setting up the Matrix to be inverted
      316. diff --git a/doc/pub/week35/html/._week35-bs024.html b/doc/pub/week35/html/._week35-bs024.html index ba79d8c9e..d779200f8 100644 --- a/doc/pub/week35/html/._week35-bs024.html +++ b/doc/pub/week35/html/._week35-bs024.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    316. Plans for week 35, August 30 -September 3
      317. -
    317. Thursday September 2
      318. +
    318. Plans for week 35
      319. +
    319. Thursday September 1
    320. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    321. Regression analysis, overarching aims
    322. Regression analysis, overarching aims II
      323. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    323. Economy-size SVD
    324. Codes for the SVD
    325. Note about SVD Calculations
      326. -
    326. Friday September 3
      327. +
    327. Friday September 2
    328. Mathematics of the SVD and implications
    329. Example Matrix
    330. Setting up the Matrix to be inverted
      331. diff --git a/doc/pub/week35/html/._week35-bs025.html b/doc/pub/week35/html/._week35-bs025.html index e8aa574d3..00ee6a323 100644 --- a/doc/pub/week35/html/._week35-bs025.html +++ b/doc/pub/week35/html/._week35-bs025.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    331. Plans for week 35, August 30 -September 3
      332. -
    332. Thursday September 2
      333. +
    333. Plans for week 35
      334. +
    334. Thursday September 1
    335. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    336. Regression analysis, overarching aims
    337. Regression analysis, overarching aims II
      338. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    338. Economy-size SVD
    339. Codes for the SVD
    340. Note about SVD Calculations
      341. -
    341. Friday September 3
      342. +
    342. Friday September 2
    343. Mathematics of the SVD and implications
    344. Example Matrix
    345. Setting up the Matrix to be inverted
      346. diff --git a/doc/pub/week35/html/._week35-bs026.html b/doc/pub/week35/html/._week35-bs026.html index af958211e..1ccaf986c 100644 --- a/doc/pub/week35/html/._week35-bs026.html +++ b/doc/pub/week35/html/._week35-bs026.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    346. Plans for week 35, August 30 -September 3
      347. -
    347. Thursday September 2
      348. +
    348. Plans for week 35
      349. +
    349. Thursday September 1
    350. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    351. Regression analysis, overarching aims
    352. Regression analysis, overarching aims II
      353. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    353. Economy-size SVD
    354. Codes for the SVD
    355. Note about SVD Calculations
      356. -
    356. Friday September 3
      357. +
    357. Friday September 2
    358. Mathematics of the SVD and implications
    359. Example Matrix
    360. Setting up the Matrix to be inverted
      361. diff --git a/doc/pub/week35/html/._week35-bs027.html b/doc/pub/week35/html/._week35-bs027.html index 4fe3f287f..acdf6cfb4 100644 --- a/doc/pub/week35/html/._week35-bs027.html +++ b/doc/pub/week35/html/._week35-bs027.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    361. Plans for week 35, August 30 -September 3
      362. -
    362. Thursday September 2
      363. +
    363. Plans for week 35
      364. +
    364. Thursday September 1
    365. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    366. Regression analysis, overarching aims
    367. Regression analysis, overarching aims II
      368. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    368. Economy-size SVD
    369. Codes for the SVD
    370. Note about SVD Calculations
      371. -
    371. Friday September 3
      372. +
    372. Friday September 2
    373. Mathematics of the SVD and implications
    374. Example Matrix
    375. Setting up the Matrix to be inverted
      376. diff --git a/doc/pub/week35/html/._week35-bs028.html b/doc/pub/week35/html/._week35-bs028.html index 76acc5ef5..f268d09bc 100644 --- a/doc/pub/week35/html/._week35-bs028.html +++ b/doc/pub/week35/html/._week35-bs028.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    376. Plans for week 35, August 30 -September 3
      377. -
    377. Thursday September 2
      378. +
    378. Plans for week 35
      379. +
    379. Thursday September 1
    380. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    381. Regression analysis, overarching aims
    382. Regression analysis, overarching aims II
      383. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    383. Economy-size SVD
    384. Codes for the SVD
    385. Note about SVD Calculations
      386. -
    386. Friday September 3
      387. +
    387. Friday September 2
    388. Mathematics of the SVD and implications
    389. Example Matrix
    390. Setting up the Matrix to be inverted
      391. diff --git a/doc/pub/week35/html/._week35-bs029.html b/doc/pub/week35/html/._week35-bs029.html index 3e9f20fc8..e49ce24d1 100644 --- a/doc/pub/week35/html/._week35-bs029.html +++ b/doc/pub/week35/html/._week35-bs029.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    391. Plans for week 35, August 30 -September 3
      392. -
    392. Thursday September 2
      393. +
    393. Plans for week 35
      394. +
    394. Thursday September 1
    395. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    396. Regression analysis, overarching aims
    397. Regression analysis, overarching aims II
      398. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    398. Economy-size SVD
    399. Codes for the SVD
    400. Note about SVD Calculations
      401. -
    401. Friday September 3
      402. +
    402. Friday September 2
    403. Mathematics of the SVD and implications
    404. Example Matrix
    405. Setting up the Matrix to be inverted
      406. diff --git a/doc/pub/week35/html/._week35-bs030.html b/doc/pub/week35/html/._week35-bs030.html index 032375288..6f48a0435 100644 --- a/doc/pub/week35/html/._week35-bs030.html +++ b/doc/pub/week35/html/._week35-bs030.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    406. Plans for week 35, August 30 -September 3
      407. -
    407. Thursday September 2
      408. +
    408. Plans for week 35
      409. +
    409. Thursday September 1
    410. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    411. Regression analysis, overarching aims
    412. Regression analysis, overarching aims II
      413. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    413. Economy-size SVD
    414. Codes for the SVD
    415. Note about SVD Calculations
      416. -
    416. Friday September 3
      417. +
    417. Friday September 2
    418. Mathematics of the SVD and implications
    419. Example Matrix
    420. Setting up the Matrix to be inverted
      421. diff --git a/doc/pub/week35/html/._week35-bs031.html b/doc/pub/week35/html/._week35-bs031.html index 44dd180dc..4c5910223 100644 --- a/doc/pub/week35/html/._week35-bs031.html +++ b/doc/pub/week35/html/._week35-bs031.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    421. Plans for week 35, August 30 -September 3
      422. -
    422. Thursday September 2
      423. +
    423. Plans for week 35
      424. +
    424. Thursday September 1
    425. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    426. Regression analysis, overarching aims
    427. Regression analysis, overarching aims II
      428. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    428. Economy-size SVD
    429. Codes for the SVD
    430. Note about SVD Calculations
      431. -
    431. Friday September 3
      432. +
    432. Friday September 2
    433. Mathematics of the SVD and implications
    434. Example Matrix
    435. Setting up the Matrix to be inverted
      436. diff --git a/doc/pub/week35/html/._week35-bs032.html b/doc/pub/week35/html/._week35-bs032.html index 36b8eb255..efae2e5e2 100644 --- a/doc/pub/week35/html/._week35-bs032.html +++ b/doc/pub/week35/html/._week35-bs032.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    436. Plans for week 35, August 30 -September 3
      437. -
    437. Thursday September 2
      438. +
    438. Plans for week 35
      439. +
    439. Thursday September 1
    440. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    441. Regression analysis, overarching aims
    442. Regression analysis, overarching aims II
      443. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    443. Economy-size SVD
    444. Codes for the SVD
    445. Note about SVD Calculations
      446. -
    446. Friday September 3
      447. +
    447. Friday September 2
    448. Mathematics of the SVD and implications
    449. Example Matrix
    450. Setting up the Matrix to be inverted
      451. diff --git a/doc/pub/week35/html/._week35-bs033.html b/doc/pub/week35/html/._week35-bs033.html index 8fd9e9ed1..4c4736573 100644 --- a/doc/pub/week35/html/._week35-bs033.html +++ b/doc/pub/week35/html/._week35-bs033.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    451. Plans for week 35, August 30 -September 3
      452. -
    452. Thursday September 2
      453. +
    453. Plans for week 35
      454. +
    454. Thursday September 1
    455. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    456. Regression analysis, overarching aims
    457. Regression analysis, overarching aims II
      458. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    458. Economy-size SVD
    459. Codes for the SVD
    460. Note about SVD Calculations
      461. -
    461. Friday September 3
      462. +
    462. Friday September 2
    463. Mathematics of the SVD and implications
    464. Example Matrix
    465. Setting up the Matrix to be inverted
      466. diff --git a/doc/pub/week35/html/._week35-bs034.html b/doc/pub/week35/html/._week35-bs034.html index ea05a5100..a61237e51 100644 --- a/doc/pub/week35/html/._week35-bs034.html +++ b/doc/pub/week35/html/._week35-bs034.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    466. Plans for week 35, August 30 -September 3
      467. -
    467. Thursday September 2
      468. +
    468. Plans for week 35
      469. +
    469. Thursday September 1
    470. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    471. Regression analysis, overarching aims
    472. Regression analysis, overarching aims II
      473. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    473. Economy-size SVD
    474. Codes for the SVD
    475. Note about SVD Calculations
      476. -
    476. Friday September 3
      477. +
    477. Friday September 2
    478. Mathematics of the SVD and implications
    479. Example Matrix
    480. Setting up the Matrix to be inverted
      481. diff --git a/doc/pub/week35/html/._week35-bs035.html b/doc/pub/week35/html/._week35-bs035.html index 1e38b42c5..072aa3c34 100644 --- a/doc/pub/week35/html/._week35-bs035.html +++ b/doc/pub/week35/html/._week35-bs035.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    481. Plans for week 35, August 30 -September 3
      482. -
    482. Thursday September 2
      483. +
    483. Plans for week 35
      484. +
    484. Thursday September 1
    485. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    486. Regression analysis, overarching aims
    487. Regression analysis, overarching aims II
      488. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    488. Economy-size SVD
    489. Codes for the SVD
    490. Note about SVD Calculations
      491. -
    491. Friday September 3
      492. +
    492. Friday September 2
    493. Mathematics of the SVD and implications
    494. Example Matrix
    495. Setting up the Matrix to be inverted
      496. diff --git a/doc/pub/week35/html/._week35-bs036.html b/doc/pub/week35/html/._week35-bs036.html index 8a1590040..d1ea92104 100644 --- a/doc/pub/week35/html/._week35-bs036.html +++ b/doc/pub/week35/html/._week35-bs036.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    496. Plans for week 35, August 30 -September 3
      497. -
    497. Thursday September 2
      498. +
    498. Plans for week 35
      499. +
    499. Thursday September 1
    500. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    501. Regression analysis, overarching aims
    502. Regression analysis, overarching aims II
      503. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    503. Economy-size SVD
    504. Codes for the SVD
    505. Note about SVD Calculations
      506. -
    506. Friday September 3
      507. +
    507. Friday September 2
    508. Mathematics of the SVD and implications
    509. Example Matrix
    510. Setting up the Matrix to be inverted
      511. diff --git a/doc/pub/week35/html/._week35-bs037.html b/doc/pub/week35/html/._week35-bs037.html index 4817e7bd5..bcfa59dff 100644 --- a/doc/pub/week35/html/._week35-bs037.html +++ b/doc/pub/week35/html/._week35-bs037.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    511. Plans for week 35, August 30 -September 3
      512. -
    512. Thursday September 2
      513. +
    513. Plans for week 35
      514. +
    514. Thursday September 1
    515. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    516. Regression analysis, overarching aims
    517. Regression analysis, overarching aims II
      518. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    518. Economy-size SVD
    519. Codes for the SVD
    520. Note about SVD Calculations
      521. -
    521. Friday September 3
      522. +
    522. Friday September 2
    523. Mathematics of the SVD and implications
    524. Example Matrix
    525. Setting up the Matrix to be inverted
      526. diff --git a/doc/pub/week35/html/._week35-bs038.html b/doc/pub/week35/html/._week35-bs038.html index 9fed27ee2..2c9c5a63f 100644 --- a/doc/pub/week35/html/._week35-bs038.html +++ b/doc/pub/week35/html/._week35-bs038.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    526. Plans for week 35, August 30 -September 3
      527. -
    527. Thursday September 2
      528. +
    528. Plans for week 35
      529. +
    529. Thursday September 1
    530. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    531. Regression analysis, overarching aims
    532. Regression analysis, overarching aims II
      533. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    533. Economy-size SVD
    534. Codes for the SVD
    535. Note about SVD Calculations
      536. -
    536. Friday September 3
      537. +
    537. Friday September 2
    538. Mathematics of the SVD and implications
    539. Example Matrix
    540. Setting up the Matrix to be inverted
      541. diff --git a/doc/pub/week35/html/._week35-bs039.html b/doc/pub/week35/html/._week35-bs039.html index 39c486f19..b8c91d596 100644 --- a/doc/pub/week35/html/._week35-bs039.html +++ b/doc/pub/week35/html/._week35-bs039.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    541. Plans for week 35, August 30 -September 3
      542. -
    542. Thursday September 2
      543. +
    543. Plans for week 35
      544. +
    544. Thursday September 1
    545. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    546. Regression analysis, overarching aims
    547. Regression analysis, overarching aims II
      548. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    548. Economy-size SVD
    549. Codes for the SVD
    550. Note about SVD Calculations
      551. -
    551. Friday September 3
      552. +
    552. Friday September 2
    553. Mathematics of the SVD and implications
    554. Example Matrix
    555. Setting up the Matrix to be inverted
      556. diff --git a/doc/pub/week35/html/._week35-bs040.html b/doc/pub/week35/html/._week35-bs040.html index b3534289e..738eb46db 100644 --- a/doc/pub/week35/html/._week35-bs040.html +++ b/doc/pub/week35/html/._week35-bs040.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    556. Plans for week 35, August 30 -September 3
      557. -
    557. Thursday September 2
      558. +
    558. Plans for week 35
      559. +
    559. Thursday September 1
    560. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    561. Regression analysis, overarching aims
    562. Regression analysis, overarching aims II
      563. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    563. Economy-size SVD
    564. Codes for the SVD
    565. Note about SVD Calculations
      566. -
    566. Friday September 3
      567. +
    567. Friday September 2
    568. Mathematics of the SVD and implications
    569. Example Matrix
    570. Setting up the Matrix to be inverted
      571. diff --git a/doc/pub/week35/html/._week35-bs041.html b/doc/pub/week35/html/._week35-bs041.html index b6d2dd85e..faa165a9a 100644 --- a/doc/pub/week35/html/._week35-bs041.html +++ b/doc/pub/week35/html/._week35-bs041.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    571. Plans for week 35, August 30 -September 3
      572. -
    572. Thursday September 2
      573. +
    573. Plans for week 35
      574. +
    574. Thursday September 1
    575. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    576. Regression analysis, overarching aims
    577. Regression analysis, overarching aims II
      578. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    578. Economy-size SVD
    579. Codes for the SVD
    580. Note about SVD Calculations
      581. -
    581. Friday September 3
      582. +
    582. Friday September 2
    583. Mathematics of the SVD and implications
    584. Example Matrix
    585. Setting up the Matrix to be inverted
      586. diff --git a/doc/pub/week35/html/._week35-bs042.html b/doc/pub/week35/html/._week35-bs042.html index 9c5c42553..cb8c3c730 100644 --- a/doc/pub/week35/html/._week35-bs042.html +++ b/doc/pub/week35/html/._week35-bs042.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    586. Plans for week 35, August 30 -September 3
      587. -
    587. Thursday September 2
      588. +
    588. Plans for week 35
      589. +
    589. Thursday September 1
    590. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    591. Regression analysis, overarching aims
    592. Regression analysis, overarching aims II
      593. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    593. Economy-size SVD
    594. Codes for the SVD
    595. Note about SVD Calculations
      596. -
    596. Friday September 3
      597. +
    597. Friday September 2
    598. Mathematics of the SVD and implications
    599. Example Matrix
    600. Setting up the Matrix to be inverted
      601. diff --git a/doc/pub/week35/html/._week35-bs043.html b/doc/pub/week35/html/._week35-bs043.html index 6ae948f18..d797ab5fc 100644 --- a/doc/pub/week35/html/._week35-bs043.html +++ b/doc/pub/week35/html/._week35-bs043.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    601. Plans for week 35, August 30 -September 3
      602. -
    602. Thursday September 2
      603. +
    603. Plans for week 35
      604. +
    604. Thursday September 1
    605. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    606. Regression analysis, overarching aims
    607. Regression analysis, overarching aims II
      608. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    608. Economy-size SVD
    609. Codes for the SVD
    610. Note about SVD Calculations
      611. -
    611. Friday September 3
      612. +
    612. Friday September 2
    613. Mathematics of the SVD and implications
    614. Example Matrix
    615. Setting up the Matrix to be inverted
      616. diff --git a/doc/pub/week35/html/._week35-bs044.html b/doc/pub/week35/html/._week35-bs044.html index ce5f5ea90..fe536c8a8 100644 --- a/doc/pub/week35/html/._week35-bs044.html +++ b/doc/pub/week35/html/._week35-bs044.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    616. Plans for week 35, August 30 -September 3
      617. -
    617. Thursday September 2
      618. +
    618. Plans for week 35
      619. +
    619. Thursday September 1
    620. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    621. Regression analysis, overarching aims
    622. Regression analysis, overarching aims II
      623. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    623. Economy-size SVD
    624. Codes for the SVD
    625. Note about SVD Calculations
      626. -
    626. Friday September 3
      627. +
    627. Friday September 2
    628. Mathematics of the SVD and implications
    629. Example Matrix
    630. Setting up the Matrix to be inverted
      631. diff --git a/doc/pub/week35/html/._week35-bs045.html b/doc/pub/week35/html/._week35-bs045.html index 6e83a9f37..fddcbe802 100644 --- a/doc/pub/week35/html/._week35-bs045.html +++ b/doc/pub/week35/html/._week35-bs045.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    631. Plans for week 35, August 30 -September 3
      632. -
    632. Thursday September 2
      633. +
    633. Plans for week 35
      634. +
    634. Thursday September 1
    635. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    636. Regression analysis, overarching aims
    637. Regression analysis, overarching aims II
      638. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    638. Economy-size SVD
    639. Codes for the SVD
    640. Note about SVD Calculations
      641. -
    641. Friday September 3
      642. +
    642. Friday September 2
    643. Mathematics of the SVD and implications
    644. Example Matrix
    645. Setting up the Matrix to be inverted
      646. diff --git a/doc/pub/week35/html/._week35-bs046.html b/doc/pub/week35/html/._week35-bs046.html index 800e39296..59e530495 100644 --- a/doc/pub/week35/html/._week35-bs046.html +++ b/doc/pub/week35/html/._week35-bs046.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    646. Plans for week 35, August 30 -September 3
      647. -
    647. Thursday September 2
      648. +
    648. Plans for week 35
      649. +
    649. Thursday September 1
    650. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    651. Regression analysis, overarching aims
    652. Regression analysis, overarching aims II
      653. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    653. Economy-size SVD
    654. Codes for the SVD
    655. Note about SVD Calculations
      656. -
    656. Friday September 3
      657. +
    657. Friday September 2
    658. Mathematics of the SVD and implications
    659. Example Matrix
    660. Setting up the Matrix to be inverted
      661. diff --git a/doc/pub/week35/html/._week35-bs047.html b/doc/pub/week35/html/._week35-bs047.html index c278aa85d..13450aee1 100644 --- a/doc/pub/week35/html/._week35-bs047.html +++ b/doc/pub/week35/html/._week35-bs047.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    661. Plans for week 35, August 30 -September 3
      662. -
    662. Thursday September 2
      663. +
    663. Plans for week 35
      664. +
    664. Thursday September 1
    665. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    666. Regression analysis, overarching aims
    667. Regression analysis, overarching aims II
      668. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    668. Economy-size SVD
    669. Codes for the SVD
    670. Note about SVD Calculations
      671. -
    671. Friday September 3
      672. +
    672. Friday September 2
    673. Mathematics of the SVD and implications
    674. Example Matrix
    675. Setting up the Matrix to be inverted
      676. @@ -375,11 +372,7 @@ MathJax.Hub.Config({

       

       

       

      -

      Friday September 3

      - -

      Video of Lecture from 2020 and handwritten notes

      - -

      More material will be added here, see handwritten notes also. Note that this material will be cleaned up after the lecture of Friday September 3. See the handwritten notes from Friday's lecture at https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021.

      +

      Friday September 2

      diff --git a/doc/pub/week35/html/._week35-bs048.html b/doc/pub/week35/html/._week35-bs048.html index 91f5fc815..6bb5131a1 100644 --- a/doc/pub/week35/html/._week35-bs048.html +++ b/doc/pub/week35/html/._week35-bs048.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d

    676. Plans for week 35, August 30 -September 3
      677. -
    677. Thursday September 2
      678. +
    678. Plans for week 35
      679. +
    679. Thursday September 1
    680. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    681. Regression analysis, overarching aims
    682. Regression analysis, overarching aims II
      683. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    683. Economy-size SVD
    684. Codes for the SVD
    685. Note about SVD Calculations
      686. -
    686. Friday September 3
      687. +
    687. Friday September 2
    688. Mathematics of the SVD and implications
    689. Example Matrix
    690. Setting up the Matrix to be inverted
      691. diff --git a/doc/pub/week35/html/._week35-bs049.html b/doc/pub/week35/html/._week35-bs049.html index 417930650..68b81a6f1 100644 --- a/doc/pub/week35/html/._week35-bs049.html +++ b/doc/pub/week35/html/._week35-bs049.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    691. Plans for week 35, August 30 -September 3
      692. -
    692. Thursday September 2
      693. +
    693. Plans for week 35
      694. +
    694. Thursday September 1
    695. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    696. Regression analysis, overarching aims
    697. Regression analysis, overarching aims II
      698. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    698. Economy-size SVD
    699. Codes for the SVD
    700. Note about SVD Calculations
      701. -
    701. Friday September 3
      702. +
    702. Friday September 2
    703. Mathematics of the SVD and implications
    704. Example Matrix
    705. Setting up the Matrix to be inverted
      706. diff --git a/doc/pub/week35/html/._week35-bs050.html b/doc/pub/week35/html/._week35-bs050.html index efb51d14f..33f421c60 100644 --- a/doc/pub/week35/html/._week35-bs050.html +++ b/doc/pub/week35/html/._week35-bs050.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    706. Plans for week 35, August 30 -September 3
      707. -
    707. Thursday September 2
      708. +
    708. Plans for week 35
      709. +
    709. Thursday September 1
    710. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    711. Regression analysis, overarching aims
    712. Regression analysis, overarching aims II
      713. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    713. Economy-size SVD
    714. Codes for the SVD
    715. Note about SVD Calculations
      716. -
    716. Friday September 3
      717. +
    717. Friday September 2
    718. Mathematics of the SVD and implications
    719. Example Matrix
    720. Setting up the Matrix to be inverted
      721. diff --git a/doc/pub/week35/html/._week35-bs051.html b/doc/pub/week35/html/._week35-bs051.html index 9692ca676..1b56e8180 100644 --- a/doc/pub/week35/html/._week35-bs051.html +++ b/doc/pub/week35/html/._week35-bs051.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    721. Plans for week 35, August 30 -September 3
      722. -
    722. Thursday September 2
      723. +
    723. Plans for week 35
      724. +
    724. Thursday September 1
    725. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    726. Regression analysis, overarching aims
    727. Regression analysis, overarching aims II
      728. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    728. Economy-size SVD
    729. Codes for the SVD
    730. Note about SVD Calculations
      731. -
    731. Friday September 3
      732. +
    732. Friday September 2
    733. Mathematics of the SVD and implications
    734. Example Matrix
    735. Setting up the Matrix to be inverted
      736. diff --git a/doc/pub/week35/html/._week35-bs052.html b/doc/pub/week35/html/._week35-bs052.html index 841981e05..1486eedaa 100644 --- a/doc/pub/week35/html/._week35-bs052.html +++ b/doc/pub/week35/html/._week35-bs052.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    736. Plans for week 35, August 30 -September 3
      737. -
    737. Thursday September 2
      738. +
    738. Plans for week 35
      739. +
    739. Thursday September 1
    740. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    741. Regression analysis, overarching aims
    742. Regression analysis, overarching aims II
      743. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    743. Economy-size SVD
    744. Codes for the SVD
    745. Note about SVD Calculations
      746. -
    746. Friday September 3
      747. +
    747. Friday September 2
    748. Mathematics of the SVD and implications
    749. Example Matrix
    750. Setting up the Matrix to be inverted
      751. diff --git a/doc/pub/week35/html/._week35-bs053.html b/doc/pub/week35/html/._week35-bs053.html index 12ab8d2f1..25f343261 100644 --- a/doc/pub/week35/html/._week35-bs053.html +++ b/doc/pub/week35/html/._week35-bs053.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    751. Plans for week 35, August 30 -September 3
      752. -
    752. Thursday September 2
      753. +
    753. Plans for week 35
      754. +
    754. Thursday September 1
    755. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    756. Regression analysis, overarching aims
    757. Regression analysis, overarching aims II
      758. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    758. Economy-size SVD
    759. Codes for the SVD
    760. Note about SVD Calculations
      761. -
    761. Friday September 3
      762. +
    762. Friday September 2
    763. Mathematics of the SVD and implications
    764. Example Matrix
    765. Setting up the Matrix to be inverted
      766. diff --git a/doc/pub/week35/html/._week35-bs054.html b/doc/pub/week35/html/._week35-bs054.html index f7c64d982..376f7d9fd 100644 --- a/doc/pub/week35/html/._week35-bs054.html +++ b/doc/pub/week35/html/._week35-bs054.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    766. Plans for week 35, August 30 -September 3
      767. -
    767. Thursday September 2
      768. +
    768. Plans for week 35
      769. +
    769. Thursday September 1
    770. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    771. Regression analysis, overarching aims
    772. Regression analysis, overarching aims II
      773. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    773. Economy-size SVD
    774. Codes for the SVD
    775. Note about SVD Calculations
      776. -
    776. Friday September 3
      777. +
    777. Friday September 2
    778. Mathematics of the SVD and implications
    779. Example Matrix
    780. Setting up the Matrix to be inverted
      781. diff --git a/doc/pub/week35/html/._week35-bs055.html b/doc/pub/week35/html/._week35-bs055.html index 0c84e8e04..2f94e3584 100644 --- a/doc/pub/week35/html/._week35-bs055.html +++ b/doc/pub/week35/html/._week35-bs055.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    781. Plans for week 35, August 30 -September 3
      782. -
    782. Thursday September 2
      783. +
    783. Plans for week 35
      784. +
    784. Thursday September 1
    785. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    786. Regression analysis, overarching aims
    787. Regression analysis, overarching aims II
      788. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    788. Economy-size SVD
    789. Codes for the SVD
    790. Note about SVD Calculations
      791. -
    791. Friday September 3
      792. +
    792. Friday September 2
    793. Mathematics of the SVD and implications
    794. Example Matrix
    795. Setting up the Matrix to be inverted
      796. diff --git a/doc/pub/week35/html/._week35-bs056.html b/doc/pub/week35/html/._week35-bs056.html index f4f487e95..b64953477 100644 --- a/doc/pub/week35/html/._week35-bs056.html +++ b/doc/pub/week35/html/._week35-bs056.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    796. Plans for week 35, August 30 -September 3
      797. -
    797. Thursday September 2
      798. +
    798. Plans for week 35
      799. +
    799. Thursday September 1
    800. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    801. Regression analysis, overarching aims
    802. Regression analysis, overarching aims II
      803. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    803. Economy-size SVD
    804. Codes for the SVD
    805. Note about SVD Calculations
      806. -
    806. Friday September 3
      807. +
    807. Friday September 2
    808. Mathematics of the SVD and implications
    809. Example Matrix
    810. Setting up the Matrix to be inverted
      811. diff --git a/doc/pub/week35/html/._week35-bs057.html b/doc/pub/week35/html/._week35-bs057.html index 1bf34488c..496e239a7 100644 --- a/doc/pub/week35/html/._week35-bs057.html +++ b/doc/pub/week35/html/._week35-bs057.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    811. Plans for week 35, August 30 -September 3
      812. -
    812. Thursday September 2
      813. +
    813. Plans for week 35
      814. +
    814. Thursday September 1
    815. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    816. Regression analysis, overarching aims
    817. Regression analysis, overarching aims II
      818. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    818. Economy-size SVD
    819. Codes for the SVD
    820. Note about SVD Calculations
      821. -
    821. Friday September 3
      822. +
    822. Friday September 2
    823. Mathematics of the SVD and implications
    824. Example Matrix
    825. Setting up the Matrix to be inverted
      826. diff --git a/doc/pub/week35/html/._week35-bs058.html b/doc/pub/week35/html/._week35-bs058.html index e0a360ae8..14717e2b1 100644 --- a/doc/pub/week35/html/._week35-bs058.html +++ b/doc/pub/week35/html/._week35-bs058.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    826. Plans for week 35, August 30 -September 3
      827. -
    827. Thursday September 2
      828. +
    828. Plans for week 35
      829. +
    829. Thursday September 1
    830. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    831. Regression analysis, overarching aims
    832. Regression analysis, overarching aims II
      833. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    833. Economy-size SVD
    834. Codes for the SVD
    835. Note about SVD Calculations
      836. -
    836. Friday September 3
      837. +
    837. Friday September 2
    838. Mathematics of the SVD and implications
    839. Example Matrix
    840. Setting up the Matrix to be inverted
      841. diff --git a/doc/pub/week35/html/._week35-bs059.html b/doc/pub/week35/html/._week35-bs059.html index 403f33a25..7284f94e1 100644 --- a/doc/pub/week35/html/._week35-bs059.html +++ b/doc/pub/week35/html/._week35-bs059.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    841. Plans for week 35, August 30 -September 3
      842. -
    842. Thursday September 2
      843. +
    843. Plans for week 35
      844. +
    844. Thursday September 1
    845. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    846. Regression analysis, overarching aims
    847. Regression analysis, overarching aims II
      848. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    848. Economy-size SVD
    849. Codes for the SVD
    850. Note about SVD Calculations
      851. -
    851. Friday September 3
      852. +
    852. Friday September 2
    853. Mathematics of the SVD and implications
    854. Example Matrix
    855. Setting up the Matrix to be inverted
      856. diff --git a/doc/pub/week35/html/._week35-bs060.html b/doc/pub/week35/html/._week35-bs060.html index 4c1a4cf00..e5835d6c5 100644 --- a/doc/pub/week35/html/._week35-bs060.html +++ b/doc/pub/week35/html/._week35-bs060.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    856. Plans for week 35, August 30 -September 3
      857. -
    857. Thursday September 2
      858. +
    858. Plans for week 35
      859. +
    859. Thursday September 1
    860. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    861. Regression analysis, overarching aims
    862. Regression analysis, overarching aims II
      863. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    863. Economy-size SVD
    864. Codes for the SVD
    865. Note about SVD Calculations
      866. -
    866. Friday September 3
      867. +
    867. Friday September 2
    868. Mathematics of the SVD and implications
    869. Example Matrix
    870. Setting up the Matrix to be inverted
      871. diff --git a/doc/pub/week35/html/._week35-bs061.html b/doc/pub/week35/html/._week35-bs061.html index 882a589e3..01d6060d0 100644 --- a/doc/pub/week35/html/._week35-bs061.html +++ b/doc/pub/week35/html/._week35-bs061.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    871. Plans for week 35, August 30 -September 3
      872. -
    872. Thursday September 2
      873. +
    873. Plans for week 35
      874. +
    874. Thursday September 1
    875. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    876. Regression analysis, overarching aims
    877. Regression analysis, overarching aims II
      878. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    878. Economy-size SVD
    879. Codes for the SVD
    880. Note about SVD Calculations
      881. -
    881. Friday September 3
      882. +
    882. Friday September 2
    883. Mathematics of the SVD and implications
    884. Example Matrix
    885. Setting up the Matrix to be inverted
      886. diff --git a/doc/pub/week35/html/._week35-bs062.html b/doc/pub/week35/html/._week35-bs062.html index 8ecdb0b6e..8a7fa30c3 100644 --- a/doc/pub/week35/html/._week35-bs062.html +++ b/doc/pub/week35/html/._week35-bs062.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    886. Plans for week 35, August 30 -September 3
      887. -
    887. Thursday September 2
      888. +
    888. Plans for week 35
      889. +
    889. Thursday September 1
    890. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    891. Regression analysis, overarching aims
    892. Regression analysis, overarching aims II
      893. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    893. Economy-size SVD
    894. Codes for the SVD
    895. Note about SVD Calculations
      896. -
    896. Friday September 3
      897. +
    897. Friday September 2
    898. Mathematics of the SVD and implications
    899. Example Matrix
    900. Setting up the Matrix to be inverted
      901. diff --git a/doc/pub/week35/html/._week35-bs063.html b/doc/pub/week35/html/._week35-bs063.html index 8a34331dc..5655185e8 100644 --- a/doc/pub/week35/html/._week35-bs063.html +++ b/doc/pub/week35/html/._week35-bs063.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    901. Plans for week 35, August 30 -September 3
      902. -
    902. Thursday September 2
      903. +
    903. Plans for week 35
      904. +
    904. Thursday September 1
    905. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    906. Regression analysis, overarching aims
    907. Regression analysis, overarching aims II
      908. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    908. Economy-size SVD
    909. Codes for the SVD
    910. Note about SVD Calculations
      911. -
    911. Friday September 3
      912. +
    912. Friday September 2
    913. Mathematics of the SVD and implications
    914. Example Matrix
    915. Setting up the Matrix to be inverted
      916. diff --git a/doc/pub/week35/html/._week35-bs064.html b/doc/pub/week35/html/._week35-bs064.html index ad6fc6a47..3c3b8210d 100644 --- a/doc/pub/week35/html/._week35-bs064.html +++ b/doc/pub/week35/html/._week35-bs064.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    916. Plans for week 35, August 30 -September 3
      917. -
    917. Thursday September 2
      918. +
    918. Plans for week 35
      919. +
    919. Thursday September 1
    920. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    921. Regression analysis, overarching aims
    922. Regression analysis, overarching aims II
      923. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    923. Economy-size SVD
    924. Codes for the SVD
    925. Note about SVD Calculations
      926. -
    926. Friday September 3
      927. +
    927. Friday September 2
    928. Mathematics of the SVD and implications
    929. Example Matrix
    930. Setting up the Matrix to be inverted
      931. diff --git a/doc/pub/week35/html/._week35-bs065.html b/doc/pub/week35/html/._week35-bs065.html index bbf82b1ac..07b75c5c6 100644 --- a/doc/pub/week35/html/._week35-bs065.html +++ b/doc/pub/week35/html/._week35-bs065.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    931. Plans for week 35, August 30 -September 3
      932. -
    932. Thursday September 2
      933. +
    933. Plans for week 35
      934. +
    934. Thursday September 1
    935. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    936. Regression analysis, overarching aims
    937. Regression analysis, overarching aims II
      938. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    938. Economy-size SVD
    939. Codes for the SVD
    940. Note about SVD Calculations
      941. -
    941. Friday September 3
      942. +
    942. Friday September 2
    943. Mathematics of the SVD and implications
    944. Example Matrix
    945. Setting up the Matrix to be inverted
      946. diff --git a/doc/pub/week35/html/._week35-bs066.html b/doc/pub/week35/html/._week35-bs066.html index 9bdcb712d..63fc9acbe 100644 --- a/doc/pub/week35/html/._week35-bs066.html +++ b/doc/pub/week35/html/._week35-bs066.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    946. Plans for week 35, August 30 -September 3
      947. -
    947. Thursday September 2
      948. +
    948. Plans for week 35
      949. +
    949. Thursday September 1
    950. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    951. Regression analysis, overarching aims
    952. Regression analysis, overarching aims II
      953. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    953. Economy-size SVD
    954. Codes for the SVD
    955. Note about SVD Calculations
      956. -
    956. Friday September 3
      957. +
    957. Friday September 2
    958. Mathematics of the SVD and implications
    959. Example Matrix
    960. Setting up the Matrix to be inverted
      961. diff --git a/doc/pub/week35/html/._week35-bs067.html b/doc/pub/week35/html/._week35-bs067.html index 09d18adea..f318f3b9b 100644 --- a/doc/pub/week35/html/._week35-bs067.html +++ b/doc/pub/week35/html/._week35-bs067.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    961. Plans for week 35, August 30 -September 3
      962. -
    962. Thursday September 2
      963. +
    963. Plans for week 35
      964. +
    964. Thursday September 1
    965. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    966. Regression analysis, overarching aims
    967. Regression analysis, overarching aims II
      968. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    968. Economy-size SVD
    969. Codes for the SVD
    970. Note about SVD Calculations
      971. -
    971. Friday September 3
      972. +
    972. Friday September 2
    973. Mathematics of the SVD and implications
    974. Example Matrix
    975. Setting up the Matrix to be inverted
      976. diff --git a/doc/pub/week35/html/._week35-bs068.html b/doc/pub/week35/html/._week35-bs068.html index 085cd6c92..8790032aa 100644 --- a/doc/pub/week35/html/._week35-bs068.html +++ b/doc/pub/week35/html/._week35-bs068.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    976. Plans for week 35, August 30 -September 3
      977. -
    977. Thursday September 2
      978. +
    978. Plans for week 35
      979. +
    979. Thursday September 1
    980. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    981. Regression analysis, overarching aims
    982. Regression analysis, overarching aims II
      983. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    983. Economy-size SVD
    984. Codes for the SVD
    985. Note about SVD Calculations
      986. -
    986. Friday September 3
      987. +
    987. Friday September 2
    988. Mathematics of the SVD and implications
    989. Example Matrix
    990. Setting up the Matrix to be inverted
      991. diff --git a/doc/pub/week35/html/._week35-bs069.html b/doc/pub/week35/html/._week35-bs069.html index a06aabd22..928f92d40 100644 --- a/doc/pub/week35/html/._week35-bs069.html +++ b/doc/pub/week35/html/._week35-bs069.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    991. Plans for week 35, August 30 -September 3
      992. -
    992. Thursday September 2
      993. +
    993. Plans for week 35
      994. +
    994. Thursday September 1
    995. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    996. Regression analysis, overarching aims
    997. Regression analysis, overarching aims II
      998. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    998. Economy-size SVD
    999. Codes for the SVD
    1000. Note about SVD Calculations
      1001. -
    1001. Friday September 3
      1002. +
    1002. Friday September 2
    1003. Mathematics of the SVD and implications
    1004. Example Matrix
    1005. Setting up the Matrix to be inverted
      1006. diff --git a/doc/pub/week35/html/week35-bs.html b/doc/pub/week35/html/week35-bs.html index f6f977e68..e6f5e6ee0 100644 --- a/doc/pub/week35/html/week35-bs.html +++ b/doc/pub/week35/html/week35-bs.html @@ -36,11 +36,8 @@ doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=d
    1006. Plans for week 35, August 30 -September 3
      1007. -
    1007. Thursday September 2
      1008. +
    1008. Plans for week 35
      1009. +
    1009. Thursday September 1
    1010. Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
    1011. Regression analysis, overarching aims
    1012. Regression analysis, overarching aims II
      1013. @@ -339,7 +336,7 @@ MathJax.Hub.Config({
    1013. Economy-size SVD
    1014. Codes for the SVD
    1015. Note about SVD Calculations
      1016. -
    1016. Friday September 3
      1017. +
    1017. Friday September 2
    1018. Mathematics of the SVD and implications
    1019. Example Matrix
    1020. Setting up the Matrix to be inverted
      1021. @@ -393,7 +390,7 @@ MathJax.Hub.Config({
      -

      Nov 3, 2021

      +

      Aug 23, 2022


      @@ -432,7 +429,7 @@ MathJax.Hub.Config({ -->
      - © 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license + © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
      diff --git a/doc/pub/week35/html/week35-reveal.html b/doc/pub/week35/html/week35-reveal.html index de9c10b7e..65b2bf9ba 100644 --- a/doc/pub/week35/html/week35-reveal.html +++ b/doc/pub/week35/html/week35-reveal.html @@ -184,30 +184,28 @@ MathJax.Hub.Config({
      -

      Nov 3, 2021

      +

      Aug 23, 2022


      - © 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license + © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
      -

      Plans for week 35, August 30 -September 3

      +

      Plans for week 35

      -

      Thursday September 2

      +

      Thursday September 1

      The main topics on Thursday are:

        @@ -2384,11 +2382,7 @@ example
      -

      Friday September 3

      - -

      Video of Lecture from 2020 and handwritten notes

      - -

      More material will be added here, see handwritten notes also. Note that this material will be cleaned up after the lecture of Friday September 3. See the handwritten notes from Friday's lecture at https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021.

      +

      Friday September 2

      diff --git a/doc/pub/week35/html/week35-solarized.html b/doc/pub/week35/html/week35-solarized.html index 553b1e071..78cf9e358 100644 --- a/doc/pub/week35/html/week35-solarized.html +++ b/doc/pub/week35/html/week35-solarized.html @@ -63,11 +63,8 @@ div.toc p,a {










      -

      Plans for week 35, August 30 -September 3

      +

      Plans for week 35











      -

      Thursday September 2

      +

      Thursday September 1

      The main topics on Thursday are:

        @@ -2381,11 +2376,7 @@ example











        -

        Friday September 3

        - -

        Video of Lecture from 2020 and handwritten notes

        - -

        More material will be added here, see handwritten notes also. Note that this material will be cleaned up after the lecture of Friday September 3. See the handwritten notes from Friday's lecture at https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021.

        +

        Friday September 2











        Mathematics of the SVD and implications

        @@ -3688,7 +3679,7 @@ model fits the data best.
        - © 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license + © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
        diff --git a/doc/pub/week35/html/week35.html b/doc/pub/week35/html/week35.html index c058a7206..3f4304905 100644 --- a/doc/pub/week35/html/week35.html +++ b/doc/pub/week35/html/week35.html @@ -140,11 +140,8 @@ div.toc p,a {










        -

        Plans for week 35, August 30 -September 3

        +

        Plans for week 35











        -

        Thursday September 2

        +

        Thursday September 1

        The main topics on Thursday are:

          @@ -2458,11 +2453,7 @@ example











          -

          Friday September 3

          - -

          Video of Lecture from 2020 and handwritten notes

          - -

          More material will be added here, see handwritten notes also. Note that this material will be cleaned up after the lecture of Friday September 3. See the handwritten notes from Friday's lecture at https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021.

          +

          Friday September 2











          Mathematics of the SVD and implications

          @@ -3765,7 +3756,7 @@ model fits the data best.
          - © 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license + © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
          diff --git a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz index f2a68d3a0..ed3d0298f 100644 Binary files a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz and b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz differ diff --git a/doc/pub/week35/ipynb/week35.ipynb b/doc/pub/week35/ipynb/week35.ipynb index c71ce6a89..4b48ffc7e 100644 --- a/doc/pub/week35/ipynb/week35.ipynb +++ b/doc/pub/week35/ipynb/week35.ipynb @@ -2,8 +2,10 @@ "cells": [ { "cell_type": "markdown", - "id": "26ae76a1", - "metadata": {}, + "id": "6d1e5582", + "metadata": { + "editable": true + }, "source": [ "\n", @@ -12,41 +14,43 @@ }, { "cell_type": "markdown", - "id": "890d8431", - "metadata": {}, + "id": "46eaf2aa", + "metadata": { + "editable": true + }, "source": [ "# Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression\n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **Nov 3, 2021**\n", + "Date: **Aug 23, 2022**\n", "\n", - "Copyright 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license" + "Copyright 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license" ] }, { "cell_type": "markdown", - "id": "434881ac", - "metadata": {}, + "id": "36c46d50", + "metadata": { + "editable": true + }, "source": [ - "## Plans for week 35, August 30 -September 3\n", + "## Plans for week 35\n", "\n", "* Thursday: Review of ordinary Least Squares with applications and discussion of Ridge Regression and Singular Value Decomposition\n", "\n", - "* [Video of lecture Thursday](https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember2.mp4?vrtx=view-as-webpage).\n", - "\n", "* Friday: Analysis of Ridge and Lasso Regression and links with Singular Value Decomposition\n", "\n", - "* [Video of lecture Friday](https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember3.mp4?vrtx=view-as-webpage)\n", - "\n", "* [Video series on the SVD](http://databookuw.com/page-2/page-4/). Highly recommended." ] }, { "cell_type": "markdown", - "id": "797fbc70", - "metadata": {}, + "id": "141bd80f", + "metadata": { + "editable": true + }, "source": [ - "## Thursday September 2\n", + "## Thursday September 1\n", "\n", "The main topics on Thursday are:\n", "1. Repetition from last week on linear regression\n", @@ -60,8 +64,10 @@ }, { "cell_type": "markdown", - "id": "a28f0549", - "metadata": {}, + "id": "0feb829b", + "metadata": { + "editable": true + }, "source": [ "## Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week\n", "\n", @@ -92,8 +98,10 @@ }, { "cell_type": "markdown", - "id": "9f12cdfb", - "metadata": {}, + "id": "e29e758f", + "metadata": { + "editable": true + }, "source": [ "## Regression analysis, overarching aims\n", "\n", @@ -112,8 +120,10 @@ }, { "cell_type": "markdown", - "id": "fe22bbd9", - "metadata": {}, + "id": "56fea34b", + "metadata": { + "editable": true + }, "source": [ "## Regression analysis, overarching aims II\n", "\n", @@ -138,8 +148,10 @@ }, { "cell_type": "markdown", - "id": "88accdb4", - "metadata": {}, + "id": "873b3cb3", + "metadata": { + "editable": true + }, "source": [ "## Examples\n", "In order to understand the relation among the predictors $p$, the set of data $n$ and the target (outcome, output etc) $\\boldsymbol{y}$,\n", @@ -151,8 +163,10 @@ }, { "cell_type": "markdown", - "id": "9e3bb9b4", - "metadata": {}, + "id": "268b1767", + "metadata": { + "editable": true + }, "source": [ "$$\n", "BE(A) = a_0+a_1A+a_2A^{2/3}+a_3A^{-1/3}+a_4A^{-1},\n", @@ -161,8 +175,10 @@ }, { "cell_type": "markdown", - "id": "e7cf3568", - "metadata": {}, + "id": "1b6c2011", + "metadata": { + "editable": true + }, "source": [ "we have five predictors, that is the intercept, the $A$ dependent term, the $A^{2/3}$ term and the $A^{-1/3}$ and $A^{-1}$ terms.\n", "This gives $p=0,1,2,3,4$. Furthermore we have $n$ entries for each predictor. It means that our design matrix is a \n", @@ -174,8 +190,10 @@ }, { "cell_type": "markdown", - "id": "28d154ab", - "metadata": {}, + "id": "43a1b529", + "metadata": { + "editable": true + }, "source": [ "## General linear models\n", "Before we proceed let us study a case from linear algebra where we aim at fitting a set of data $\\boldsymbol{y}=[y_0,y_1,\\dots,y_{n-1}]$. We could think of these data as a result of an experiment or a complicated numerical experiment. These data are functions of a series of variables $\\boldsymbol{x}=[x_0,x_1,\\dots,x_{n-1}]$, that is $y_i = y(x_i)$ with $i=0,1,2,\\dots,n-1$. The variables $x_i$ could represent physical quantities like time, temperature, position etc. We assume that $y(x)$ is a smooth function. \n", @@ -185,8 +203,10 @@ }, { "cell_type": "markdown", - "id": "471571ac", - "metadata": {}, + "id": "2fdc6a4a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y=y(x) \\rightarrow y(x_i)=\\tilde{y}_i+\\epsilon_i=\\sum_{j=0}^{n-1} \\beta_j x_i^j+\\epsilon_i,\n", @@ -195,16 +215,20 @@ }, { "cell_type": "markdown", - "id": "55f3ec65", - "metadata": {}, + "id": "19f0111e", + "metadata": { + "editable": true + }, "source": [ "where $\\epsilon_i$ is the error in our approximation." ] }, { "cell_type": "markdown", - "id": "a8364a31", - "metadata": {}, + "id": "323ebc87", + "metadata": { + "editable": true + }, "source": [ "## Rewriting the fitting procedure as a linear algebra problem\n", "For every set of values $y_i,x_i$ we have thus the corresponding set of equations" @@ -212,8 +236,10 @@ }, { "cell_type": "markdown", - "id": "4a97ef95", - "metadata": {}, + "id": "0296a976", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -228,8 +254,10 @@ }, { "cell_type": "markdown", - "id": "f6fa4c72", - "metadata": {}, + "id": "5f9d2c53", + "metadata": { + "editable": true + }, "source": [ "## Rewriting the fitting procedure as a linear algebra problem, more details\n", "Defining the vectors" @@ -237,8 +265,10 @@ }, { "cell_type": "markdown", - "id": "c9ca1dc8", - "metadata": {}, + "id": "c6df848b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{y} = [y_0,y_1, y_2,\\dots, y_{n-1}]^T,\n", @@ -247,16 +277,20 @@ }, { "cell_type": "markdown", - "id": "8b769bbc", - "metadata": {}, + "id": "7d6cf42a", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "1bb26ed0", - "metadata": {}, + "id": "e63839de", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\beta} = [\\beta_0,\\beta_1, \\beta_2,\\dots, \\beta_{n-1}]^T,\n", @@ -265,16 +299,20 @@ }, { "cell_type": "markdown", - "id": "9dda37f7", - "metadata": {}, + "id": "8285f1f7", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "01376567", - "metadata": {}, + "id": "2cd71f12", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\epsilon} = [\\epsilon_0,\\epsilon_1, \\epsilon_2,\\dots, \\epsilon_{n-1}]^T,\n", @@ -283,16 +321,20 @@ }, { "cell_type": "markdown", - "id": "6d470e53", - "metadata": {}, + "id": "9a192c37", + "metadata": { + "editable": true + }, "source": [ "and the design matrix" ] }, { "cell_type": "markdown", - "id": "923ff5eb", - "metadata": {}, + "id": "9811a878", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}=\n", @@ -308,16 +350,20 @@ }, { "cell_type": "markdown", - "id": "15ccdf9e", - "metadata": {}, + "id": "15ee0e7c", + "metadata": { + "editable": true + }, "source": [ "we can rewrite our equations as" ] }, { "cell_type": "markdown", - "id": "b7d4c290", - "metadata": {}, + "id": "1c4bc46a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta}+\\boldsymbol{\\epsilon}.\n", @@ -326,16 +372,20 @@ }, { "cell_type": "markdown", - "id": "27af50a7", - "metadata": {}, + "id": "0787965f", + "metadata": { + "editable": true + }, "source": [ "The above design matrix is called a [Vandermonde matrix](https://en.wikipedia.org/wiki/Vandermonde_matrix)." ] }, { "cell_type": "markdown", - "id": "7dd2cd83", - "metadata": {}, + "id": "fbb75ec9", + "metadata": { + "editable": true + }, "source": [ "## Generalizing the fitting procedure as a linear algebra problem\n", "\n", @@ -348,8 +398,10 @@ }, { "cell_type": "markdown", - "id": "635ecdc8", - "metadata": {}, + "id": "5ed9e388", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -366,16 +418,20 @@ }, { "cell_type": "markdown", - "id": "24e2fd35", - "metadata": {}, + "id": "fc197985", + "metadata": { + "editable": true + }, "source": [ "**Note that we have $p=n$ here. The matrix is symmetric. This is generally not the case!**" ] }, { "cell_type": "markdown", - "id": "480d9d03", - "metadata": {}, + "id": "09c5f4cd", + "metadata": { + "editable": true + }, "source": [ "## Generalizing the fitting procedure as a linear algebra problem\n", "We redefine in turn the matrix $\\boldsymbol{X}$ as" @@ -383,8 +439,10 @@ }, { "cell_type": "markdown", - "id": "3d9b2af3", - "metadata": {}, + "id": "c882cf68", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}=\n", @@ -400,16 +458,20 @@ }, { "cell_type": "markdown", - "id": "a3ced18b", - "metadata": {}, + "id": "d7131338", + "metadata": { + "editable": true + }, "source": [ "and without loss of generality we rewrite again our equations as" ] }, { "cell_type": "markdown", - "id": "1f72e12d", - "metadata": {}, + "id": "d6467190", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta}+\\boldsymbol{\\epsilon}.\n", @@ -418,16 +480,20 @@ }, { "cell_type": "markdown", - "id": "47eda213", - "metadata": {}, + "id": "23b406d4", + "metadata": { + "editable": true + }, "source": [ "The left-hand side of this equation is kwown. Our error vector $\\boldsymbol{\\epsilon}$ and the parameter vector $\\boldsymbol{\\beta}$ are our unknow quantities. How can we obtain the optimal set of $\\beta_i$ values?" ] }, { "cell_type": "markdown", - "id": "169cfe9d", - "metadata": {}, + "id": "9bc80165", + "metadata": { + "editable": true + }, "source": [ "## Optimizing our parameters\n", "We have defined the matrix $\\boldsymbol{X}$ via the equations" @@ -435,8 +501,10 @@ }, { "cell_type": "markdown", - "id": "a2180298", - "metadata": {}, + "id": "588a135a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -453,8 +521,10 @@ }, { "cell_type": "markdown", - "id": "d515ebce", - "metadata": {}, + "id": "8fa1a482", + "metadata": { + "editable": true + }, "source": [ "As we noted above, we stayed with a system with the design matrix \n", " $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times n}$, that is we have $p=n$. For reasons to come later (algorithmic arguments) we will hereafter define \n", @@ -463,8 +533,10 @@ }, { "cell_type": "markdown", - "id": "7d67b025", - "metadata": {}, + "id": "ae140b67", + "metadata": { + "editable": true + }, "source": [ "## Our model for the nuclear binding energies\n", "\n", @@ -476,161 +548,12 @@ { "cell_type": "code", "execution_count": 1, - "id": "be62aa5c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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          " - ], - "text/plain": [ - " 1 A A^(2/3) A^(-1/3) 1/A\n", - "A \n", - "4 1.0 4.0 2.519842 0.629961 0.250000\n", - "5 1.0 5.0 2.924018 0.584804 0.200000\n", - "6 1.0 6.0 3.301927 0.550321 0.166667\n", - "7 1.0 7.0 3.659306 0.522758 0.142857\n", - "8 1.0 8.0 4.000000 0.500000 0.125000\n", - ".. ... ... ... ... ...\n", - "264 1.0 264.0 41.153106 0.155883 0.003788\n", - "265 1.0 265.0 41.256962 0.155687 0.003774\n", - "266 1.0 266.0 41.360688 0.155491 0.003759\n", - "269 1.0 269.0 41.671089 0.154911 0.003717\n", - "270 1.0 270.0 41.774300 0.154720 0.003704\n", - "\n", - "[264 rows x 5 columns]" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "id": "a29a6b0c", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "%matplotlib inline\n", "\n", @@ -707,16 +630,20 @@ }, { "cell_type": "markdown", - "id": "3ae8b693", - "metadata": {}, + "id": "b9c79b70", + "metadata": { + "editable": true + }, "source": [ "With $\\boldsymbol{\\beta}\\in {\\mathbb{R}}^{p\\times 1}$, it means that we will hereafter write our equations for the approximation as" ] }, { "cell_type": "markdown", - "id": "bbb85729", - "metadata": {}, + "id": "ba640b20", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\tilde{y}}= \\boldsymbol{X}\\boldsymbol{\\beta},\n", @@ -725,16 +652,20 @@ }, { "cell_type": "markdown", - "id": "5acf922c", - "metadata": {}, + "id": "063863e9", + "metadata": { + "editable": true + }, "source": [ "throughout these lectures." ] }, { "cell_type": "markdown", - "id": "919a84f2", - "metadata": {}, + "id": "31d6838d", + "metadata": { + "editable": true + }, "source": [ "## Optimizing our parameters, more details\n", "With the above we use the design matrix to define the approximation $\\boldsymbol{\\tilde{y}}$ via the unknown quantity $\\boldsymbol{\\beta}$ as" @@ -742,8 +673,10 @@ }, { "cell_type": "markdown", - "id": "1b793777", - "metadata": {}, + "id": "649a8d7a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\tilde{y}}= \\boldsymbol{X}\\boldsymbol{\\beta},\n", @@ -752,16 +685,20 @@ }, { "cell_type": "markdown", - "id": "7556c68c", - "metadata": {}, + "id": "186cda54", + "metadata": { + "editable": true + }, "source": [ "and in order to find the optimal parameters $\\beta_i$ instead of solving the above linear algebra problem, we define a function which gives a measure of the spread between the values $y_i$ (which represent hopefully the exact values) and the parameterized values $\\tilde{y}_i$, namely" ] }, { "cell_type": "markdown", - "id": "aa335b7c", - "metadata": {}, + "id": "4507e794", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{\\beta})=\\frac{1}{n}\\sum_{i=0}^{n-1}\\left(y_i-\\tilde{y}_i\\right)^2=\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}}\\right)\\right\\},\n", @@ -770,16 +707,20 @@ }, { "cell_type": "markdown", - "id": "b33853bc", - "metadata": {}, + "id": "3514ca65", + "metadata": { + "editable": true + }, "source": [ "or using the matrix $\\boldsymbol{X}$ and in a more compact matrix-vector notation as" ] }, { "cell_type": "markdown", - "id": "b6930121", - "metadata": {}, + "id": "07d2822f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{\\beta})=\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right\\}.\n", @@ -788,8 +729,10 @@ }, { "cell_type": "markdown", - "id": "6fd23574", - "metadata": {}, + "id": "fb1facee", + "metadata": { + "editable": true + }, "source": [ "This function is one possible way to define the so-called cost function.\n", "\n", @@ -799,8 +742,10 @@ }, { "cell_type": "markdown", - "id": "e1214ba2", - "metadata": {}, + "id": "7df401c6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{\\beta})=\\frac{1}{2n}\\sum_{i=0}^{n-1}\\left(y_i-\\tilde{y}_i\\right)^2,\n", @@ -809,16 +754,20 @@ }, { "cell_type": "markdown", - "id": "c51c03b5", - "metadata": {}, + "id": "9e849b79", + "metadata": { + "editable": true + }, "source": [ "since when taking the first derivative with respect to the unknown parameters $\\beta$, the factor of $2$ cancels out." ] }, { "cell_type": "markdown", - "id": "fbeeb5c1", - "metadata": {}, + "id": "3b11f9a6", + "metadata": { + "editable": true + }, "source": [ "## Interpretations and optimizing our parameters\n", "\n", @@ -827,8 +776,10 @@ }, { "cell_type": "markdown", - "id": "bbf3d893", - "metadata": {}, + "id": "22331d1b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{\\beta})=\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right\\},\n", @@ -837,8 +788,10 @@ }, { "cell_type": "markdown", - "id": "0ed621c2", - "metadata": {}, + "id": "3cef7e7c", + "metadata": { + "editable": true + }, "source": [ "can be linked to the variance of the quantity $y_i$ if we interpret the latter as the mean value. \n", "When linking (see the discussion below) with the maximum likelihood approach below, we will indeed interpret $y_i$ as a mean value" @@ -846,8 +799,10 @@ }, { "cell_type": "markdown", - "id": "9be95ee2", - "metadata": {}, + "id": "f16afb29", + "metadata": { + "editable": true + }, "source": [ "$$\n", "y_{i}=\\langle y_i \\rangle = \\beta_0x_{i,0}+\\beta_1x_{i,1}+\\beta_2x_{i,2}+\\dots+\\beta_{n-1}x_{i,n-1}+\\epsilon_i,\n", @@ -856,8 +811,10 @@ }, { "cell_type": "markdown", - "id": "234ddf49", - "metadata": {}, + "id": "6519e27d", + "metadata": { + "editable": true + }, "source": [ "where $\\langle y_i \\rangle$ is the mean value. Keep in mind also that\n", "till now we have treated $y_i$ as the exact value. Normally, the\n", @@ -873,8 +830,10 @@ }, { "cell_type": "markdown", - "id": "ef177e0d", - "metadata": {}, + "id": "35f502e2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", @@ -884,16 +843,20 @@ }, { "cell_type": "markdown", - "id": "066c1c10", - "metadata": {}, + "id": "c4514d1f", + "metadata": { + "editable": true + }, "source": [ "In practical terms it means we will require" ] }, { "cell_type": "markdown", - "id": "e0e0d740", - "metadata": {}, + "id": "c800e873", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial C(\\boldsymbol{\\beta})}{\\partial \\beta_j} = \\frac{\\partial }{\\partial \\beta_j}\\left[ \\frac{1}{n}\\sum_{i=0}^{n-1}\\left(y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}\\right)^2\\right]=0,\n", @@ -902,16 +865,20 @@ }, { "cell_type": "markdown", - "id": "623edac9", - "metadata": {}, + "id": "6d783225", + "metadata": { + "editable": true + }, "source": [ "which results in" ] }, { "cell_type": "markdown", - "id": "787d2117", - "metadata": {}, + "id": "71a87f0d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial C(\\boldsymbol{\\beta})}{\\partial \\beta_j} = -\\frac{2}{n}\\left[ \\sum_{i=0}^{n-1}x_{ij}\\left(y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}\\right)\\right]=0,\n", @@ -920,16 +887,20 @@ }, { "cell_type": "markdown", - "id": "877597cf", - "metadata": {}, + "id": "5174c8a4", + "metadata": { + "editable": true + }, "source": [ "or in a matrix-vector form as" ] }, { "cell_type": "markdown", - "id": "8d770e9d", - "metadata": {}, + "id": "d0763025", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial C(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = 0 = \\boldsymbol{X}^T\\left( \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right).\n", @@ -938,8 +909,10 @@ }, { "cell_type": "markdown", - "id": "b1dfe8bf", - "metadata": {}, + "id": "789238c8", + "metadata": { + "editable": true + }, "source": [ "## Interpretations and optimizing our parameters\n", "We can rewrite" @@ -947,8 +920,10 @@ }, { "cell_type": "markdown", - "id": "0c3505c9", - "metadata": {}, + "id": "0938c59b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial C(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = 0 = \\boldsymbol{X}^T\\left( \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right),\n", @@ -957,16 +932,20 @@ }, { "cell_type": "markdown", - "id": "6096739c", - "metadata": {}, + "id": "c6540fd2", + "metadata": { + "editable": true + }, "source": [ "as" ] }, { "cell_type": "markdown", - "id": "435f4a55", - "metadata": {}, + "id": "54964148", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{y} = \\boldsymbol{X}^T\\boldsymbol{X}\\boldsymbol{\\beta},\n", @@ -975,16 +954,20 @@ }, { "cell_type": "markdown", - "id": "dbf7ae4d", - "metadata": {}, + "id": "da0322ca", + "metadata": { + "editable": true + }, "source": [ "and if the matrix $\\boldsymbol{X}^T\\boldsymbol{X}$ is invertible we have the solution" ] }, { "cell_type": "markdown", - "id": "6745642f", - "metadata": {}, + "id": "b9c08b48", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\beta} =\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n", @@ -993,8 +976,10 @@ }, { "cell_type": "markdown", - "id": "ddda6f20", - "metadata": {}, + "id": "7281f2ba", + "metadata": { + "editable": true + }, "source": [ "We note also that since our design matrix is defined as $\\boldsymbol{X}\\in\n", "{\\mathbb{R}}^{n\\times p}$, the product $\\boldsymbol{X}^T\\boldsymbol{X} \\in\n", @@ -1012,8 +997,10 @@ }, { "cell_type": "markdown", - "id": "b9cf4eae", - "metadata": {}, + "id": "333c8590", + "metadata": { + "editable": true + }, "source": [ "## Some useful matrix and vector expressions\n", "\n", @@ -1023,8 +1010,10 @@ }, { "cell_type": "markdown", - "id": "be7471e0", - "metadata": {}, + "id": "92e4efbe", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial (\\boldsymbol{b}^T\\boldsymbol{a})}{\\partial \\boldsymbol{a}} = \\boldsymbol{b},\n", @@ -1033,8 +1022,10 @@ }, { "cell_type": "markdown", - "id": "345c6f7c", - "metadata": {}, + "id": "4d4b642a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial (\\boldsymbol{a}^T\\boldsymbol{A}\\boldsymbol{a})}{\\partial \\boldsymbol{a}} = (\\boldsymbol{A}+\\boldsymbol{A}^T)\\boldsymbol{a},\n", @@ -1043,8 +1034,10 @@ }, { "cell_type": "markdown", - "id": "9fd2aec7", - "metadata": {}, + "id": "8319b7a5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial tr(\\boldsymbol{B}\\boldsymbol{A})}{\\partial \\boldsymbol{A}} = \\boldsymbol{B}^T,\n", @@ -1053,8 +1046,10 @@ }, { "cell_type": "markdown", - "id": "8f327bae", - "metadata": {}, + "id": "bd90a54b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial \\log{\\vert\\boldsymbol{A}\\vert}}{\\partial \\boldsymbol{A}} = (\\boldsymbol{A}^{-1})^T.\n", @@ -1063,8 +1058,10 @@ }, { "cell_type": "markdown", - "id": "37b8427f", - "metadata": {}, + "id": "7a693f02", + "metadata": { + "editable": true + }, "source": [ "## Meet the Hessian Matrix\n", "\n", @@ -1077,8 +1074,10 @@ }, { "cell_type": "markdown", - "id": "84f05dc0", - "metadata": {}, + "id": "34b447d8", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial}{\\partial \\boldsymbol{\\beta}^T}\\frac{\\partial C(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} =\\frac{\\partial}{\\partial \\boldsymbol{\\beta}}\\left[-\\frac{2}{n}\\boldsymbol{X}^T\\left( \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right]=\\frac{2}{n}\\boldsymbol{X}^T\\boldsymbol{X}.\n", @@ -1087,16 +1086,20 @@ }, { "cell_type": "markdown", - "id": "f6b69e17", - "metadata": {}, + "id": "00da1668", + "metadata": { + "editable": true + }, "source": [ "The Hessian matrix plays an important role and is defined here as" ] }, { "cell_type": "markdown", - "id": "5ad43036", - "metadata": {}, + "id": "b6ddebf8", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{H}=\\boldsymbol{X}^T\\boldsymbol{X}.\n", @@ -1105,8 +1108,10 @@ }, { "cell_type": "markdown", - "id": "e0697e67", - "metadata": {}, + "id": "0af94b91", + "metadata": { + "editable": true + }, "source": [ "For ordinary least squares, it is inversely proportional (derivation\n", "next week) with the variance of the optimal parameters\n", @@ -1121,8 +1126,10 @@ }, { "cell_type": "markdown", - "id": "318716a4", - "metadata": {}, + "id": "51cc7a74", + "metadata": { + "editable": true + }, "source": [ "## Interpretations and optimizing our parameters\n", "The residuals $\\boldsymbol{\\epsilon}$ are in turn given by" @@ -1130,8 +1137,10 @@ }, { "cell_type": "markdown", - "id": "9bf30c19", - "metadata": {}, + "id": "ff17b4b8", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\epsilon} = \\boldsymbol{y}-\\boldsymbol{\\tilde{y}} = \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta},\n", @@ -1140,16 +1149,20 @@ }, { "cell_type": "markdown", - "id": "c6505dc1", - "metadata": {}, + "id": "835f5615", + "metadata": { + "editable": true + }, "source": [ "and with" ] }, { "cell_type": "markdown", - "id": "1271eed1", - "metadata": {}, + "id": "b233c766", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\left( \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)= 0,\n", @@ -1158,16 +1171,20 @@ }, { "cell_type": "markdown", - "id": "d38159b8", - "metadata": {}, + "id": "d27bde55", + "metadata": { + "editable": true + }, "source": [ "we have" ] }, { "cell_type": "markdown", - "id": "d7bb1d6d", - "metadata": {}, + "id": "c85f01ba", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{\\epsilon}=\\boldsymbol{X}^T\\left( \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)= 0,\n", @@ -1176,16 +1193,20 @@ }, { "cell_type": "markdown", - "id": "b7dd96c9", - "metadata": {}, + "id": "b055d0e6", + "metadata": { + "editable": true + }, "source": [ "meaning that the solution for $\\boldsymbol{\\beta}$ is the one which minimizes the residuals. Later we will link this with the maximum likelihood approach." ] }, { "cell_type": "markdown", - "id": "4b6e485f", - "metadata": {}, + "id": "f9396899", + "metadata": { + "editable": true + }, "source": [ "## Own code for Ordinary Least Squares\n", "\n", @@ -1196,8 +1217,11 @@ { "cell_type": "code", "execution_count": 2, - "id": "20e8cb33", - "metadata": {}, + "id": "1864d601", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "# matrix inversion to find beta\n", @@ -1208,8 +1232,10 @@ }, { "cell_type": "markdown", - "id": "77ef22e3", - "metadata": {}, + "id": "5ccc40c0", + "metadata": { + "editable": true + }, "source": [ "Alternatively, you can use the least squares functionality in **Numpy** as" ] @@ -1217,8 +1243,11 @@ { "cell_type": "code", "execution_count": 3, - "id": "0c7e2e85", - "metadata": {}, + "id": "29089ff7", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "fit = np.linalg.lstsq(X, Energies, rcond =None)[0]\n", @@ -1227,8 +1256,10 @@ }, { "cell_type": "markdown", - "id": "776d3539", - "metadata": {}, + "id": "2e68bc90", + "metadata": { + "editable": true + }, "source": [ "And finally we plot our fit with and compare with data" ] @@ -1236,22 +1267,12 @@ { "cell_type": "code", "execution_count": 4, - "id": "fe76261f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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tL/urU712tf+H19WfBGBJo62jagxALBQgFgqcvTLbzWfuZvMeJwdTJI+m6X5tmPShFOmDafKdGWJpj9rDSu5gHsgDKdJ1Qzy+4ASPLQmwcGMda65tZONlTTbr7CwqZQ1/m4h8B3gZ/x1/hWL5ptyO/bSXUBISLcLJJcrLR/oZTueJBF2a7Y/PmAkJBRyWNcehOc4Vm5vHHldPyRzLkDqYYuT1JEOvj5A4lGJgIMNgZ47MwSw818MReni9TnBWhGjZUMvKaxu5/PpmwnV2rcBMqfrpkVWVJ+/fSfe+BPtuD3Jy/ZmzDtYsrOHP7lo3620wptqop2S6MqTeSHH6tSGOvzrE0IERRkZyeOMWJhMHIu0Rmq6sYfk1jSy6qo7IyohdNXwRNj3yRaTfTJPtzJCLQOymWhhIEgm5bFpSz7s3TmAVbmPMpIkjRJZFiCyL0PiuRi4HtKAkOlIceqmPo68M0L8/AV05UkfSHDuS5thPenAcIRYLULMmRsP6OMuubaB+fQ2hRXax2ERUZeAnMnk+9y+vc9PqZjb8vEA6V+DUBpffvXk5kaBLa22YoJ1JYExJiSvUro6xeXWMzfe1A9A7kOa1bT107OhncO8IkWN5vP4ciZ2DnNw5yP5HjxNwHeINQcJrIzRfWcvizfW0XFlLsMFKQeeqysDf0dnP0b4k/9Q9wr9/OkYm59G9KcKyppidMmbMHNLcEOG2O9q57Y52VJX+ZI5XD/RxcvcQfa8NkzuUofZ4gXxvBnoznH5hkH10EXCFQGsId3WY5g21NF9Zw8prGonVVPeHQFUGfqgY6o1HPfq704w0C20b6izsjZnDRISmeIh3XL0Irl4EgOcpxwdTvLF/gL7dCXr3DFM4nCF2okD+ZAZOZhj5xRBHgJcdyC10cVdFiK+LU7c+RvsVdSxrjlMTro4orI5eniOT99chbT3ocXo4Q/e1LptsmUJj5h3HEdobY7TfGIMb/cdUlZP9aU6+PkT37gT9e4bJv5mBriyhEwU4MUL6FyOkgWMR+OkiB10VIrg2SsuVNbQtjLOwLsLSpiixUGVFZGX1ZoLSuQJ4SuuhAtk8nF4b4PKFFvjGVAIRoa0pStuNUbhx4djj2ZE83XuG6Xp5gKG9I2QPpMj05Qh1FtCONDydJiv97G0WftXmMNTm4KwOs2htDU01YZY0RFnWFGNJY3TeHuOrysBPZgvUnVKCKUg1CCwOsrIlXu5mGWNmUSgeYMn1jSy5vhHwvwnkunMM70lwatcwg3sSJA4myaYKtL7ukX4thz6ZIxdJcHqRwxttDkNtQmKxS0tLhLb6KG31/s/VC+K01oTn/JlCVRv4TZ3+yb69yx3+3TvXELLzeo2pKiJCaEGI5gVNNL/Tn1TOy3ikDqZIvp4ksW+E3leHSfZkyfV7pE4XSG0vkMnnSDRnGGwbZkebw2CbkGoQXNdhZUucVa1x2htjLGuK0d4YnVMfAlUZ+OlcgaYjHnXRIHfft+KsqWSNMdXLCTvEN8SJb4jTSisrit8CkvuTY7eRgynSmTyZ4x6ZTo9UrsCQk6e3FQYX53ixbYinFgleUIiHA2xYXMd91y+jPlr+M4SqMvBTgzkaTng0tUa54jab9tgYc36j3wJCC0I03NoAgJctfgsY9yGQ789TyHmMHCiQ2lMgVfDobihwqjXH4cUZvtQ1QjIKG5c0cO81S4gEy7OOQFUGvhzKIgqhNRHcmC3gYIyZOCfkEF8fJ77eP+6n478F7EsysneE9OE0y1XJnPA49GqC/D8PkqoXji9O8PkVp7j6nYu46e0LCQVcXEdKdhC4KgPfPZwFILbBDtQaY6bnfN8CCqkCydeTJPcmCewYoOOlftrEZeBQjtS+ND2Pd/C9cAeDbQ6DSxxar6rj6rcv4Oq1TYQDszcIrcrADx7JAVCzLlbmlhhjKpEbdandXEvt5loW3r+QzQUl3ZlmZM8Ih7b10bmtD6c3R+sRj+YOD37Rxxtf7ePVhS7ZFQFGlrr86Z9ePePrCFdd4Ht5j8gxf+77hg01ZW6NMaYaiCtEV/kLwrfc3cLbgGxPluTeJL2vDtO5rY/+AyPIiQKxEwXqXgT945mfybjqAj99OA0ZJdkg1LSEy90cY0yVCrWECN3ql4FW/+FSCqkCJ14ZJLkvSSjrHyuYaVUX+IP7/GXXRha7NneOMWbOcKMu7Tc1wU1Nl37xFFVd4iXe8JcuzC2pus86Y0yVK1ngi8jlIrJz3G1IRP6oFPv+/ivH+Msf7yWb90geTgGQX2yBb4ypLqVc0/Z1YDOAiLjAMeCxUuz7R7uOA/ByRx/SmQFAlpT/qjdjjCmlcpV03gUcUtXOUu40fTxDPl0gXSuEbDUcY0yVKVfg3wdsPfdBEXlQRLaLyPbu7u4Z32mmI0PBUxItQjRkV9gaY6pLyQNfRELA+4Bvn/ucqj6sqltUdUtr68zPceN1Zf3AbxViZZrLwhhjyqUcI/y7gJdV9VSpd+ydyJEvKMlGh/qYlXSMMdWlHIH/u5ynnDNbVM9creadzpEreCQbhYZYqFRNMMaYOaGkgS8iceA3gO+Vap95rxj4qnDKD/xUg9AwB+amNsaYUirpyeiqOgI0l3KfuYK/slVoBLy0RzoM+YjQaCN8Y0yVqfirj3IFf4Qf61fynjJUXNyqwWr4xpgqU/FTK+SLI/zogEeu4DFQ689fXRexwDfGVJeKD/yxEf6Aki8oqQahPhrEcebOwsLGGFMKVRD4oyN8P/iTDWLlHGNMVaqawI8M+4GfqbUzdIwx1akKAt8P+nAx8NO1QkPcztAxxlSfig/8vOfh5JVQCjwXsnFotsA3xlShig/8XEEJJ/zRfTYuuK7DzatbytwqY4wpvSo4D98jPAzhoMPCtbXcf996YqGK77YxxrxFFYzwPSLDSjTocvm6Bgt7Y0zVqoLAV8LDiiNCqNVq98aY6lXxgZ8veIQTiggEW+10TGNM9ar4wM8VlEhxhB9sscA3xlSvKgh8j/BwcYRvgW+MqWJVEfihpCIiBBrtgK0xpnpVfODncx7BNDgCgToLfGNM9Sr1ilcNIvIdEdkvIvtE5MbZ3mc+UUAUJO4irs2QaYypXqUe8n4ReEJVf0dEQkBstndYGMgjgFPvzvaujDFmTitZ4ItIPXAr8GEAVc0C2dnerw4X/MCvs8A3xlS3UpZ0VgLdwP8SkVdE5H8WFzWfVd5gAQC3wer3xpjqVsrADwDXAH+nqlcDI8Anxr9ARB4Uke0isr27u3tGdqrDxcC3Eb4xpsqVMvC7gC5V3Vb893fwPwDGqOrDqrpFVbe0trbOzF6H/MAPNtg5+MaY6laywFfVk8BREbm8+NC7gL2zvuOEv+JVoN5KOsaY6lbqFPz3wDeLZ+i8CXxktncow37gB62Gb4ypcpdMQRH5G+BRVf3FdHemqjuBLdPdzmQ4xcAPN1pJxxhT3SZS0jkAfE5EOkTkv4vI1bPdqJnkjBRH+DatgjGmyl0y8FX1i6p6I3Ab0Av8ffFK2U+KyGWz3sJpchM2wjfGGJjEQVtV7VTVzxZPqfxd4DeBfbPVsJng5T0kq6hAuNZG+MaY6jbhwBeRgIjcLSLfBB4HXgfunbWWzQBvxMNTyIchFKz4eeKMMeaiJnLQ9jfwR/TvBl4EvgU8qKojs9y2acsn8qgq+bAQcCzwjTHVbSJ1jj8DHgX+WFX7Z7k9M6qvO40qODGHUMAC3xhT3S4Z+Kr6awDi+z1glap+WkSWAYtU9cXZbuRkpbIF/u65QzQf8XCBiF1la4wxk7rS9m+BG/HLOwDDwN/MeItmwCtH+9lzbJB9hwYAiFvgG2PMpK60fZuqXiMirwCoan/xitk5Jx7yuxXIKAC1jeFyNscYY+aEyYzwcyLiAgogIq2ANyutmiYpLmwVyPg/61ss8I0xZjKB/yXgMWCBiPwV8Dzw32alVdPk+QN7Aln/TlNzpIytMcaYuWHCJR1V/aaI7MCf5VKA31TVOXnhlaof9MG0/++6pjlZeTLGmJKa1OWnqrof2D9LbZkxXjHwAxlY0hjFrbHFT4wxZiIXXv3wYs+r6vtmrjkzo5j3LI1GaKkJWuAbYwwTG+HfCBwFtgLb8Ms5c9poDd9N+3fcuAW+McZMJPAXAaPTK9wP/DOwVVX3zGbDpmO0pOOk/ZOILPCNMWZi0yMXVPUJVf0QcANwEHhWRP5w1ls3RWcCvzjCt5KOMcZM7KCtiISB9+CP8ldw5hTNSRGRDvwrdAtAXlVnZfWr0Rq+m1IIghO3eXSMMWYiB22/DlwJ/AT4lKq+Ns19vlNVe6a5jYtSBckrkgdccMIW+MYYM5ER/u8BI8BDwEMiUhw/I4Cqat1sNW6qPFUCWb+BbtxFZM4fZzbGmFk3kaHvLUCdqtYWb3XFW+0Uwl6BJ0Vkh4g8eO6TIvKgiGwXke3d3d2T3PQZfuArCLgxq98bYwxMLPA/COwQkW+JyIdFZNE09neLql4D3AV8TERuHf+kqj6sqltUdUtra+uUd6IKbs4f4TsRK+cYYwxMbD78fwcgIlfgB/XXRKQeeAZ4AviFqhYmsjNVPVb8eVpEHgOuB/51im2/IE8VJ+ffl7CVc4wxBia3iPl+Vf28qt4J/Br+5Gnvx78Y65JEJC4itaP3gduB6R4AvkBbwc0rgtgI3xhjiiY1l84oVU3hn7Xzk0n82kLgseIB1ADwqKo+MZX9X4qnipsDxEo6xhgzakqBPxWq+iZwVSn25Sm4xbN07JRMY4zxTTrwReTbQBwI4V9ApcUyz5yhqrj54tW2NsI3xhhgcgugAKCq7we2A3cAdwI/nelGTZc3epaOgBO1wDfGGJh6SecyYAmQA1bNXHNmhlKs4WMlHWOMGTXVwP8k8B/wL6T68sw1Z2Z4Ck7OSjrGGDPeVM/SeR34kxluy4zxPC2WdOy0TGOMGTWlwBeR/wRswD8GoKp6/4y2aprOKulY4BtjDDD1ko6o6r+Z0ZbMIM8DN6d2WqYxxowz1cBfLSLvx59FE1WdzAVYs06xuXSMMeZcUw3854BY8aaXeG3JjdbwwQLfGGNGTeXCq5uBbs4sZj73Al8VJ+9Pj2wlHWOM8U1lhN8ENHLmoi1v5pozM6ykY4wxbzWVK21/BCzCX+P23fiTos0pY5OnIXalrTHGFE01DVtV9f2q+gHmZOAXz9Kxko4xxoyZSg3/PUCbiHyw+NB0VsCaFaqKk/fvW0nHGGN8l0xDEdlwzkMt+BOmOcXb3Js8Le/h5v3J0yRkK14ZYwxMbIT/DeAaABF5QFX/5+gTIhJT1eRsNW7KssUTh8IOxQVXjDGm6k2k3jE+MT96znM/n8G2zBjN+IFvo3tjjDljIoE//jz7cxN00gVyEXFF5BUR+fFkf3fCRgPfDtgaY8yYiSTiIhH5sIhczVsDfyoXXT0E7JvC702YZouXBoRthG+MMaMmUsP/C+Ba4CNAu4jsxQ/s/fgHcCdMRNrxz9//K+A/Tqqlk1Ec4dspmcYYc8YlA19VHx7/72JobwQ2Af86yf19Afi/gdrzPSkiDwIPAixbtmySmx4nayUdY4w516TPw1fVLqALeHwyvyci7wVOq+oOEXnHBbb9MPAwwJYtW6Y8R4/m7KCtMcacq5RD4JuB94lIB/At4NdE5B9nZU/5Yg0/aIFvjDGjShb4qvpnqtquqiuA+4CnVfX3ZmVno1MjByzwjTFmVEUWuTVfLOnYCN8YY8ZMdQGUaVHVZ4FnZ2v7UqzhO8GK/DwzxpgpqchEHDtoayN8Y4wZU5GBL3k7S8cYY85VkYFvNXxjjHmrigx8RufCtxq+McaMqcxEzI8etLURvjHGjKrIwBc7aGuMMW9RkYHP2EHbyuyeMcZMRWUmotXwjTHmLSozEa2Gb4wxb1GRgT96Hr5r5+EbY8yYigx8CsWZlW3yNGOMGVORgS/FGn7ADtoaY8yYikxEm1rBGGPeqqID37URvjHGjKnMRCyWdOzCK2OMOaMiA99G+MYY81YVmYhS8H+6duGVMcaMKVkiikhERF4UkV0iskdEPjVr+xqbHtkC3xhjRpVyicMM8GuqmhCRIPC8iDyuqi/M+J6KNXwr6RhjzBklC3xVVSBR/GeweNPZ2JdTUDzAidhBW2OMGVXSIbCIuCKyEzgN/FRVt53z/IMisl1Etnd3d09pH6o6duGVjfCNMeaMkiaiqhZUdTPQDlwvIlee8/zDqrpFVbe0trZObR8FRQF1wHVshG+MMaPKMgRW1QHgGeDOGd92TgHFc0GwwDfGmFGlPEunVUQaivejwG8A+2d6P5pVVPED3/LeGGPGlPIsnTbgH0TExf+g+SdV/fFM78TLef5PV3As8Y0xZkwpz9J5Fbh61veT82v4ngtWwjfGmDMq7jQWzSsoeAFshG+MMeNUXOB7Wb+ko1bDN8aYs1Rg4PvXcvkHbS3xjTFmVMUFfmF0hG/LGxpjzFkqL/AzZ0o6xhhjzqi4wB89LdNG+MYYc7YKDHy/hq+lvMLAGGPmgcoLfKvhG2PMeVVc4BeKI3xcC3xjjBmv4gL/TA2/zA0xxpg5puJiMXpNLbt+M0iwOVjuphhjzJxScYEfaAnQt8KlPmrnZRpjzHiVV9IplvDtKltjjDlbBQa+n/g2U6Yxxpyt4ko6o4FvA3xj5p5cLkdXVxfpdLrcTZn3IpEI7e3tBIMTP15ZcYHP6FmZNsQ3Zs7p6uqitraWFStWWNl1GlSV3t5eurq6WLly5YR/rwJLOqP37I/JmLkmnU7T3NxsYT9NIkJzc/OkvymVck3bpSLyjIjsFZE9IvLQbOzHavjGzG0W9jNjKv8dS1nSyQN/rKovi0gtsENEfqqqe2dyJ2cC3/6ojDFmvJKN8FX1hKq+XLw/DOwDlsz8fvyfNsI3xlzI97//fUSE/fv3z8j2vvnNb7Jp0yY2btzITTfdxK5du8aee+KJJ7j88stZs2YNn/nMZ8Ye/8pXvsKaNWsQEXp6es7a3rPPPsvmzZvZsGEDt91224y0EcpUwxeRFfgLmm875/EHRWS7iGzv7u6e0rbVzsM3xlzC1q1bueWWW9i6deuMbG/lypU899xz7N69mz//8z/nwQcfBKBQKPCxj32Mxx9/nL1797J161b27vWLGjfffDNPPfUUy5cvP2tbAwMDfPSjH+WHP/whe/bs4dvf/vaMtBHKcJaOiNQA3wX+SFWHxj+nqg8DDwNs2bJFz/Prl1Sw0zKNmRd+/2svzcp2H/nwdRd9PpFI8Pzzz/PMM89w991386lPfYpnn32WT37ykzQ0NLB7924+8IEPsHHjRr74xS+SSqX4/ve/z+rVq+nu7uYP/uAPOHLkCABf+MIXuPnmm7npppvGtn/DDTfQ1dUFwIsvvsiaNWtYtWoVAPfddx8/+MEPWL9+PVdfffV52/foo49y7733smzZMgAWLFgw7f8mo0o6wheRIH7Yf1NVvzcb+7AavjHmYn7wgx9w5513ctlll9Hc3MyOHTsA2LVrF1/96lfZt28f3/jGNzhw4AAvvvgiDzzwAF/+8pcBeOihh/j4xz/OSy+9xHe/+10eeOCBt2z/kUce4a677gLg2LFjLF26dOy59vZ2jh07dtH2HThwgP7+ft7xjndw7bXX8vWvf32mul66Eb74NZZHgH2q+teztR+r4RszP1xqJD5btm7dykMP+ScJ3nfffWzdupX3vve9XHfddbS1tQGwevVqbr/9dgA2btzIM888A8BTTz01VpIBGBoaIpFIUFNTA8AzzzzDI488wvPPPz/l9uXzeXbs2MHPfvYzUqkUN954IzfccAOXXXbZlLc5qpQlnZuBDwK7RWRn8bH/pKo/mcmdqI3wjTEX0NfXx9NPP83u3bsREQqFAiLCe97zHsLh8NjrHMcZ+7fjOOTzeQA8z+OFF14gEom8ZduvvvoqDzzwAI8//jjNzc0ALFmyhKNHj469pquriyVLLn6uSnt7O83NzcTjceLxOLfeeiu7du2akcAv5Vk6z6uqqOomVd1cvM1o2INNnmaMubDvfOc7fPCDH6Szs5OOjg6OHj3KypUr+fnPfz6h37/99tvHyjsAO3fuBODIkSPce++9fOMb3zgrmK+77jreeOMNDh8+TDab5Vvf+hbve9/7LrqPe+65h+eff558Pk8ymWTbtm2sW7du8p09jwq80tYO2hpjzm/r1q381m/91lmP/fZv//aEz9b50pe+xPbt29m0aRPr16/nq1/9KgCf/vSn6e3t5aMf/SibN29my5YtAAQCAb7yla9wxx13sG7dOj7wgQ+wYcOGsW21t7fT1dXFpk2bxo4HrFu3jjvvvJNNmzZx/fXX88ADD3DllVfOSP9ltAQy12zZskW3b98+6d/bc3yQv37yAFe01fKnd1wxCy0zxkzVvn37Zmy0as7/31NEdqjqlvO9vuJG+GcO2toQ3xhjxqvYwLcavjHGnK3iAt8mTzPGmPOr2MAXmx7ZGGPOUoGB7/+0Eb4xxpyt4gJ/dMkrxxLfGGPOUnGBf+bCq/K2wxgzN7muy+bNm8duHR0dY5OfdXR08Oijj5a5hbOn4ta09TybWsEYc2HRaHTsCtlRv/zlL4EzgX///feXoWWzr/ICf3SEX95mGGMuYffdu2dluxt/tHHSv1NTU0MikeATn/gE+/btY/PmzXzoQx/i4x//+Cy0sHwqLvBHrxx2rYZvjDmPVCrF5s2bAX/hkscee2zsuc985jN87nOf48c//nGZWje7Ki/wiz/twitj5rapjMRnwvlKOtWiAg/ajp6Hb4wxZryKC/yCZ1faGmOmpra2luHh4XI3Y9ZUXOCPlnTsPHxjzGRt2rQJ13W56qqr+PznP1/u5sy4iqvhBx2H2kiASMAtd1OMMXNQIpG44GPBYJCnn3661E0qmVKuafv3wHuB06o6M7P5n8cta1u4ZW3LbG3eGGPmrVKWdL4G3FnC/RljjBmnlGva/ivQV6r9GWPmprm6yt58M5X/jnPqoK2IPCgi20Vke3d3d7mbY4yZYZFIhN7eXgv9aVJVent7iUQik/q9OXXQVlUfBh4Gf03bMjfHGDPDRhfttgHd9EUiEdrb2yf1O3Mq8I0xlS0YDLJy5cpyN6NqzamSjjHGmNlTssAXka3Ar4DLRaRLRH6/VPs2xhhTwpKOqv5uqfZljDHmrWSuHi0XkW6gc4IvbwF6ZrE5c4H1sXJUQz+tj+WzXFVbz/fEnA38yRCR7aq6pdztmE3Wx8pRDf20Ps5NdtDWGGOqhAW+McZUiUoJ/IfL3YASsD5Wjmrop/VxDqqIGr4xxphLq5QRvjHGmEuwwDfGmCox7wNfRO4UkddF5KCIfKLc7ZkpItIhIrtFZKeIbC8+1iQiPxWRN4o/G8vdzskQkb8XkdMi8tq4x87bJ/F9qfi+vioi15Sv5RN3gT7+hYgcK76XO0Xk3eOe+7NiH18XkTvK0+rJEZGlIvKMiOwVkT0i8lDx8Yp5Ly/Sx/n9XqrqvL0BLnAIWAWEgF3A+nK3a4b61gG0nPPYfwc+Ubz/CeCz5W7nJPt0K3AN8Nql+gS8G3gcEOAGYFu52z+NPv4F8Cfnee364t9sGFhZ/Ft2y92HCfSxDbimeL8WOFDsS8W8lxfp47x+L+f7CP964KCqvqmqWeBbwD1lbtNsugf4h+L9fwB+s3xNmTw9/yI4F+rTPcDX1fcC0CAibSVp6DRcoI8Xcg/wLVXNqOph4CD+3/ScpqonVPXl4v1hYB+whAp6Ly/SxwuZF+/lfA/8JcDRcf/u4uJvynyiwJMiskNEHiw+tlBVTxTvnwQWlqdpM+pCfaq09/YPi+WMvx9Xipv3fRSRFcDVwDYq9L08p48wj9/L+R74lewWVb0GuAv4mIjcOv5J9b9HVtQ5tZXYp6K/A1YDm4ETwP9b1tbMEBGpAb4L/JGqDo1/rlLey/P0cV6/l/M98I8BS8f9u7342LynqseKP08Dj+F/PTw1+lW4+PN0+Vo4Yy7Up4p5b1X1lKoWVNUD/j/OfNWft30UkSB+EH5TVb9XfLii3svz9XG+v5fzPfBfAtaKyEoRCQH3AT8sc5umTUTiIlI7eh+4HXgNv28fKr7sQ8APytPCGXWhPv0Q+D+KZ3jcAAyOKxfMK+fUq38L/70Ev4/3iUhYRFYCa4EXS92+yRIRAR4B9qnqX497qmLeywv1cd6/l+U+ajzdG/4ZAAfwj4r/53K3Z4b6tAr/iP8uYM9ov4Bm4GfAG8BTQFO52zrJfm3F/xqcw69x/v6F+oR/RsffFN/X3cCWcrd/Gn38RrEPr+IHQ9u41//nYh9fB+4qd/sn2Mdb8Ms1rwI7i7d3V9J7eZE+zuv30qZWMMaYKjHfSzrGGGMmyALfGGOqhAW+McZUCQt8Y4ypEhb4xhhTJSzwjTGmSljgG2NMlbDAN1VBRL4sIp3T3Mb/JSIqIuvGPbaveGXlVLb3v8bNq75TRE6KyERn2jRm0izwTcUrznb4TiA0OmXFFG3Ev+LyPcXtRvBnhOy4wH7fISJfu9DGVPUjqrpZVTfjX6afBz48jfYZc1EW+KYafAr4S2AvsGEa29kEfJZi4OMverFfp3m5uoi0AE8A/1VV5/1cUGbussA3FU1ENgBXAv8bfxGLK8/zmp+fU1oZvf36OS9djz8h2AIRqccf8b86zfbFgB8B/6Sq/2M62zLmUgLlboAxs+wvgf+iqioi+zjPCF9V336pjYjIUqBXVVMi8lPgDvwR/+7zvHYb/lJ3NUCTiOwsPvX/qOq/jHudi79K235V/fNJ98yYSbLANxVLRN4G3AlcLSJ/A0Q4f0D/HH/d0nP9iao+Vby/cdzv/gT4N/jrnn7/3F9S1bcVt/sO4MOq+uELNPFvgSDwbyfSH2OmywLfVLL/Btw9GtoishB45dwXTWSEz9mj+eeA/wFEOc8HyESIyCeBa4F3qGp+KtswZrKshm8qUrH+Hho3QkdVTwE1ItI0hU2OjfBVNYNfu8+q6sAU2rYC+Av8+eOfH3fM4H9PoV3GTJjNh2+MMVXCRvjGGFMlLPCNMaZKWOAbY0yVsMA3xpgqYYFvjDFVwgLfGGOqhAW+McZUif8fLKN5S8wF8OUAAAAASUVORK5CYII=\n", - "text/plain": [ - "
          " - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "id": "26c5b551", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "Masses['Eapprox'] = ytilde\n", "# Generate a plot comparing the experimental with the fitted values values.\n", @@ -1269,8 +1290,10 @@ }, { "cell_type": "markdown", - "id": "34d28ed3", - "metadata": {}, + "id": "d6de96f2", + "metadata": { + "editable": true + }, "source": [ "## Adding error analysis and training set up\n", "\n", @@ -1281,8 +1304,11 @@ { "cell_type": "code", "execution_count": 5, - "id": "46c39015", - "metadata": {}, + "id": "8184ef25", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "def R2(y_data, y_model):\n", @@ -1291,8 +1317,10 @@ }, { "cell_type": "markdown", - "id": "09150482", - "metadata": {}, + "id": "5026f8cd", + "metadata": { + "editable": true + }, "source": [ "and we would be using it as" ] @@ -1300,25 +1328,22 @@ { "cell_type": "code", "execution_count": 6, - "id": "c60fc160", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.9549351910143222\n" - ] - } - ], + "id": "3baf2f69", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "print(R2(Energies,ytilde))" ] }, { "cell_type": "markdown", - "id": "ea9d7abe", - "metadata": {}, + "id": "40e1b50a", + "metadata": { + "editable": true + }, "source": [ "We can easily add our **MSE** score as" ] @@ -1326,17 +1351,12 @@ { "cell_type": "code", "execution_count": 7, - "id": "7399848c", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.022022882954618378\n" - ] - } - ], + "id": "13946831", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "def MSE(y_data,y_model):\n", " n = np.size(y_model)\n", @@ -1347,8 +1367,10 @@ }, { "cell_type": "markdown", - "id": "0ca43616", - "metadata": {}, + "id": "c5ca0b3e", + "metadata": { + "editable": true + }, "source": [ "and finally the relative error as" ] @@ -1356,29 +1378,12 @@ { "cell_type": "code", "execution_count": 8, - "id": "602b9969", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "A \n", - "4 0 1.093247\n", - "5 2 0.275341\n", - "6 7 0.060080\n", - "7 12 0.019587\n", - "8 17 0.117986\n", - " ... \n", - "264 3297 0.000148\n", - "265 3303 0.001263\n", - "266 3310 0.002948\n", - "269 3331 0.000599\n", - "270 3337 0.002526\n", - "Name: Ebinding, Length: 264, dtype: float64\n" - ] - } - ], + "id": "c0c34dee", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "def RelativeError(y_data,y_model):\n", " return abs((y_data-y_model)/y_data)\n", @@ -1387,8 +1392,10 @@ }, { "cell_type": "markdown", - "id": "c6c9d23d", - "metadata": {}, + "id": "a2fbebeb", + "metadata": { + "editable": true + }, "source": [ "## Splitting our Data in Training and Test data\n", "\n", @@ -1406,8 +1413,10 @@ }, { "cell_type": "markdown", - "id": "46f46d43", - "metadata": {}, + "id": "74bef878", + "metadata": { + "editable": true + }, "source": [ "## Examples" ] @@ -1415,25 +1424,12 @@ { "cell_type": "code", "execution_count": 9, - "id": "dd175e90", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 2.03375565 -0.13375039 5.11903387]\n", - "Training R2\n", - "0.9959996952892793\n", - "Training MSE\n", - "0.01068532836259297\n", - "Test R2\n", - "0.9937238687985773\n", - "Test MSE\n", - "0.01196777141422897\n" - ] - } - ], + "id": "0cf20471", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "import os\n", "import numpy as np\n", @@ -1477,8 +1473,10 @@ }, { "cell_type": "markdown", - "id": "1afc59cc", - "metadata": {}, + "id": "54b660c0", + "metadata": { + "editable": true + }, "source": [ "## Making your own test-train splitting" ] @@ -1486,8 +1484,11 @@ { "cell_type": "code", "execution_count": 10, - "id": "ec006afe", - "metadata": {}, + "id": "c03145a7", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "# equivalently in numpy\n", @@ -1508,8 +1509,10 @@ }, { "cell_type": "markdown", - "id": "a7ec2fdb", - "metadata": {}, + "id": "4f3decd4", + "metadata": { + "editable": true + }, "source": [ "But since **scikit-learn** has its own function for doing this and since\n", "it interfaces easily with **tensorflow** and other libraries, we\n", @@ -1518,8 +1521,10 @@ }, { "cell_type": "markdown", - "id": "875d7248", - "metadata": {}, + "id": "39c1120a", + "metadata": { + "editable": true + }, "source": [ "## The Boston housing data example\n", "\n", @@ -1560,8 +1565,10 @@ }, { "cell_type": "markdown", - "id": "c0f8545d", - "metadata": {}, + "id": "83b291f8", + "metadata": { + "editable": true + }, "source": [ "## Housing data, the code\n", "We start by importing the libraries" @@ -1570,8 +1577,11 @@ { "cell_type": "code", "execution_count": 11, - "id": "81237355", - "metadata": {}, + "id": "a54ea4d0", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import numpy as np\n", @@ -1583,8 +1593,10 @@ }, { "cell_type": "markdown", - "id": "f1962254", - "metadata": {}, + "id": "7852523e", + "metadata": { + "editable": true + }, "source": [ "and load the Boston Housing DataSet from **Scikit-Learn**" ] @@ -1592,62 +1604,12 @@ { "cell_type": "code", "execution_count": 12, - "id": "dee9e300", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/opt/homebrew/lib/python3.9/site-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function load_boston is deprecated; `load_boston` is deprecated in 1.0 and will be removed in 1.2.\n", - "\n", - " The Boston housing prices dataset has an ethical problem. You can refer to\n", - " the documentation of this function for further details.\n", - "\n", - " The scikit-learn maintainers therefore strongly discourage the use of this\n", - " dataset unless the purpose of the code is to study and educate about\n", - " ethical issues in data science and machine learning.\n", - "\n", - " In this special case, you can fetch the dataset from the original\n", - " source::\n", - "\n", - " import pandas as pd\n", - " import numpy as np\n", - "\n", - "\n", - " data_url = \"http://lib.stat.cmu.edu/datasets/boston\"\n", - " raw_df = pd.read_csv(data_url, sep=\"\\s+\", skiprows=22, header=None)\n", - " data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])\n", - " target = raw_df.values[1::2, 2]\n", - "\n", - " Alternative datasets include the California housing dataset (i.e.\n", - " :func:`~sklearn.datasets.fetch_california_housing`) and the Ames housing\n", - " dataset. You can load the datasets as follows::\n", - "\n", - " from sklearn.datasets import fetch_california_housing\n", - " housing = fetch_california_housing()\n", - "\n", - " for the California housing dataset and::\n", - "\n", - " from sklearn.datasets import fetch_openml\n", - " housing = fetch_openml(name=\"house_prices\", as_frame=True)\n", - "\n", - " for the Ames housing dataset.\n", - " \n", - " warnings.warn(msg, category=FutureWarning)\n" - ] - }, - { - "data": { - "text/plain": [ - "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename', 'data_module'])" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], + "id": "4c01a3e0", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "from sklearn.datasets import load_boston\n", "\n", @@ -1660,8 +1622,10 @@ }, { "cell_type": "markdown", - "id": "bef0eb82", - "metadata": {}, + "id": "c98759d9", + "metadata": { + "editable": true + }, "source": [ "Then we invoke Pandas" ] @@ -1669,8 +1633,11 @@ { "cell_type": "code", "execution_count": 13, - "id": "a29ff8af", - "metadata": {}, + "id": "95fc544a", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names)\n", @@ -1680,8 +1647,10 @@ }, { "cell_type": "markdown", - "id": "8396e85f", - "metadata": {}, + "id": "44605765", + "metadata": { + "editable": true + }, "source": [ "and preprocess the data" ] @@ -1689,34 +1658,12 @@ { "cell_type": "code", "execution_count": 14, - "id": "16d25b94", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "CRIM 0\n", - "ZN 0\n", - "INDUS 0\n", - "CHAS 0\n", - "NOX 0\n", - "RM 0\n", - "AGE 0\n", - "DIS 0\n", - "RAD 0\n", - "TAX 0\n", - "PTRATIO 0\n", - "B 0\n", - "LSTAT 0\n", - "MEDV 0\n", - "dtype: int64" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], + "id": "85e16609", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "# check for missing values in all the columns\n", "boston.isnull().sum()" @@ -1724,8 +1671,10 @@ }, { "cell_type": "markdown", - "id": "2e90d9ef", - "metadata": {}, + "id": "6d5a1ba3", + "metadata": { + "editable": true + }, "source": [ "We can then visualize the data" ] @@ -1733,28 +1682,12 @@ { "cell_type": "code", "execution_count": 15, - "id": "ac2fac03", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/opt/homebrew/lib/python3.9/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n", - " warnings.warn(msg, FutureWarning)\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
          " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "id": "248c9dd2", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "# set the size of the figure\n", "sns.set(rc={'figure.figsize':(11.7,8.27)})\n", @@ -1766,8 +1699,10 @@ }, { "cell_type": "markdown", - "id": "b5cdd9d1", - "metadata": {}, + "id": "ef8a330a", + "metadata": { + "editable": true + }, "source": [ "It is now useful to look at the correlation matrix" ] @@ -1775,30 +1710,12 @@ { "cell_type": "code", "execution_count": 16, - "id": "37a352c6", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
          " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "id": "910d9a46", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "# compute the pair wise correlation for all columns \n", "correlation_matrix = boston.corr().round(2)\n", @@ -1809,8 +1726,10 @@ }, { "cell_type": "markdown", - "id": "d43fa5cd", - "metadata": {}, + "id": "2672c6d9", + "metadata": { + "editable": true + }, "source": [ "From the above coorelation plot we can see that **MEDV** is strongly correlated to **LSTAT** and **RM**. We see also that **RAD** and **TAX** are stronly correlated, but we don't include this in our features together to avoid multi-colinearity" ] @@ -1818,20 +1737,12 @@ { "cell_type": "code", "execution_count": 17, - "id": "1fc2b42e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
          " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "id": "92c78b0f", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "plt.figure(figsize=(20, 5))\n", "\n", @@ -1850,8 +1761,10 @@ }, { "cell_type": "markdown", - "id": "69cafd8a", - "metadata": {}, + "id": "da68c38a", + "metadata": { + "editable": true + }, "source": [ "Now we start training our model" ] @@ -1859,8 +1772,11 @@ { "cell_type": "code", "execution_count": 18, - "id": "48a04777", - "metadata": {}, + "id": "a6b3a9d5", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "X = pd.DataFrame(np.c_[boston['LSTAT'], boston['RM']], columns = ['LSTAT','RM'])\n", @@ -1869,8 +1785,10 @@ }, { "cell_type": "markdown", - "id": "e21c7f03", - "metadata": {}, + "id": "b80ca360", + "metadata": { + "editable": true + }, "source": [ "We split the data into training and test sets" ] @@ -1878,20 +1796,12 @@ { "cell_type": "code", "execution_count": 19, - "id": "fa0eca85", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(404, 2)\n", - "(102, 2)\n", - "(404,)\n", - "(102,)\n" - ] - } - ], + "id": "f6257185", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "from sklearn.model_selection import train_test_split\n", "\n", @@ -1906,8 +1816,10 @@ }, { "cell_type": "markdown", - "id": "598473cc", - "metadata": {}, + "id": "7ba8dedb", + "metadata": { + "editable": true + }, "source": [ "Then we use the linear regression functionality from **Scikit-Learn**" ] @@ -1915,26 +1827,12 @@ { "cell_type": "code", "execution_count": 20, - "id": "adc72931", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The model performance for training set\n", - "--------------------------------------\n", - "RMSE is 5.6371293350711955\n", - "R2 score is 0.6300745149331701\n", - "\n", - "\n", - "The model performance for testing set\n", - "--------------------------------------\n", - "RMSE is 5.137400784702911\n", - "R2 score is 0.6628996975186952\n" - ] - } - ], + "id": "381d739f", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "from sklearn.linear_model import LinearRegression\n", "from sklearn.metrics import mean_squared_error, r2_score\n", @@ -1972,20 +1870,12 @@ { "cell_type": "code", "execution_count": 21, - "id": "5bf0e806", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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rDiAAYCkhFmqUlQ1RlTR7hTMPQR+A9BJioUblNkRlLaQ1a4UzL0EfgPSysQtqlJUNUUnKSucDALJLiIUaaflUmaAPQLMpJ4Aa1bohqh1rQ7PS+QCA7LISCzUaHNgQd2zdtBDIerq74o6tm0oG0/na0PlAN18bOjY+2dIxt5rergA0m5VYqEO1G6LytAmsVud3dsTs2V/9+yMXdsbn/vt/yf01A9A6Qiw0UTvWhi7tTBARMXtmrsx3AEDtlBNAE7XjJjCdCQBoBSEWmqgda0PbcfUZgNZTTgBN1OxTsdLo1y44L97/4FzJxwGgUYRYaLJmnYqVVh0dHTU9DgD1EGKhCdqxN+y8U6fP1vQ4ANRDiIUGW7o7f743bMR/lhfkOeQ66ACAVrCxCxqs0u78vB+AUGozW0TEB7Nnc3ONACTPSiw0WKXd+Y08AKHRK7qNeL75r//f/+f/LioheP+Dc8tWpAGgXkIsNFil2+nVtqCqFCirKVuoRSOfb3BgQ4yMTiyrg22X08oAaD7lBNBglXrDVnMAQjUlB40+VKDRz6dfLADNJMRCgw0ObIg7tm5aCKU93V1xx9ZNC6uP1RyAUE2gbHRIbPTzteNpZQC0jnICaIJyvWGrOQChmkDZ6C4A9T7fSmUPw4X+ReUJEfk/rQyA1hFiIQGVDkCoJlA2OiTW83zV1NHmtZUYAMkSYiGFqgmU9YbElVZO63m+Sp0W2u20MgBaR4iFFKo2UNYaEiutnNb6fDZvAZAUIRZSqhmrmI3sURvhdC4AkiPEQko142jaRq+c2rwFQFKEWEihRh9kMK/RK6eVyh6aEcQBIEKIJcXaMQB9+JqXasRpV6VWTiN+FZLvffyluo+ZLfU9zQriABDhsANSqpoTq/Jm6TWXstoNU0sPYlj63I38GTf6BDAA+DAhllRqxwBU6pqXasSGqcGBDfHIF64p+VyN/BnrXABAMyknIJXaMQBVurZqNkzVUoLR7J+xzgUANJMQSyq1YwBa6ZrnP1epXrXWGtRaf8a11ijrXABAMyknIJWGC/2xtnPx9Mx7AFrpmj+/7ePxyBeuqbgZqtYSjFp+xvXUKC+tv+3p7oo7tm6yqQuAhrASSyrVe6Rqlq32mmstD6jl9eo9JMGxswA0ixBLarVjAFrNNddTglHt67VjjTIA6aacAHKimSUYKwXhPNcoA5BuQizkRDNrUNuxRhmAdFNOADnSrBKMdqxRBiDdhFjIgVYc0duONcoApJcQCyW0IhQ2Sq39YUt9f1auFQDmqYmFJerpiZqk1RzRm7VrBYB5VmJhiXp7ojZDNaukq2l/laZrBYBaCLFtwi3j6qWlJ2q5MoGbr1u38HWrOaI3LdcKALVSTtAGkrplPDY+Gfc+/lLcued7ce/jL2XmFnVaeqJWWyawmvZXablWAKiVENsGVlMzWa8s11qmpSdqtaukq+kPm5ZrBYBaVVVO8PWvfz0OHDgQERGFQiH+/M//PA4dOhQPPvhgzMzMxNatW2PXrl1NHSj1S+KWcVZqLcuVWSRZflEu7JdaJa23/VUarhUA6lExxB46dCh+8IMfxHPPPRcdHR3xZ3/2Z7Fv37549NFH45vf/GZcdtllcdddd8Xo6GgUCoVWjJkaraZmsl5ZqLWs1JoqySBXbpW80aukSV9rnqg9B2idiuUEvb29cf/998fatWvj/PPPj/7+/jh69GhcccUVsXHjxujs7Ixt27bFwYMHWzFe6pDELeMs1FomUWZRrXJhXyhKpyyX0ABkUcWV2CuvvHLh30ePHo39+/fHH//xH0dvb+/C4319fXHs2LHmjJBVS+KW8XChf9EqZ0T6ai3TvFqcxOo5q7PSm6K//YcfW50FaIKqW2y98cYbcdddd8V9990XnZ2dceTIkUWf7+joqOmFe3o+UtPXt5Pe3nWVv6hGN1+3Lm6+7srKX9jA1+ted0E8feBwnHz3dHz04gvjv23qi+d/cCT+14v/Fh+9+MLYsfVjcd3VG1s2pqV6L74wTrx7uuTjzfgd1OJPbhqIr3/r1Zg5c27hsa7zz4s/uWlgYWxJj5HF3lnhzc/7H5yL9z/41e9xanomnj744+hed0HL5r55QjXME6qRtnlSVYh95ZVXYufOnfHAAw/E0NBQvPzyy3Hy5MmFzx8/fjz6+vpqeuGpqVMxN1esbbRtoLd3XZw48V7Sw2iIgcvXx0N3DUbE8vrTE++ejv/x7I9i+r0PEluVuvX3f7PkavGtv/+bif8OBi5fHzu2/NdlK3gDl6+PEyfey9U8yYtLVlg9X2rmzLl4ct94DFy+vuljMk+ohnlCNZKYJ2vWdJRd9KwYYt9+++344he/GHv37o3BwV8FkquuuiqOHDkSb775ZvzGb/xG7Nu3L2677bbGjZrcSWO3grTvzLfhKltKldCsJA0lKwBZVzHEfuMb34iZmZnYs2fPwmPbt2+PPXv2xD333BMzMzNRKBRiy5YtTR0o2ZbW+tNKQbHe3eZ2qbefUm+KZs6ci1Onzy77WrXNAKtXMcTu3r07du/eXfJzL7zwQsMHRD5lcaNSpRZcjf4+sm/pm6KlcyEifRscAbLKiV20RBZPhqq3BVeaW3fRWqs5TQ2A8qruTgCrMf+f9t/+w48XdmqvPT/Z91CVbvnXWwKR1tIJkqG2GaA5rMTSUmfO/mdHilOnzybWDL6axvT1HtiQhYMeACDrhFhaJk232asZS70lEFksnQCArFFOQMuk6TZ7NWOptwVX2lt3AUAeCLG0TJo6FFQ7lnrrGdVBAkBzKSegZdJ0mz1NYwEAamcllpZJ0232NI0FAKidEEtNVnsSVZpus6dpLABAbYRYquYkKgAgLdTEUrU0tcgCANqblVhWtLR0IE0tstrBaks3ACDPhFhKKlU6sBInUTVetaUbSQRd4RqANFBOQEmlSgdK0ZaqOaop3ajm6NxGS+I1AaAUIZaSqll57enuiju2brIK1wTVlG4kUaOsLhqAtFBOQEnlTrR65AvXJDCi9jB/q34lHy7dSKJGWV00AGlhJZaSnGjVektv1S+19Oe/Ui1yM2uUk3hNACjFSiwlOdFqsVZsZipXh1zqNYcL/Ys2f0U0/41GEq8JAKUIsazIiVa/0qpDHsrdki9VwpHEGw1vbgBICyEWKii3mamR4a1cHfJKPvxGY361+H+++G9NDZfe3ACQBmpioYJWbWZaTR2y1lcAtBshFipo1WamwYENccfWTXW1MNP6CoB2o5wAKmjlZqZ6b9VrfQVAuxFioYJWbmaqtwtCPfW0AJBlQiyZ1Yq2V/NasZlpNV0QtL4CoN2oiSWT8riRaTV1rauppwWALLISy4paudJZq2rbXqX5GpZabV2r1lcAtBMhlpJa1eC/XtUEvrRfw1LqWgGgesoJKCntLZuqaXuV9mtYajV9YgGg3QixlJT2lk3VBL60X8NS6loBoHrKCSip1lvbra49rabtVRZvz6trBYDqCLGUVEvLpqRqTysFPm2nACC/lBNQUi23ttNae+r2PADkl5VYVlTtre001566PQ8A+STEsmpZrD2ltCz11QWgvSknYNW0hsqHPJ6CBkB+CbGsmtrTfEhrbTMAlKKcgJqtdMtZaM22NNc2A8BSVmKpiVvO+VXNKWgAkBZCLDVxyzm/1DYDkCXKCaiJW875Vc0paACQFkIsNdFOK9/UNgOQFcoJqIlbzgBAGliJpSZuOQMAaSDEUjO3nAGApCknAAAgc4RYAAAyR4gFACBzhFgAADJHiAUAIHOEWAAAMkeIBQAgc4RYAAAyx2EHNN3Y+KQTvgCAhhJiaaqx8cl46sDrMXt2LiIipqZn4qkDr0dECLIAQN2UE9BUI6MTCwF23uzZuRgZnUhoRABAHgixNNXU9ExNjwMAVEOIpal6urtqehwAoBpCLE01XOiPtZ2Lp9nazjUxXOhPaEQAQB7Y2FUDu+xrN//z8XMDABpJiK2SXfb1GxzY0NCfkTcTAIBygirZZZ8O828m5jeGzb+ZGBufTHhkAEArCbFVsss+HbyZAAAihNiq2WWfDt5MAAARQmzV7LJPB28mAIAIG7uqlqZd9u28sWm40L9og12ENxMA0I6E2Bo0epd9Pdq9S0Ka3kwAAMkRYmuQhhXQchub2iXIpeHNRKukYc4BQBoJsVVKywqojU3to9ycu/m6dUkODQASZ2NXldLS2snGpvaRljkHAGkkxFYpLSuguiS0j7TMOQBIIyG2SmlZAR0c2BB3bN208Lo93V1xx9ZN6iRzKC1zDgDSSE1sldLU2qmdNja1szTNOQBIGyG2Slo70WrmHACsTIitgRVQWs2cA4DS1MQCAJA5VmJhBQ4aAID0EmKhhLQcbgEAlKacAEpw0AAApJsQCyU4aAAA0k2IhRIcNAAA6SbEQgmO9wWAdLOxC0pw0AAApJsQCytw0AAApJdyAgAAMkeIBQAgc9qinMDJSwAA+ZL7EOvkJQCA/Ml9OYGTlwAA8qfqEHvq1Km46aab4q233oqIiEOHDsW2bdti8+bNsXfv3qYNcLWcvAQAkD9VhdhXX301Pve5z8XRo0cjIuKDDz6IBx54IB5//PHYv39//Ou//muMjo42c5x1c/ISAED+VBVin3322fjKV74SfX19ERHx2muvxRVXXBEbN26Mzs7O2LZtWxw8eLCpA62Xk5cAAPKnqo1dX/3qVxd9fPz48ejt7V34uK+vL44dO1bTC/f0fKSmr6/Xzdeti+51F8TTBw7HyXdPx0cvvjB2bP1YXHf1xpa8fj16e9clPQQywDyhGuYJ1TBPqEba5kld3QmKxeKyxzo6Omp6jqmpUzE3t/x5mmHg8vXx0F2Dix47ceK9lrx2rXp716V2bKSHeUI1zBOqYZ5QjSTmyZo1HWUXPevqTnDppZfGyZMnFz4+fvz4QqkBAAA0W10h9qqrroojR47Em2++GefOnYt9+/bFtdde2+ixAQBASXWVE3R1dcWePXvinnvuiZmZmSgUCrFly5ZGjw0AAEq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          " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "id": "5bacb92a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "# plotting the y_test vs y_pred\n", "# ideally should have been a straight line\n", @@ -1995,8 +1885,10 @@ }, { "cell_type": "markdown", - "id": "115406d0", - "metadata": {}, + "id": "debdedcf", + "metadata": { + "editable": true + }, "source": [ "## Reducing the number of degrees of freedom, overarching view\n", "\n", @@ -2022,8 +1914,10 @@ }, { "cell_type": "markdown", - "id": "98df56e6", - "metadata": {}, + "id": "57b1e446", + "metadata": { + "editable": true + }, "source": [ "## Preprocessing our data\n", "\n", @@ -2045,8 +1939,10 @@ }, { "cell_type": "markdown", - "id": "1de59215", - "metadata": {}, + "id": "5ecd4e8c", + "metadata": { + "editable": true + }, "source": [ "## Functionality in Scikit-Learn\n", "\n", @@ -2063,8 +1959,10 @@ }, { "cell_type": "markdown", - "id": "e1c1b7ee", - "metadata": {}, + "id": "ecab4f44", + "metadata": { + "editable": true + }, "source": [ "## More preprocessing\n", "\n", @@ -2088,8 +1986,10 @@ }, { "cell_type": "markdown", - "id": "a35f95ed", - "metadata": {}, + "id": "05a84d19", + "metadata": { + "editable": true + }, "source": [ "## Frequently used scaling functions\n", "\n", @@ -2099,8 +1999,10 @@ }, { "cell_type": "markdown", - "id": "804df448", - "metadata": {}, + "id": "c559aba3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "x_j^{(i)} \\rightarrow \\frac{x_j^{(i)} - \\overline{x}_j}{\\sigma(x_j)},\n", @@ -2109,8 +2011,10 @@ }, { "cell_type": "markdown", - "id": "8495ae4c", - "metadata": {}, + "id": "c3143bae", + "metadata": { + "editable": true + }, "source": [ "where $\\overline{x}_j$ and $\\sigma(x_j)$ are the mean and standard deviation, respectively, of the feature $x_j$.\n", "This ensures that each feature has zero mean and unit standard deviation. For data sets where we do not have the standard deviation or don't wish to calculate it, it is then common to simply set it to one." @@ -2118,8 +2022,10 @@ }, { "cell_type": "markdown", - "id": "9ebd107f", - "metadata": {}, + "id": "538fa93c", + "metadata": { + "editable": true + }, "source": [ "## Example of own Standard scaling\n", "\n", @@ -2132,418 +2038,12 @@ { "cell_type": "code", "execution_count": 22, - "id": "8b62f35a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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"metadata": { + "editable": true + }, "source": [ "## Min-Max Scaling\n", "\n", @@ -2593,8 +2097,10 @@ }, { "cell_type": "markdown", - "id": "3a48d095", - "metadata": {}, + "id": "07d28ab3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "x_j^{(i)} \\rightarrow (b-a)\\frac{x_j^{(i)} - \\min(x_j)}{\\max(x_j) - \\min(x_j)} - a\n", @@ -2603,16 +2109,20 @@ }, { "cell_type": "markdown", - "id": "b836623d", - "metadata": {}, + "id": "8dd69e21", + "metadata": { + "editable": true + }, "source": [ "where $\\min(x_j)$ and $\\max(x_j)$ return the minimum and maximum value of $x_j$ over the data set, respectively." ] }, { "cell_type": "markdown", - "id": "0cf9ca3e", - "metadata": {}, + "id": "0691d9ee", + "metadata": { + "editable": true + }, "source": [ "## Testing the Means Squared Error as function of Complexity\n", "One of \n", @@ -2625,8 +2135,11 @@ { "cell_type": "code", "execution_count": 23, - "id": "409e549f", - "metadata": {}, + "id": "2dddedb3", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "np.random.seed()\n", @@ -2639,8 +2152,10 @@ }, { "cell_type": "markdown", - "id": "ed762bab", - "metadata": {}, + "id": "c53156de", + "metadata": { + "editable": true + }, "source": [ "where $y$ is the function we want to fit with a given polynomial.\n", "\n", @@ -2650,20 +2165,12 @@ { "cell_type": "code", "execution_count": 24, - "id": "a2d186a5", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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          " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "id": "e12b421a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", @@ -2705,8 +2212,10 @@ }, { "cell_type": "markdown", - "id": "8f34fae7", - "metadata": {}, + "id": "47115e0d", + "metadata": { + "editable": true + }, "source": [ "## More preprocessing examples, Franke function and regression" ] @@ -2714,42 +2223,12 @@ { "cell_type": "code", "execution_count": 25, - "id": "5fc132f0", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "MSE before scaling: 0.00\n", - "R2 score before scaling 1.00\n", - "Feature min values before scaling:\n", - " [1.00000000e+00 6.97906022e-03 2.43639284e-03 4.87072815e-05\n", - " 1.70037324e-05 5.93601008e-06 3.39931051e-07 1.18670072e-07\n", - " 4.14277718e-08 1.44624525e-08 2.37239927e-09 8.28205578e-10\n", - " 2.89126914e-10 1.00934327e-10 3.52362157e-11 1.65571174e-11\n", - " 5.78009660e-12 2.01783414e-12 7.04426744e-13 2.45915671e-13\n", - " 8.58492636e-14]\n", - "Feature max values before scaling:\n", - " [1. 0.99970894 0.99978365 0.99941797 0.99949266 0.99956735\n", - " 0.99912709 0.99920175 0.99927642 0.9993511 0.99883628 0.99891093\n", - " 0.99898558 0.99906023 0.99913489 0.99854557 0.99862019 0.99869482\n", - " 0.99876945 0.99884409 0.99891873]\n", - "Feature min values after scaling:\n", - " [ 0. -1.71761101 -1.75770568 -1.12330033 -1.12591227 -1.12871842\n", - " -0.88613493 -0.884669 -0.88323026 -0.88182591 -0.75269037 -0.75050135\n", - " -0.74829661 -0.74607851 -0.74384949 -0.6652177 -0.66294408 -0.66064822\n", - " -0.65833132 -0.65599456 -0.6536392 ]\n", - "Feature max values after scaling:\n", - " [0. 1.71737253 1.75576555 2.20916295 2.23971032 2.26995402\n", - " 2.60543038 2.63162342 2.65743689 2.68286725 2.94273542 2.96631321\n", - " 2.98947894 3.01222822 3.034557 3.24159785 3.26297455 3.28391978\n", - " 3.30442964 3.32450054 3.34412923]\n", - "MSE after scaling: 0.00\n", - "R2 score for scaled data: 1.00\n" - ] - } - ], + "id": "4107c2c2", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "# Common imports\n", "import os\n", @@ -2847,8 +2326,10 @@ }, { "cell_type": "markdown", - "id": "ad5b41a1", - "metadata": {}, + "id": "2d2b728f", + "metadata": { + "editable": true + }, "source": [ "## Mathematical Interpretation of Ordinary Least Squares\n", "\n", @@ -2859,8 +2340,10 @@ }, { "cell_type": "markdown", - "id": "a93ce01c", - "metadata": {}, + "id": "aad9c099", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\hat{\\boldsymbol{\\beta}} = \\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n", @@ -2869,8 +2352,10 @@ }, { "cell_type": "markdown", - "id": "2f89cf96", - "metadata": {}, + "id": "0e368ba4", + "metadata": { + "editable": true + }, "source": [ "The **hat** over $\\boldsymbol{\\beta}$ means we have the optimal parameters after minimization of the cost function.\n", "\n", @@ -2879,8 +2364,10 @@ }, { "cell_type": "markdown", - "id": "1bdec2cd", - "metadata": {}, + "id": "fc63cdcb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\tilde{\\boldsymbol{y}}=\\boldsymbol{X}\\hat{\\boldsymbol{\\beta}} = \\boldsymbol{X}\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n", @@ -2889,16 +2376,20 @@ }, { "cell_type": "markdown", - "id": "d6090b0f", - "metadata": {}, + "id": "3469f96c", + "metadata": { + "editable": true + }, "source": [ "We now define a matrix" ] }, { "cell_type": "markdown", - "id": "71edebd0", - "metadata": {}, + "id": "b31ae9d4", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}=\\boldsymbol{X}\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T.\n", @@ -2907,16 +2398,20 @@ }, { "cell_type": "markdown", - "id": "fc1b8e60", - "metadata": {}, + "id": "cb84304f", + "metadata": { + "editable": true + }, "source": [ "We can rewrite" ] }, { "cell_type": "markdown", - "id": "c407cc78", - "metadata": {}, + "id": "00ec7e13", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\tilde{\\boldsymbol{y}}=\\boldsymbol{X}\\hat{\\boldsymbol{\\beta}} = \\boldsymbol{A}\\boldsymbol{y}.\n", @@ -2925,8 +2420,10 @@ }, { "cell_type": "markdown", - "id": "e674f439", - "metadata": {}, + "id": "0420fb1e", + "metadata": { + "editable": true + }, "source": [ "The matrix $\\boldsymbol{A}$ has the important property that $\\boldsymbol{A}^2=\\boldsymbol{A}$. This is the definition of a projection matrix.\n", "We can then interpret our optimal model $\\tilde{\\boldsymbol{y}}$ as being represented by an orthogonal projection of $\\boldsymbol{y}$ onto a space defined by the column vectors of $\\boldsymbol{X}$. In our case here the matrix $\\boldsymbol{A}$ is a square matrix. If it is a general rectangular matrix we have an oblique projection matrix." @@ -2934,8 +2431,10 @@ }, { "cell_type": "markdown", - "id": "6b5a2484", - "metadata": {}, + "id": "b598bd0a", + "metadata": { + "editable": true + }, "source": [ "## Residual Error\n", "\n", @@ -2944,8 +2443,10 @@ }, { "cell_type": "markdown", - "id": "631571fe", - "metadata": {}, + "id": "93865bfb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\epsilon}=\\boldsymbol{y}-\\tilde{\\boldsymbol{y}}=\\left[\\boldsymbol{I}-\\boldsymbol{X}\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\right]\\boldsymbol{y}.\n", @@ -2954,16 +2455,20 @@ }, { "cell_type": "markdown", - "id": "03e7938e", - "metadata": {}, + "id": "8425236f", + "metadata": { + "editable": true + }, "source": [ "The residual errors are then the projections of $\\boldsymbol{y}$ onto the orthogonal component of the space defined by the column vectors of $\\boldsymbol{X}$." ] }, { "cell_type": "markdown", - "id": "89c1cbc1", - "metadata": {}, + "id": "71d814fc", + "metadata": { + "editable": true + }, "source": [ "## Simple case\n", "\n", @@ -2972,8 +2477,10 @@ }, { "cell_type": "markdown", - "id": "997c8992", - "metadata": {}, + "id": "18b5777e", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{X}=\\boldsymbol{X}\\boldsymbol{X}^T = \\boldsymbol{I}.\n", @@ -2982,16 +2489,20 @@ }, { "cell_type": "markdown", - "id": "7c3ad56e", - "metadata": {}, + "id": "244dd800", + "metadata": { + "editable": true + }, "source": [ "In this case the matrix $\\boldsymbol{A}$ becomes" ] }, { "cell_type": "markdown", - "id": "4cc0e3f1", - "metadata": {}, + "id": "f056abef", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}=\\boldsymbol{X}\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T)=\\boldsymbol{I},\n", @@ -3000,16 +2511,20 @@ }, { "cell_type": "markdown", - "id": "7304c055", - "metadata": {}, + "id": "9b06ee67", + "metadata": { + "editable": true + }, "source": [ "and we have the obvious case" ] }, { "cell_type": "markdown", - "id": "0a8db981", - "metadata": {}, + "id": "179dd59f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\epsilon}=\\boldsymbol{y}-\\tilde{\\boldsymbol{y}}=0.\n", @@ -3018,16 +2533,20 @@ }, { "cell_type": "markdown", - "id": "d04ddf92", - "metadata": {}, + "id": "02a755af", + "metadata": { + "editable": true + }, "source": [ "This serves also as a useful test of our codes." ] }, { "cell_type": "markdown", - "id": "044bd0ca", - "metadata": {}, + "id": "aa4dd8c0", + "metadata": { + "editable": true + }, "source": [ "## The singular value decomposition\n", "\n", @@ -3064,8 +2583,10 @@ }, { "cell_type": "markdown", - "id": "ef9e05c1", - "metadata": {}, + "id": "9d9a43c2", + "metadata": { + "editable": true + }, "source": [ "## Linear Regression Problems\n", "\n", @@ -3079,8 +2600,10 @@ }, { "cell_type": "markdown", - "id": "d63adf14", - "metadata": {}, + "id": "eb0e61db", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -3100,8 +2623,10 @@ }, { "cell_type": "markdown", - "id": "5e78a531", - "metadata": {}, + "id": "f36d477e", + "metadata": { + "editable": true + }, "source": [ "The columns of $\\boldsymbol{X}$ are linearly dependent. We see this easily since the \n", "the first column is the row-wise sum of the other two columns. The rank (more correct,\n", @@ -3115,8 +2640,10 @@ }, { "cell_type": "markdown", - "id": "2744881a", - "metadata": {}, + "id": "f70cb326", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -3132,8 +2659,10 @@ }, { "cell_type": "markdown", - "id": "037e81db", - "metadata": {}, + "id": "0a7ac34e", + "metadata": { + "editable": true + }, "source": [ "We see easily that $\\mbox{det}(\\boldsymbol{X}) = x_{11} x_{22} - x_{12} x_{21} = 1 \\times (-1) - 1 \\times (-1) = 0$. Hence, $\\mathbf{X}$ is singular and its inverse is undefined.\n", "This is equivalent to saying that the matrix $\\boldsymbol{X}$ has at least an eigenvalue which is zero." @@ -3141,8 +2670,10 @@ }, { "cell_type": "markdown", - "id": "f21e5f16", - "metadata": {}, + "id": "80fc7ab8", + "metadata": { + "editable": true + }, "source": [ "## Fixing the singularity\n", "\n", @@ -3151,8 +2682,10 @@ }, { "cell_type": "markdown", - "id": "46f92b4a", - "metadata": {}, + "id": "d2a1e8f1", + "metadata": { + "editable": true + }, "source": [ "\n", "
          \n", @@ -3167,8 +2700,10 @@ }, { "cell_type": "markdown", - "id": "30476b84", - "metadata": {}, + "id": "3ef5d6bd", + "metadata": { + "editable": true + }, "source": [ "has linearly dependent column vectors, we will not be able to compute the inverse\n", "of $\\boldsymbol{X}^T\\boldsymbol{X}$ and we cannot find the parameters (estimators) $\\beta_i$. \n", @@ -3181,8 +2716,10 @@ }, { "cell_type": "markdown", - "id": "36716f3b", - "metadata": {}, + "id": "22032de1", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^{T} \\boldsymbol{X} \\rightarrow \\boldsymbol{X}^{T} \\boldsymbol{X}+\\lambda \\boldsymbol{I},\n", @@ -3191,16 +2728,20 @@ }, { "cell_type": "markdown", - "id": "a56a9662", - "metadata": {}, + "id": "3fd3d85a", + "metadata": { + "editable": true + }, "source": [ "where $\\boldsymbol{I}$ is the identity matrix. When we discuss **Ridge** regression this is actually what we end up evaluating. The parameter $\\lambda$ is called a hyperparameter. More about this later." ] }, { "cell_type": "markdown", - "id": "9484e1b3", - "metadata": {}, + "id": "2b3c587c", + "metadata": { + "editable": true + }, "source": [ "## Basic math of the SVD\n", "\n", @@ -3212,8 +2753,10 @@ }, { "cell_type": "markdown", - "id": "7d0e79fd", - "metadata": {}, + "id": "8967c4c4", + "metadata": { + "editable": true + }, "source": [ "$$\n", "(\\lambda_1,\\boldsymbol{u}_1),\\dots, (\\lambda_n,\\boldsymbol{u}_n),\n", @@ -3222,16 +2765,20 @@ }, { "cell_type": "markdown", - "id": "957d1974", - "metadata": {}, + "id": "4fbd74d7", + "metadata": { + "editable": true + }, "source": [ "and the eigenvalues are given by the diagonal matrix" ] }, { "cell_type": "markdown", - "id": "4da24ddd", - "metadata": {}, + "id": "74a6d631", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\Sigma}=\\mathrm{Diag}(\\lambda_1, \\dots,\\lambda_n).\n", @@ -3240,16 +2787,20 @@ }, { "cell_type": "markdown", - "id": "63934409", - "metadata": {}, + "id": "f18674dc", + "metadata": { + "editable": true + }, "source": [ "The matrix $\\boldsymbol{X}$ can be written in terms of an orthogonal/unitary transformation $\\boldsymbol{U}$" ] }, { "cell_type": "markdown", - "id": "3710e8a3", - "metadata": {}, + "id": "7785284e", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X} = \\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T,\n", @@ -3258,8 +2809,10 @@ }, { "cell_type": "markdown", - "id": "6fc2de6c", - "metadata": {}, + "id": "3a6c8bf4", + "metadata": { + "editable": true + }, "source": [ "with $\\boldsymbol{U}\\boldsymbol{U}^T=\\boldsymbol{I}$ or $\\boldsymbol{U}\\boldsymbol{U}^{\\dagger}=\\boldsymbol{I}$.\n", "\n", @@ -3268,8 +2821,10 @@ }, { "cell_type": "markdown", - "id": "5c7cbfc4", - "metadata": {}, + "id": "5dbc9b48", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X} = \\begin{bmatrix} \n", @@ -3281,8 +2836,10 @@ }, { "cell_type": "markdown", - "id": "30e83681", - "metadata": {}, + "id": "199aa6b0", + "metadata": { + "editable": true + }, "source": [ "is not diagonalizable, it is a so-called [defective matrix](https://en.wikipedia.org/wiki/Defective_matrix). It is easy to see that the condition\n", "$\\boldsymbol{X}\\boldsymbol{X}^T=\\boldsymbol{X}^T\\boldsymbol{X}$ is not fulfilled." @@ -3290,8 +2847,10 @@ }, { "cell_type": "markdown", - "id": "10f85da7", - "metadata": {}, + "id": "95f50728", + "metadata": { + "editable": true + }, "source": [ "## The SVD, a Fantastic Algorithm\n", "\n", @@ -3308,8 +2867,10 @@ }, { "cell_type": "markdown", - "id": "f9269daa", - "metadata": {}, + "id": "b8cb1b13", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X} = \\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T\n", @@ -3318,16 +2879,20 @@ }, { "cell_type": "markdown", - "id": "558c53b6", - "metadata": {}, + "id": "df9d2f8d", + "metadata": { + "editable": true + }, "source": [ "As an example, the above defective matrix can be decomposed as" ] }, { "cell_type": "markdown", - "id": "5f32a26d", - "metadata": {}, + "id": "cfc446e3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X} = \\frac{1}{\\sqrt{2}}\\begin{bmatrix} 1& 1 \\\\ 1& -1\\\\ \\end{bmatrix} \\begin{bmatrix} 2& 0 \\\\ 0& 0\\\\ \\end{bmatrix} \\frac{1}{\\sqrt{2}}\\begin{bmatrix} 1& -1 \\\\ 1& 1\\\\ \\end{bmatrix}=\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T,\n", @@ -3336,8 +2901,10 @@ }, { "cell_type": "markdown", - "id": "42617846", - "metadata": {}, + "id": "c633f00f", + "metadata": { + "editable": true + }, "source": [ "with eigenvalues $\\sigma_1=2$ and $\\sigma_2=0$. \n", "The SVD exits always! \n", @@ -3363,8 +2930,10 @@ }, { "cell_type": "markdown", - "id": "cc45bdee", - "metadata": {}, + "id": "e6633145", + "metadata": { + "editable": true + }, "source": [ "## Economy-size SVD\n", "\n", @@ -3388,8 +2957,10 @@ }, { "cell_type": "markdown", - "id": "f77eda9e", - "metadata": {}, + "id": "e3b9ee63", + "metadata": { + "editable": true + }, "source": [ "## Codes for the SVD" ] @@ -3397,8 +2968,11 @@ { "cell_type": "code", "execution_count": 26, - "id": "87edcbe8", - "metadata": {}, + "id": "460a54c6", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import numpy as np\n", @@ -3434,8 +3008,10 @@ }, { "cell_type": "markdown", - "id": "9594d07b", - "metadata": {}, + "id": "dd7e793f", + "metadata": { + "editable": true + }, "source": [ "The matrix $\\boldsymbol{X}$ has columns that are linearly dependent. The first\n", "column is the row-wise sum of the other two columns. The rank of a\n", @@ -3449,8 +3025,10 @@ }, { "cell_type": "markdown", - "id": "83495077", - "metadata": {}, + "id": "21a28d2f", + "metadata": { + "editable": true + }, "source": [ "## Note about SVD Calculations\n", "\n", @@ -3470,20 +3048,20 @@ }, { "cell_type": "markdown", - "id": "1f811c23", - "metadata": {}, + "id": "0466e9e9", + "metadata": { + "editable": true + }, "source": [ - "## Friday September 3\n", - "\n", - "[Video of Lecture from 2020](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureSeptember11.mp4?vrtx=view-as-webpage) and [handwritten notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesSeptember11.pdf)\n", - "\n", - "More material will be added here, see handwritten notes also. Note that this material will be cleaned up after the lecture of Friday September 3. See the handwritten notes from Friday's lecture at ." + "## Friday September 2" ] }, { "cell_type": "markdown", - "id": "4a266ed5", - "metadata": {}, + "id": "cbc489a5", + "metadata": { + "editable": true + }, "source": [ "## Mathematics of the SVD and implications\n", "\n", @@ -3494,8 +3072,10 @@ }, { "cell_type": "markdown", - "id": "175eb163", - "metadata": {}, + "id": "7a2e30f8", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}=\\begin{bmatrix}\n", @@ -3511,16 +3091,20 @@ }, { "cell_type": "markdown", - "id": "19a5e14c", - "metadata": {}, + "id": "083352fe", + "metadata": { + "editable": true + }, "source": [ "We can SVD decompose our matrix as" ] }, { "cell_type": "markdown", - "id": "11cf192a", - "metadata": {}, + "id": "eafaedd0", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}=\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T,\n", @@ -3529,8 +3113,10 @@ }, { "cell_type": "markdown", - "id": "f3e550d5", - "metadata": {}, + "id": "77c9a500", + "metadata": { + "editable": true + }, "source": [ "where $\\boldsymbol{U}$ is an orthogonal matrix of dimension $n\\times n$, meaning that $\\boldsymbol{U}\\boldsymbol{U}^T=\\boldsymbol{U}^T\\boldsymbol{U}=\\boldsymbol{I}_n$. Here $\\boldsymbol{I}_n$ is the unit matrix of dimension $n \\times n$.\n", "\n", @@ -3541,8 +3127,10 @@ }, { "cell_type": "markdown", - "id": "d53bb578", - "metadata": {}, + "id": "fe70b7df", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\sigma_0 > \\sigma_1 > \\sigma_2 > \\dots > \\sigma_{p-1} > 0.\n", @@ -3551,16 +3139,20 @@ }, { "cell_type": "markdown", - "id": "57f2f89f", - "metadata": {}, + "id": "544809ac", + "metadata": { + "editable": true + }, "source": [ "All values beyond $p-1$ are all zero." ] }, { "cell_type": "markdown", - "id": "0458c51f", - "metadata": {}, + "id": "01643345", + "metadata": { + "editable": true + }, "source": [ "## Example Matrix\n", "\n", @@ -3569,8 +3161,10 @@ }, { "cell_type": "markdown", - "id": "58155af6", - "metadata": {}, + "id": "bb30ad0f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\Sigma}=\n", @@ -3584,16 +3178,20 @@ }, { "cell_type": "markdown", - "id": "a1996d9b", - "metadata": {}, + "id": "3725c7e1", + "metadata": { + "editable": true + }, "source": [ "The singular values are $\\sigma_0=2$ and $\\sigma_1=1$. It is common to rewrite the matrix $\\boldsymbol{\\Sigma}$ as" ] }, { "cell_type": "markdown", - "id": "583c5e45", - "metadata": {}, + "id": "237832a1", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\Sigma}=\n", @@ -3606,16 +3204,20 @@ }, { "cell_type": "markdown", - "id": "988f38ae", - "metadata": {}, + "id": "64722e29", + "metadata": { + "editable": true + }, "source": [ "where" ] }, { "cell_type": "markdown", - "id": "542eb473", - "metadata": {}, + "id": "1a4c89e2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\tilde{\\Sigma}}=\n", @@ -3628,16 +3230,20 @@ }, { "cell_type": "markdown", - "id": "81dfd087", - "metadata": {}, + "id": "8e035efe", + "metadata": { + "editable": true + }, "source": [ "contains only the singular values. Note also (and we will use this below) that" ] }, { "cell_type": "markdown", - "id": "98e874a5", - "metadata": {}, + "id": "57bc943e", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\Sigma}^T\\boldsymbol{\\Sigma}=\n", @@ -3650,16 +3256,20 @@ }, { "cell_type": "markdown", - "id": "431542eb", - "metadata": {}, + "id": "212af7c2", + "metadata": { + "editable": true + }, "source": [ "which is a $2\\times 2 $ matrix while" ] }, { "cell_type": "markdown", - "id": "3b821038", - "metadata": {}, + "id": "1a1a5efc", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\Sigma}\\boldsymbol{\\Sigma}^T=\n", @@ -3673,8 +3283,10 @@ }, { "cell_type": "markdown", - "id": "0279e1cb", - "metadata": {}, + "id": "4e24ea2c", + "metadata": { + "editable": true + }, "source": [ "is a $3\\times 3 $ matrix. The last row and column of this last matrix\n", "contain only zeros. This will have important consequences for our SVD\n", @@ -3683,8 +3295,10 @@ }, { "cell_type": "markdown", - "id": "9d85ed00", - "metadata": {}, + "id": "2fb73025", + "metadata": { + "editable": true + }, "source": [ "## Setting up the Matrix to be inverted\n", "\n", @@ -3693,8 +3307,10 @@ }, { "cell_type": "markdown", - "id": "4224af8b", - "metadata": {}, + "id": "438ffaba", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{X}=\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T,\n", @@ -3703,16 +3319,20 @@ }, { "cell_type": "markdown", - "id": "8312e008", - "metadata": {}, + "id": "99129c0f", + "metadata": { + "editable": true + }, "source": [ "and using the orthogonality of the matrix $\\boldsymbol{U}$ we have" ] }, { "cell_type": "markdown", - "id": "9674e71f", - "metadata": {}, + "id": "870c52eb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{X}=\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{\\Sigma}\\boldsymbol{V}^T.\n", @@ -3721,8 +3341,10 @@ }, { "cell_type": "markdown", - "id": "1dc69f6e", - "metadata": {}, + "id": "4494e480", + "metadata": { + "editable": true + }, "source": [ "We define $\\boldsymbol{\\Sigma}^T\\boldsymbol{\\Sigma}=\\tilde{\\boldsymbol{\\Sigma}}^2$ which is a diagonal matrix containing only the singular values squared. It has dimensionality $p \\times p$.\n", "\n", @@ -3731,8 +3353,10 @@ }, { "cell_type": "markdown", - "id": "ad5b0673", - "metadata": {}, + "id": "104993a7", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{X}=\\tilde{\\boldsymbol{\\Sigma}}^2.\n", @@ -3741,16 +3365,20 @@ }, { "cell_type": "markdown", - "id": "a955f323", - "metadata": {}, + "id": "949b0666", + "metadata": { + "editable": true + }, "source": [ "We can now insert the result for the matrix $\\boldsymbol{X}^T\\boldsymbol{X}$ into our equation for ordinary least squares where" ] }, { "cell_type": "markdown", - "id": "bb180718", - "metadata": {}, + "id": "c2c79819", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{X}\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y},\n", @@ -3759,16 +3387,20 @@ }, { "cell_type": "markdown", - "id": "d869817e", - "metadata": {}, + "id": "6e1f9777", + "metadata": { + "editable": true + }, "source": [ "and using our SVD decomposition of $\\boldsymbol{X}$ we have" ] }, { "cell_type": "markdown", - "id": "f89bdf6f", - "metadata": {}, + "id": "988a58e8", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T\\tilde{\\boldsymbol{\\Sigma}}^{-2}\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T\\boldsymbol{y},\n", @@ -3777,16 +3409,20 @@ }, { "cell_type": "markdown", - "id": "a0b18249", - "metadata": {}, + "id": "fe62c7ba", + "metadata": { + "editable": true + }, "source": [ "which gives us, using the orthogonality of the matrices $\\boldsymbol{U}$ and $\\boldsymbol{V}$," ] }, { "cell_type": "markdown", - "id": "638cd1cd", - "metadata": {}, + "id": "fa7270b8", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\tilde{y}_{\\mathrm{OLS}}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_i\\boldsymbol{u}^T_j\\boldsymbol{y},\n", @@ -3795,16 +3431,20 @@ }, { "cell_type": "markdown", - "id": "3f302527", - "metadata": {}, + "id": "f845749b", + "metadata": { + "editable": true + }, "source": [ "Note here that when we perform the multiplication of the various matrices, the orthogonal vectors of the matrix $\\boldsymbol{U}$" ] }, { "cell_type": "markdown", - "id": "8db82136", - "metadata": {}, + "id": "00150f9b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{U}=[\\boldsymbol{u}_0,\\boldsymbol{u}_1,\\dots,\\boldsymbol{u}_{n-1}],\n", @@ -3813,8 +3453,10 @@ }, { "cell_type": "markdown", - "id": "cf0ac2c9", - "metadata": {}, + "id": "5ad9b501", + "metadata": { + "editable": true + }, "source": [ "that belong to $i>p-1$, result in only zeros when we perform the multiplications. This means that the sum above has non-zero elements only up to $i=p-1$. This corresponds also to the number of singular values (these are all non-zero).\n", "\n", @@ -3823,8 +3465,10 @@ }, { "cell_type": "markdown", - "id": "cfa84fdc", - "metadata": {}, + "id": "72f20405", + "metadata": { + "editable": true + }, "source": [ "## Further properties (important for our analyses later)\n", "\n", @@ -3833,8 +3477,10 @@ }, { "cell_type": "markdown", - "id": "f308d879", - "metadata": {}, + "id": "2a3128af", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{X}=\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T=\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{\\Sigma}\\boldsymbol{V}^T.\n", @@ -3843,16 +3489,20 @@ }, { "cell_type": "markdown", - "id": "cfc8d50e", - "metadata": {}, + "id": "b1c729b1", + "metadata": { + "editable": true + }, "source": [ "If we now multiply from the right with $\\boldsymbol{V}$ (using the orthogonality of $\\boldsymbol{V}$) we get" ] }, { "cell_type": "markdown", - "id": "4578a076", - "metadata": {}, + "id": "7c162a1c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)\\boldsymbol{V}=\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{\\Sigma}.\n", @@ -3861,8 +3511,10 @@ }, { "cell_type": "markdown", - "id": "ceaea02f", - "metadata": {}, + "id": "73e8c5dd", + "metadata": { + "editable": true + }, "source": [ "This means the vectors $\\boldsymbol{v}_i$ of the orthogonal matrix $\\boldsymbol{V}$ are the eigenvectors of the matrix $\\boldsymbol{X}^T\\boldsymbol{X}$\n", "with eigenvalues given by the singular values squared, that is" @@ -3870,8 +3522,10 @@ }, { "cell_type": "markdown", - "id": "5595d033", - "metadata": {}, + "id": "abc2c7fb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)\\boldsymbol{v}_i=\\boldsymbol{v}_i\\sigma_i^2.\n", @@ -3880,16 +3534,20 @@ }, { "cell_type": "markdown", - "id": "a2b4b94e", - "metadata": {}, + "id": "e66e44f6", + "metadata": { + "editable": true + }, "source": [ "Similarly, if we use the SVD decomposition for the matrix $\\boldsymbol{X}\\boldsymbol{X}^T$, we have" ] }, { "cell_type": "markdown", - "id": "af283d4c", - "metadata": {}, + "id": "cc07831e", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}\\boldsymbol{X}^T=\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T=\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T.\n", @@ -3898,16 +3556,20 @@ }, { "cell_type": "markdown", - "id": "2bdfba47", - "metadata": {}, + "id": "c23c98fb", + "metadata": { + "editable": true + }, "source": [ "If we now multiply from the right with $\\boldsymbol{U}$ (using the orthogonality of $\\boldsymbol{U}$) we get" ] }, { "cell_type": "markdown", - "id": "bb3c855d", - "metadata": {}, + "id": "8df03787", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\boldsymbol{X}\\boldsymbol{X}^T\\right)\\boldsymbol{U}=\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{\\Sigma}^T.\n", @@ -3916,8 +3578,10 @@ }, { "cell_type": "markdown", - "id": "f4d2ed1b", - "metadata": {}, + "id": "445bddc2", + "metadata": { + "editable": true + }, "source": [ "This means the vectors $\\boldsymbol{u}_i$ of the orthogonal matrix $\\boldsymbol{U}$ are the eigenvectors of the matrix $\\boldsymbol{X}\\boldsymbol{X}^T$\n", "with eigenvalues given by the singular values squared, that is" @@ -3925,8 +3589,10 @@ }, { "cell_type": "markdown", - "id": "3250e943", - "metadata": {}, + "id": "1923e2b6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\boldsymbol{X}\\boldsymbol{X}^T\\right)\\boldsymbol{u}_i=\\boldsymbol{u}_i\\sigma_i^2.\n", @@ -3935,8 +3601,10 @@ }, { "cell_type": "markdown", - "id": "122744d7", - "metadata": {}, + "id": "60533116", + "metadata": { + "editable": true + }, "source": [ "**Important note**: we have defined our design matrix $\\boldsymbol{X}$ to be an\n", "$n\\times p$ matrix. In most supervised learning cases we have that $n\n", @@ -3951,8 +3619,10 @@ }, { "cell_type": "markdown", - "id": "c970d800", - "metadata": {}, + "id": "cead831a", + "metadata": { + "editable": true + }, "source": [ "## Meet the Covariance Matrix\n", "\n", @@ -3965,8 +3635,10 @@ }, { "cell_type": "markdown", - "id": "1b3fd7ba", - "metadata": {}, + "id": "25a006c7", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial^2 C(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}^T\\partial \\boldsymbol{\\beta}} =\\frac{2}{n}\\boldsymbol{X}^T\\boldsymbol{X}.\n", @@ -3975,8 +3647,10 @@ }, { "cell_type": "markdown", - "id": "622b35d2", - "metadata": {}, + "id": "52846f89", + "metadata": { + "editable": true + }, "source": [ "This quantity defines was what is called the Hessian matrix (the second derivative of a function we want to optimize).\n", "\n", @@ -3985,8 +3659,10 @@ }, { "cell_type": "markdown", - "id": "bb65ea69", - "metadata": {}, + "id": "77ab000c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{H}=\\boldsymbol{X}^T\\boldsymbol{X}.\n", @@ -3995,8 +3671,10 @@ }, { "cell_type": "markdown", - "id": "dd5b2301", - "metadata": {}, + "id": "0a3ddc06", + "metadata": { + "editable": true + }, "source": [ "The Hessian matrix for ordinary least squares is also proportional to\n", "the covariance matrix. This means also that we can use the SVD to find\n", @@ -4006,8 +3684,10 @@ }, { "cell_type": "markdown", - "id": "1518b5a6", - "metadata": {}, + "id": "18b92d45", + "metadata": { + "editable": true + }, "source": [ "## Introducing the Covariance and Correlation functions\n", "\n", @@ -4020,8 +3700,10 @@ }, { "cell_type": "markdown", - "id": "32731b28", - "metadata": {}, + "id": "ce2158b2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{C}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n", @@ -4032,16 +3714,20 @@ }, { "cell_type": "markdown", - "id": "1546b8ab", - "metadata": {}, + "id": "65be741f", + "metadata": { + "editable": true + }, "source": [ "where for example" ] }, { "cell_type": "markdown", - "id": "7b3b0e00", - "metadata": {}, + "id": "7c76799d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] =\\frac{1}{n} \\sum_{i=0}^{n-1}(x_i- \\overline{x})(y_i- \\overline{y}).\n", @@ -4050,16 +3736,20 @@ }, { "cell_type": "markdown", - "id": "404a1659", - "metadata": {}, + "id": "0c26f780", + "metadata": { + "editable": true + }, "source": [ "With this definition and recalling that the variance is defined as" ] }, { "cell_type": "markdown", - "id": "3a1ff8da", - "metadata": {}, + "id": "0322a50a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathrm{var}[\\boldsymbol{x}]=\\frac{1}{n} \\sum_{i=0}^{n-1}(x_i- \\overline{x})^2,\n", @@ -4068,16 +3758,20 @@ }, { "cell_type": "markdown", - "id": "9e5fe3fe", - "metadata": {}, + "id": "1d6b6c20", + "metadata": { + "editable": true + }, "source": [ "we can rewrite the covariance matrix as" ] }, { "cell_type": "markdown", - "id": "e476e478", - "metadata": {}, + "id": "8a87cbab", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{C}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} \\mathrm{var}[\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n", @@ -4088,8 +3782,10 @@ }, { "cell_type": "markdown", - "id": "035beba2", - "metadata": {}, + "id": "6d1453cc", + "metadata": { + "editable": true + }, "source": [ "**Note:** we have used $1/n$ in the above definitions of the *sample* variance and covariance. We assume then that we can calculate the exact mean value. \n", "What you will find in essentially all statistics texts are equations\n", @@ -4103,8 +3799,10 @@ }, { "cell_type": "markdown", - "id": "ce0c8788", - "metadata": {}, + "id": "8ae68bd9", + "metadata": { + "editable": true + }, "source": [ "## Covariance and Correlation Matrix\n", "\n", @@ -4117,8 +3815,10 @@ }, { "cell_type": "markdown", - "id": "8ee8be1b", - "metadata": {}, + "id": "391376b3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}]=\\frac{\\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}]}{\\sqrt{\\mathrm{var}[\\boldsymbol{x}] \\mathrm{var}[\\boldsymbol{y}]}}.\n", @@ -4127,8 +3827,10 @@ }, { "cell_type": "markdown", - "id": "e05c764a", - "metadata": {}, + "id": "0930f21a", + "metadata": { + "editable": true + }, "source": [ "The correlation function is then given by values $\\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}]\n", "\\in [-1,1]$. This avoids eventual problems with too large values. We\n", @@ -4138,8 +3840,10 @@ }, { "cell_type": "markdown", - "id": "e351ae83", - "metadata": {}, + "id": "0960ecfd", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{K}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} 1 & \\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n", @@ -4150,16 +3854,20 @@ }, { "cell_type": "markdown", - "id": "00e81faf", - "metadata": {}, + "id": "f8c211c7", + "metadata": { + "editable": true + }, "source": [ "In the above example this is the function we constructed using **pandas**." ] }, { "cell_type": "markdown", - "id": "c2209483", - "metadata": {}, + "id": "660f0e48", + "metadata": { + "editable": true + }, "source": [ "## Correlation Function and Design/Feature Matrix\n", "\n", @@ -4169,8 +3877,10 @@ }, { "cell_type": "markdown", - "id": "fd757d09", - "metadata": {}, + "id": "c8f3a48a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}=\\begin{bmatrix}\n", @@ -4186,8 +3896,10 @@ }, { "cell_type": "markdown", - "id": "d3ddca6a", - "metadata": {}, + "id": "13852d99", + "metadata": { + "editable": true + }, "source": [ "with $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$, with the predictors/features $p$ refering to the column numbers and the\n", "entries $n$ being the row elements.\n", @@ -4196,8 +3908,10 @@ }, { "cell_type": "markdown", - "id": "0819a630", - "metadata": {}, + "id": "9caf69ed", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}=\\begin{bmatrix} \\boldsymbol{x}_0 & \\boldsymbol{x}_1 & \\boldsymbol{x}_2 & \\dots & \\dots & \\boldsymbol{x}_{p-1}\\end{bmatrix},\n", @@ -4206,16 +3920,20 @@ }, { "cell_type": "markdown", - "id": "8d70123f", - "metadata": {}, + "id": "b65b0452", + "metadata": { + "editable": true + }, "source": [ "with a given vector" ] }, { "cell_type": "markdown", - "id": "39032237", - "metadata": {}, + "id": "4fdb15c5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_i^T = \\begin{bmatrix}x_{0,i} & x_{1,i} & x_{2,i}& \\dots & \\dots x_{n-1,i}\\end{bmatrix}.\n", @@ -4224,8 +3942,10 @@ }, { "cell_type": "markdown", - "id": "616bfec3", - "metadata": {}, + "id": "b25cf3af", + "metadata": { + "editable": true + }, "source": [ "With these definitions, we can now rewrite our $2\\times 2$\n", "correlation/covariance matrix in terms of a moe general design/feature\n", @@ -4235,8 +3955,10 @@ }, { "cell_type": "markdown", - "id": "3e0872f6", - "metadata": {}, + "id": "32007df3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{C}[\\boldsymbol{x}] = \\begin{bmatrix}\n", @@ -4252,16 +3974,20 @@ }, { "cell_type": "markdown", - "id": "a95cb740", - "metadata": {}, + "id": "72695d5a", + "metadata": { + "editable": true + }, "source": [ "and the correlation matrix" ] }, { "cell_type": "markdown", - "id": "97b7477a", - "metadata": {}, + "id": "c6672ffe", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{K}[\\boldsymbol{x}] = \\begin{bmatrix}\n", @@ -4277,8 +4003,10 @@ }, { "cell_type": "markdown", - "id": "089f07ac", - "metadata": {}, + "id": "382286a5", + "metadata": { + "editable": true + }, "source": [ "## Covariance Matrix Examples\n", "\n", @@ -4293,8 +4021,10 @@ }, { "cell_type": "markdown", - "id": "25fd911d", - "metadata": {}, + "id": "b0c4c797", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{W} = \\begin{bmatrix} x_0 & x_1 & x_2 & \\dots & x_{n-2} & x_{n-1} \\\\\n", @@ -4305,8 +4035,10 @@ }, { "cell_type": "markdown", - "id": "f03f377c", - "metadata": {}, + "id": "36fba640", + "metadata": { + "editable": true + }, "source": [ "which in turn is converted into into the $2\\times 2$ covariance matrix\n", "$\\boldsymbol{C}$ via the Numpy function **np.cov()**. We note that we can also calculate\n", @@ -4318,8 +4050,11 @@ { "cell_type": "code", "execution_count": 27, - "id": "b1661961", - "metadata": {}, + "id": "bf706a0d", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "# Importing various packages\n", @@ -4336,8 +4071,10 @@ }, { "cell_type": "markdown", - "id": "f91ad28e", - "metadata": {}, + "id": "d1b4fd40", + "metadata": { + "editable": true + }, "source": [ "## Correlation Matrix\n", "\n", @@ -4351,8 +4088,11 @@ { "cell_type": "code", "execution_count": 28, - "id": "3ff08e48", - "metadata": {}, + "id": "2a6bd16e", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import numpy as np\n", @@ -4380,8 +4120,10 @@ }, { "cell_type": "markdown", - "id": "eed40eec", - "metadata": {}, + "id": "722eb589", + "metadata": { + "editable": true + }, "source": [ "We see that the matrix elements along the diagonal are one as they\n", "should be and that the matrix is symmetric. Furthermore, diagonalizing\n", @@ -4392,8 +4134,10 @@ }, { "cell_type": "markdown", - "id": "4aff4d1d", - "metadata": {}, + "id": "7f3497d4", + "metadata": { + "editable": true + }, "source": [ "## Correlation Matrix with Pandas\n", "\n", @@ -4403,8 +4147,11 @@ { "cell_type": "code", "execution_count": 29, - "id": "a3347660", - "metadata": {}, + "id": "7a301f46", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import numpy as np\n", @@ -4425,16 +4172,20 @@ }, { "cell_type": "markdown", - "id": "48a0cf23", - "metadata": {}, + "id": "50e01f52", + "metadata": { + "editable": true + }, "source": [ "We expand this model to the Franke function discussed above." ] }, { "cell_type": "markdown", - "id": "ee4d2fa0", - "metadata": {}, + "id": "f28301d6", + "metadata": { + "editable": true + }, "source": [ "## Correlation Matrix with Pandas and the Franke function" ] @@ -4442,8 +4193,11 @@ { "cell_type": "code", "execution_count": 30, - "id": "f370e6da", - "metadata": {}, + "id": "3951a832", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "# Common imports\n", @@ -4493,8 +4247,10 @@ }, { "cell_type": "markdown", - "id": "71b41cc3", - "metadata": {}, + "id": "8ad06af5", + "metadata": { + "editable": true + }, "source": [ "We note here that the covariance is zero for the first rows and\n", "columns since all matrix elements in the design matrix were set to one\n", @@ -4508,8 +4264,10 @@ }, { "cell_type": "markdown", - "id": "ec1bbf8b", - "metadata": {}, + "id": "17063f58", + "metadata": { + "editable": true + }, "source": [ "## Rewriting the Covariance and/or Correlation Matrix\n", "\n", @@ -4518,8 +4276,10 @@ }, { "cell_type": "markdown", - "id": "90bac5f3", - "metadata": {}, + "id": "4df5a82f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{C}[\\boldsymbol{x}] = \\frac{1}{n}\\boldsymbol{X}^T\\boldsymbol{X}= \\mathbb{E}[\\boldsymbol{X}^T\\boldsymbol{X}].\n", @@ -4528,16 +4288,20 @@ }, { "cell_type": "markdown", - "id": "8d0e3e56", - "metadata": {}, + "id": "bb789f76", + "metadata": { + "editable": true + }, "source": [ "To see this let us simply look at a design matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{2\\times 2}$" ] }, { "cell_type": "markdown", - "id": "a796bd05", - "metadata": {}, + "id": "bce50f33", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}=\\begin{bmatrix}\n", @@ -4551,16 +4315,20 @@ }, { "cell_type": "markdown", - "id": "860b78db", - "metadata": {}, + "id": "bbb48342", + "metadata": { + "editable": true + }, "source": [ "If we then compute the expectation value (note the $1/n$ factor instead of $1/(n-1)$)" ] }, { "cell_type": "markdown", - "id": "03e8fc84", - "metadata": {}, + "id": "c7759d29", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbb{E}[\\boldsymbol{X}^T\\boldsymbol{X}] = \\frac{1}{n}\\boldsymbol{X}^T\\boldsymbol{X}=\\frac{1}{n}\\begin{bmatrix}\n", @@ -4572,16 +4340,20 @@ }, { "cell_type": "markdown", - "id": "007e9517", - "metadata": {}, + "id": "ac240840", + "metadata": { + "editable": true + }, "source": [ "which is just" ] }, { "cell_type": "markdown", - "id": "4f59cf88", - "metadata": {}, + "id": "feac822f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]=\\begin{bmatrix} \\mathrm{var}[\\boldsymbol{x}_0] & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] \\\\\n", @@ -4592,8 +4364,10 @@ }, { "cell_type": "markdown", - "id": "1ffd6dae", - "metadata": {}, + "id": "b16a9f14", + "metadata": { + "editable": true + }, "source": [ "where we wrote $$\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]$$ to indicate that this is the covariance of the vectors $\\boldsymbol{x}$ of the design/feature matrix $\\boldsymbol{X}$.\n", "\n", @@ -4602,8 +4376,10 @@ }, { "cell_type": "markdown", - "id": "48e43aec", - "metadata": {}, + "id": "ca333d33", + "metadata": { + "editable": true + }, "source": [ "## Linking with the SVD\n", "\n", @@ -4612,8 +4388,10 @@ }, { "cell_type": "markdown", - "id": "a9e79c63", - "metadata": {}, + "id": "46fc66c6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{X}=\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T=\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{\\Sigma}\\boldsymbol{V}^T.\n", @@ -4622,16 +4400,20 @@ }, { "cell_type": "markdown", - "id": "53c6be82", - "metadata": {}, + "id": "f42055e7", + "metadata": { + "editable": true + }, "source": [ "Since the matrices here have dimension $p\\times p$, with $p$ corresponding to the singular values, we defined earlier the matrix" ] }, { "cell_type": "markdown", - "id": "f338f425", - "metadata": {}, + "id": "662ca199", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\Sigma}^T\\boldsymbol{\\Sigma} = \\begin{bmatrix} \\tilde{\\boldsymbol{\\Sigma}} & \\boldsymbol{0}\\\\ \\end{bmatrix}\\begin{bmatrix} \\tilde{\\boldsymbol{\\Sigma}} \\\\ \\boldsymbol{0}\\\\ \\end{bmatrix},\n", @@ -4640,16 +4422,20 @@ }, { "cell_type": "markdown", - "id": "99d983a1", - "metadata": {}, + "id": "143a8cf7", + "metadata": { + "editable": true + }, "source": [ "where the tilde-matrix $\\tilde{\\boldsymbol{\\Sigma}}$ is a matrix of dimension $p\\times p$ containing only the singular values $\\sigma_i$, that is" ] }, { "cell_type": "markdown", - "id": "71c5eed8", - "metadata": {}, + "id": "382c0c14", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\tilde{\\boldsymbol{\\Sigma}}=\\begin{bmatrix} \\sigma_0 & 0 & 0 & \\dots & 0 & 0 \\\\\n", @@ -4663,16 +4449,20 @@ }, { "cell_type": "markdown", - "id": "f15223b4", - "metadata": {}, + "id": "20d8d486", + "metadata": { + "editable": true + }, "source": [ "meaning we can write" ] }, { "cell_type": "markdown", - "id": "413194f6", - "metadata": {}, + "id": "8fd19fa6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{X}=\\boldsymbol{V}\\tilde{\\boldsymbol{\\Sigma}}^2\\boldsymbol{V}^T.\n", @@ -4681,16 +4471,20 @@ }, { "cell_type": "markdown", - "id": "dd296b3f", - "metadata": {}, + "id": "513650c9", + "metadata": { + "editable": true + }, "source": [ "Multiplying from the right with $\\boldsymbol{V}$ (using the orthogonality of $\\boldsymbol{V}$) we get" ] }, { "cell_type": "markdown", - "id": "9688049c", - "metadata": {}, + "id": "f263fab5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)\\boldsymbol{V}=\\boldsymbol{V}\\tilde{\\boldsymbol{\\Sigma}}^2.\n", @@ -4699,8 +4493,10 @@ }, { "cell_type": "markdown", - "id": "fe0ed0fb", - "metadata": {}, + "id": "66bab0c0", + "metadata": { + "editable": true + }, "source": [ "## What does it mean?\n", "\n", @@ -4711,8 +4507,10 @@ }, { "cell_type": "markdown", - "id": "49bcec1c", - "metadata": {}, + "id": "c5673072", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)\\boldsymbol{v}_i=\\boldsymbol{v}_i\\sigma_i^2.\n", @@ -4721,8 +4519,10 @@ }, { "cell_type": "markdown", - "id": "d217e1c2", - "metadata": {}, + "id": "07bd061b", + "metadata": { + "editable": true + }, "source": [ "In other words, each non-zero singular value of $\\boldsymbol{X}$ is a positive\n", "square root of an eigenvalue of $\\boldsymbol{X}^T\\boldsymbol{X}$. It means also that\n", @@ -4741,8 +4541,10 @@ }, { "cell_type": "markdown", - "id": "3a1e3aaf", - "metadata": {}, + "id": "7d17272c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{C}[\\boldsymbol{X}]=\\frac{1}{n}\\boldsymbol{X}^T\\boldsymbol{X},\n", @@ -4751,8 +4553,10 @@ }, { "cell_type": "markdown", - "id": "ced3b70f", - "metadata": {}, + "id": "e48cbb4c", + "metadata": { + "editable": true + }, "source": [ "meaning that every squared non-singular value of $\\boldsymbol{X}$ divided by $n$ (\n", "the number of samples) are the eigenvalues of the covariance\n", @@ -4764,8 +4568,10 @@ }, { "cell_type": "markdown", - "id": "f2589fdd", - "metadata": {}, + "id": "8a7f97b9", + "metadata": { + "editable": true + }, "source": [ "## And finally $\\boldsymbol{X}\\boldsymbol{X}^T$\n", "\n", @@ -4774,8 +4580,10 @@ }, { "cell_type": "markdown", - "id": "02248c4a", - "metadata": {}, + "id": "7996e3bc", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}\\boldsymbol{X}^T=\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T\\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T=\\boldsymbol{U}\\boldsymbol{\\Sigma}^T\\boldsymbol{\\Sigma}\\boldsymbol{U}^T.\n", @@ -4784,16 +4592,20 @@ }, { "cell_type": "markdown", - "id": "96d09d6e", - "metadata": {}, + "id": "03393c29", + "metadata": { + "editable": true + }, "source": [ "Since the matrices here have dimension $n\\times n$, we have" ] }, { "cell_type": "markdown", - "id": "4b99c87c", - "metadata": {}, + "id": "2cb552ea", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\Sigma}\\boldsymbol{\\Sigma}^T = \\begin{bmatrix} \\tilde{\\boldsymbol{\\Sigma}} \\\\ \\boldsymbol{0}\\\\ \\end{bmatrix}\\begin{bmatrix} \\tilde{\\boldsymbol{\\Sigma}} \\boldsymbol{0}\\\\ \\end{bmatrix}=\\begin{bmatrix} \\tilde{\\boldsymbol{\\Sigma}} & \\boldsymbol{0} \\\\ \\boldsymbol{0} & \\boldsymbol{0}\\\\ \\end{bmatrix},\n", @@ -4802,16 +4614,20 @@ }, { "cell_type": "markdown", - "id": "d8faf331", - "metadata": {}, + "id": "ae39e476", + "metadata": { + "editable": true + }, "source": [ "leading to" ] }, { "cell_type": "markdown", - "id": "0bb641d6", - "metadata": {}, + "id": "d6189c04", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}\\boldsymbol{X}^T=\\boldsymbol{U}\\begin{bmatrix} \\tilde{\\boldsymbol{\\Sigma}} & \\boldsymbol{0} \\\\ \\boldsymbol{0} & \\boldsymbol{0}\\\\ \\end{bmatrix}\\boldsymbol{U}^T.\n", @@ -4820,16 +4636,20 @@ }, { "cell_type": "markdown", - "id": "25ebcc39", - "metadata": {}, + "id": "b9284cba", + "metadata": { + "editable": true + }, "source": [ "Multiplying with $\\boldsymbol{U}$ from the right gives us the eigenvalue problem" ] }, { "cell_type": "markdown", - "id": "4b2f3c5f", - "metadata": {}, + "id": "99aca4c5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "(\\boldsymbol{X}\\boldsymbol{X}^T)\\boldsymbol{U}=\\boldsymbol{U}\\begin{bmatrix} \\tilde{\\boldsymbol{\\Sigma}} & \\boldsymbol{0} \\\\ \\boldsymbol{0} & \\boldsymbol{0}\\\\ \\end{bmatrix}.\n", @@ -4838,8 +4658,10 @@ }, { "cell_type": "markdown", - "id": "e9837512", - "metadata": {}, + "id": "08b82557", + "metadata": { + "editable": true + }, "source": [ "It means that the eigenvalues of $\\boldsymbol{X}\\boldsymbol{X}^T$ are again given by\n", "the non-zero singular values plus now a series of zeros. The column\n", @@ -4853,8 +4675,10 @@ }, { "cell_type": "markdown", - "id": "4d55630a", - "metadata": {}, + "id": "26e2bbec", + "metadata": { + "editable": true + }, "source": [ "## Ridge and LASSO Regression\n", "\n", @@ -4864,8 +4688,10 @@ }, { "cell_type": "markdown", - "id": "2a3f0995", - "metadata": {}, + "id": "2c67d9df", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in {\\mathbb{R}}^{p}}}\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right\\}.\n", @@ -4874,16 +4700,20 @@ }, { "cell_type": "markdown", - "id": "417b607c", - "metadata": {}, + "id": "61dff7cb", + "metadata": { + "editable": true + }, "source": [ "or we can state it as" ] }, { "cell_type": "markdown", - "id": "aef4e4c9", - "metadata": {}, + "id": "9ffd1014", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", @@ -4893,16 +4723,20 @@ }, { "cell_type": "markdown", - "id": "720d64d9", - "metadata": {}, + "id": "49d4546f", + "metadata": { + "editable": true + }, "source": [ "where we have used the definition of a norm-2 vector, that is" ] }, { "cell_type": "markdown", - "id": "580095be", - "metadata": {}, + "id": "393393c3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\vert\\vert \\boldsymbol{x}\\vert\\vert_2 = \\sqrt{\\sum_i x_i^2}.\n", @@ -4911,8 +4745,10 @@ }, { "cell_type": "markdown", - "id": "699717e7", - "metadata": {}, + "id": "1e88bc43", + "metadata": { + "editable": true + }, "source": [ "By minimizing the above equation with respect to the parameters\n", "$\\boldsymbol{\\beta}$ we could then obtain an analytical expression for the\n", @@ -4922,8 +4758,10 @@ }, { "cell_type": "markdown", - "id": "ceaebf06", - "metadata": {}, + "id": "c68d77e9", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", @@ -4933,8 +4771,10 @@ }, { "cell_type": "markdown", - "id": "2c7e22af", - "metadata": {}, + "id": "806da181", + "metadata": { + "editable": true + }, "source": [ "which leads to the Ridge regression minimization problem where we\n", "require that $\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_2^2\\le t$, where $t$ is\n", @@ -4943,8 +4783,10 @@ }, { "cell_type": "markdown", - "id": "def3adb2", - "metadata": {}, + "id": "52431ab4", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{X},\\boldsymbol{\\beta})=\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_1,\n", @@ -4953,16 +4795,20 @@ }, { "cell_type": "markdown", - "id": "73687e75", - "metadata": {}, + "id": "d929ad9b", + "metadata": { + "editable": true + }, "source": [ "we have a new optimization equation" ] }, { "cell_type": "markdown", - "id": "8e15f07f", - "metadata": {}, + "id": "80cb20da", + "metadata": { + "editable": true + }, "source": [ "$$\n", "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", @@ -4972,8 +4818,10 @@ }, { "cell_type": "markdown", - "id": "6c53998d", - "metadata": {}, + "id": "3c3ac295", + "metadata": { + "editable": true + }, "source": [ "which leads to Lasso regression. Lasso stands for least absolute shrinkage and selection operator. \n", "\n", @@ -4982,8 +4830,10 @@ }, { "cell_type": "markdown", - "id": "89b9cbc4", - "metadata": {}, + "id": "533cb25b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\vert\\vert \\boldsymbol{x}\\vert\\vert_1 = \\sum_i \\vert x_i\\vert.\n", @@ -4992,8 +4842,10 @@ }, { "cell_type": "markdown", - "id": "357f8421", - "metadata": {}, + "id": "09a7af98", + "metadata": { + "editable": true + }, "source": [ "## Deriving the Ridge Regression Equations\n", "\n", @@ -5002,8 +4854,10 @@ }, { "cell_type": "markdown", - "id": "ef7abfcd", - "metadata": {}, + "id": "b8450765", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{X},\\boldsymbol{\\beta})=\\left\\{(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})^T(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\right\\}+\\lambda\\boldsymbol{\\beta}^T\\boldsymbol{\\beta},\n", @@ -5012,8 +4866,10 @@ }, { "cell_type": "markdown", - "id": "db09d607", - "metadata": {}, + "id": "10d56ab6", + "metadata": { + "editable": true + }, "source": [ "and \n", "taking the derivatives with respect to $\\boldsymbol{\\beta}$ we obtain then\n", @@ -5024,8 +4880,10 @@ }, { "cell_type": "markdown", - "id": "1fb685f5", - "metadata": {}, + "id": "b6f870bb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\hat{\\boldsymbol{\\beta}}_{\\mathrm{Ridge}} = \\left(\\boldsymbol{X}^T\\boldsymbol{X}+\\lambda\\boldsymbol{I}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y},\n", @@ -5034,16 +4892,20 @@ }, { "cell_type": "markdown", - "id": "25fedebe", - "metadata": {}, + "id": "b1ca5c13", + "metadata": { + "editable": true + }, "source": [ "with $\\boldsymbol{I}$ being a $p\\times p$ identity matrix with the constraint that" ] }, { "cell_type": "markdown", - "id": "5de8bfbf", - "metadata": {}, + "id": "7845cebf", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\sum_{i=0}^{p-1} \\beta_i^2 \\leq t,\n", @@ -5052,8 +4914,10 @@ }, { "cell_type": "markdown", - "id": "3cdcc769", - "metadata": {}, + "id": "06812700", + "metadata": { + "editable": true + }, "source": [ "with $t$ a finite positive number. \n", "\n", @@ -5062,8 +4926,10 @@ }, { "cell_type": "markdown", - "id": "88b1d12e", - "metadata": {}, + "id": "99223f96", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\hat{\\boldsymbol{\\beta}}_{\\mathrm{Ridge}} = \\left(\\boldsymbol{X}^T\\boldsymbol{X}+n\\lambda\\boldsymbol{I}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n", @@ -5072,8 +4938,10 @@ }, { "cell_type": "markdown", - "id": "187cbef2", - "metadata": {}, + "id": "733feba7", + "metadata": { + "editable": true + }, "source": [ "In many textbooks the $1/n$ term is often omitted. Note that a library like **Scikit-Learn** does not include the $1/n$ factor in the setup of the cost function.\n", "\n", @@ -5082,8 +4950,10 @@ }, { "cell_type": "markdown", - "id": "397694ac", - "metadata": {}, + "id": "5208f63b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\hat{\\boldsymbol{\\beta}}_{\\mathrm{OLS}} = \\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y},\n", @@ -5092,8 +4962,10 @@ }, { "cell_type": "markdown", - "id": "b02cd961", - "metadata": {}, + "id": "f4757521", + "metadata": { + "editable": true + }, "source": [ "which can lead to singular matrices. However, with the SVD, we can always compute the inverse of the matrix $\\boldsymbol{X}^T\\boldsymbol{X}$.\n", "\n", @@ -5109,8 +4981,10 @@ }, { "cell_type": "markdown", - "id": "f80fdb0c", - "metadata": {}, + "id": "cbf0ce84", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\tilde{\\boldsymbol{y}}_{\\mathrm{OLS}}=\\boldsymbol{X}\\boldsymbol{\\beta} =\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}.\n", @@ -5119,16 +4993,20 @@ }, { "cell_type": "markdown", - "id": "b8421783", - "metadata": {}, + "id": "6ce5fe29", + "metadata": { + "editable": true + }, "source": [ "For Ridge regression this becomes" ] }, { "cell_type": "markdown", - "id": "615c1cb8", - "metadata": {}, + "id": "f11b7398", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\tilde{\\boldsymbol{y}}_{\\mathrm{Ridge}}=\\boldsymbol{X}\\boldsymbol{\\beta}_{\\mathrm{Ridge}} = \\boldsymbol{U\\Sigma V^T}\\left(\\boldsymbol{V}\\boldsymbol{\\Sigma}^2\\boldsymbol{V}^T+\\lambda\\boldsymbol{I} \\right)^{-1}(\\boldsymbol{U\\Sigma V^T})^T\\boldsymbol{y}=\\sum_{j=0}^{p-1}\\boldsymbol{u}_j\\boldsymbol{u}_j^T\\frac{\\sigma_j^2}{\\sigma_j^2+\\lambda}\\boldsymbol{y},\n", @@ -5137,16 +5015,20 @@ }, { "cell_type": "markdown", - "id": "dafe3b7e", - "metadata": {}, + "id": "af086f6d", + "metadata": { + "editable": true + }, "source": [ "with the vectors $\\boldsymbol{u}_j$ being the columns of $\\boldsymbol{U}$ from the SVD of the matrix $\\boldsymbol{X}$." ] }, { "cell_type": "markdown", - "id": "51dea34a", - "metadata": {}, + "id": "c2924353", + "metadata": { + "editable": true + }, "source": [ "## Interpreting the Ridge results\n", "\n", @@ -5155,8 +5037,10 @@ }, { "cell_type": "markdown", - "id": "5dd44f1b", - "metadata": {}, + "id": "2771d445", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\sigma_j^2}{\\sigma_j^2+\\lambda} \\leq 1.\n", @@ -5165,8 +5049,10 @@ }, { "cell_type": "markdown", - "id": "2f45c598", - "metadata": {}, + "id": "7a6ff466", + "metadata": { + "editable": true + }, "source": [ "Ridge regression finds the coordinates of $\\boldsymbol{y}$ with respect to the\n", "orthonormal basis $\\boldsymbol{U}$, it then shrinks the coordinates by\n", @@ -5179,8 +5065,10 @@ }, { "cell_type": "markdown", - "id": "17f9867f", - "metadata": {}, + "id": "5af821c9", + "metadata": { + "editable": true + }, "source": [ "## More interpretations\n", "\n", @@ -5189,8 +5077,10 @@ }, { "cell_type": "markdown", - "id": "583738d0", - "metadata": {}, + "id": "f5aa42bf", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{X}=(\\boldsymbol{X}^T\\boldsymbol{X})^{-1} =\\boldsymbol{I}.\n", @@ -5199,16 +5089,20 @@ }, { "cell_type": "markdown", - "id": "20d77427", - "metadata": {}, + "id": "316f57cc", + "metadata": { + "editable": true + }, "source": [ "In this case the standard OLS results in" ] }, { "cell_type": "markdown", - "id": "9e7706c5", - "metadata": {}, + "id": "c292a003", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{OLS}} = \\boldsymbol{X}^T\\boldsymbol{y}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_j\\boldsymbol{u}_j^T\\boldsymbol{y},\n", @@ -5217,16 +5111,20 @@ }, { "cell_type": "markdown", - "id": "4da844c2", - "metadata": {}, + "id": "45e5165b", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "id": "525db3d4", - "metadata": {}, + "id": "49717c92", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{Ridge}} = \\left(\\boldsymbol{I}+\\lambda\\boldsymbol{I}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}=\\left(1+\\lambda\\right)^{-1}\\boldsymbol{\\beta}^{\\mathrm{OLS}},\n", @@ -5235,8 +5133,10 @@ }, { "cell_type": "markdown", - "id": "cd528cd6", - "metadata": {}, + "id": "97a0c23b", + "metadata": { + "editable": true + }, "source": [ "that is the Ridge estimator scales the OLS estimator by the inverse of a factor $1+\\lambda$, and\n", "the Ridge estimator converges to zero when the hyperparameter goes to\n", @@ -5250,8 +5150,10 @@ }, { "cell_type": "markdown", - "id": "efbcf3aa", - "metadata": {}, + "id": "330ce73a", + "metadata": { + "editable": true + }, "source": [ "## Deriving the Lasso Regression Equations\n", "\n", @@ -5260,8 +5162,10 @@ }, { "cell_type": "markdown", - "id": "41c8f3cb", - "metadata": {}, + "id": "6d7b002d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{X},\\boldsymbol{\\beta})=\\left\\{(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})^T(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\right\\}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n", @@ -5270,16 +5174,20 @@ }, { "cell_type": "markdown", - "id": "896f0e84", - "metadata": {}, + "id": "416c99d3", + "metadata": { + "editable": true + }, "source": [ "Taking the derivative with respect to $\\boldsymbol{\\beta}$ and recalling that the derivative of the absolute value is (we drop the boldfaced vector symbol for simplicty)" ] }, { "cell_type": "markdown", - "id": "515a212f", - "metadata": {}, + "id": "d17f3500", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{d \\vert \\beta\\vert}{d \\boldsymbol{\\beta}}=\\mathrm{sgn}(\\boldsymbol{\\beta})=\\left\\{\\begin{array}{cc} 1 & \\beta > 0 \\\\ 0 & \\beta =0\\\\-1 & \\beta < 0, \\end{array}\\right.\n", @@ -5288,16 +5196,20 @@ }, { "cell_type": "markdown", - "id": "138183e2", - "metadata": {}, + "id": "bb7641db", + "metadata": { + "editable": true + }, "source": [ "we have that the derivative of the cost function is" ] }, { "cell_type": "markdown", - "id": "4e475fea", - "metadata": {}, + "id": "88cfef76", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial C(\\boldsymbol{X},\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}=-2\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})+\\lambda sgn(\\boldsymbol{\\beta})=0,\n", @@ -5306,16 +5218,20 @@ }, { "cell_type": "markdown", - "id": "4ed75094", - "metadata": {}, + "id": "9c13528c", + "metadata": { + "editable": true + }, "source": [ "and reordering we have" ] }, { "cell_type": "markdown", - "id": "d4bafc4a", - "metadata": {}, + "id": "0d7679bb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}^T\\boldsymbol{X}\\boldsymbol{\\beta})+\\lambda sgn(\\boldsymbol{\\beta})=2\\boldsymbol{X}^T(\\boldsymbol{y}.\n", @@ -5324,16 +5240,20 @@ }, { "cell_type": "markdown", - "id": "f1ba8e36", - "metadata": {}, + "id": "a6d38478", + "metadata": { + "editable": true + }, "source": [ "This equation does not lead to a nice analytical equation as in either Ridge regression or ordinary least squares. This equation can however be solved by using standard convex optimization algorithms using for example the Python package [CVXOPT](https://cvxopt.org/). We will discuss this later." ] }, { "cell_type": "markdown", - "id": "8efb3578", - "metadata": {}, + "id": "f2ea25db", + "metadata": { + "editable": true + }, "source": [ "## Exercises for week 36, September 6-10\n", "\n", @@ -5342,8 +5262,10 @@ }, { "cell_type": "markdown", - "id": "c413d900", - "metadata": {}, + "id": "3bbdcc57", + "metadata": { + "editable": true + }, "source": [ "## Exercise 1: Adding Ridge and Lasso Regression\n", "\n", @@ -5364,8 +5286,11 @@ { "cell_type": "code", "execution_count": 31, - "id": "afad0eab", - "metadata": {}, + "id": "75f7df50", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "x = np.random.rand(100)\n", @@ -5374,8 +5299,10 @@ }, { "cell_type": "markdown", - "id": "3f02a117", - "metadata": {}, + "id": "cd187f0b", + "metadata": { + "editable": true + }, "source": [ "Write your own code for the Ridge method (see chapter 3.4 of Hastie *et al.*, equations (3.43) and (3.44)) and compute the parametrization for different values of $\\lambda$. Compare and analyze your results with those from exercise 3. Study the dependence on $\\lambda$ while also varying the strength of the noise in your expression for $y(x)$. \n", "\n", @@ -5387,8 +5314,11 @@ { "cell_type": "code", "execution_count": 32, - "id": "b2c58e37", - "metadata": {}, + "id": "b405f2bc", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import os\n", @@ -5464,8 +5394,10 @@ }, { "cell_type": "markdown", - "id": "dc07b126", - "metadata": {}, + "id": "1488d7c3", + "metadata": { + "editable": true + }, "source": [ "Repeat the above but using the functionality of\n", "**Scikit-Learn**. Compare your code with the results from\n", @@ -5477,8 +5409,10 @@ }, { "cell_type": "markdown", - "id": "f4d85b30", - "metadata": {}, + "id": "a941e20b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "MSE(\\hat{y},\\hat{\\tilde{y}}) = \\frac{1}{n}\n", @@ -5488,8 +5422,10 @@ }, { "cell_type": "markdown", - "id": "e08d2eda", - "metadata": {}, + "id": "56a27876", + "metadata": { + "editable": true + }, "source": [ "and the $R^2$ score function.\n", "If $\\tilde{\\hat{y}}_i$ is the predicted value of the $i-th$ sample and $y_i$ is the corresponding true value, then the score $R^2$ is defined as" @@ -5497,8 +5433,10 @@ }, { "cell_type": "markdown", - "id": "fd872c6f", - "metadata": {}, + "id": "f80ee5a2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "R^2(\\hat{y}, \\tilde{\\hat{y}}) = 1 - \\frac{\\sum_{i=0}^{n - 1} (y_i - \\tilde{y}_i)^2}{\\sum_{i=0}^{n - 1} (y_i - \\bar{y})^2},\n", @@ -5507,16 +5445,20 @@ }, { "cell_type": "markdown", - "id": "977bd2c8", - "metadata": {}, + "id": "c1e9cced", + "metadata": { + "editable": true + }, "source": [ "where we have defined the mean value of $\\hat{y}$ as" ] }, { "cell_type": "markdown", - "id": "eeee30ad", - "metadata": {}, + "id": "e39f7404", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\bar{y} = \\frac{1}{n} \\sum_{i=0}^{n - 1} y_i.\n", @@ -5525,16 +5467,20 @@ }, { "cell_type": "markdown", - "id": "5bf6c9bc", - "metadata": {}, + "id": "34e83b50", + "metadata": { + "editable": true + }, "source": [ "Discuss these quantities as functions of the variable $\\lambda$ in the Ridge and Lasso regression methods." ] }, { "cell_type": "markdown", - "id": "c223eb1b", - "metadata": {}, + "id": "ea59251f", + "metadata": { + "editable": true + }, "source": [ "### Exercise: Linear Regression for a two-dimensional function\n", "\n", @@ -5554,8 +5500,10 @@ }, { "cell_type": "markdown", - "id": "45b1e7c9", - "metadata": {}, + "id": "e4450572", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -5567,8 +5515,10 @@ }, { "cell_type": "markdown", - "id": "425075fd", - "metadata": {}, + "id": "a137f836", + "metadata": { + "editable": true + }, "source": [ "The function will be defined for $x,y\\in [0,1]$. Our first step will\n", "be to perform an OLS regression analysis of this function, trying out\n", @@ -5585,8 +5535,11 @@ { "cell_type": "code", "execution_count": 33, - "id": "05e1fa34", - "metadata": {}, + "id": "b25ec6b4", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", @@ -5632,8 +5585,10 @@ }, { "cell_type": "markdown", - "id": "b1e5347d", - "metadata": {}, + "id": "c8665f13", + "metadata": { + "editable": true + }, "source": [ "We will generate our own dataset for a function\n", "$\\mathrm{FrankeFunction}(x,y)$ with $x,y \\in [0,1]$. The function\n", @@ -5650,8 +5605,10 @@ }, { "cell_type": "markdown", - "id": "f60027f0", - "metadata": {}, + "id": "5f0a0382", + "metadata": { + "editable": true + }, "source": [ "$$\n", "MSE(\\hat{y},\\hat{\\tilde{y}}) = \\frac{1}{n}\n", @@ -5661,8 +5618,10 @@ }, { "cell_type": "markdown", - "id": "0c95b9d2", - "metadata": {}, + "id": "2c1525e9", + "metadata": { + "editable": true + }, "source": [ "and the $R^2$ score function. If $\\tilde{\\hat{y}}_i$ is the predicted\n", "value of the $i-th$ sample and $y_i$ is the corresponding true value,\n", @@ -5671,8 +5630,10 @@ }, { "cell_type": "markdown", - "id": "baf15958", - "metadata": {}, + "id": "e672995a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "R^2(\\hat{y}, \\tilde{\\hat{y}}) = 1 - \\frac{\\sum_{i=0}^{n - 1} (y_i - \\tilde{y}_i)^2}{\\sum_{i=0}^{n - 1} (y_i - \\bar{y})^2},\n", @@ -5681,16 +5642,20 @@ }, { "cell_type": "markdown", - "id": "d7f9b2c0", - "metadata": {}, + "id": "74440d03", + "metadata": { + "editable": true + }, "source": [ "where we have defined the mean value of $\\hat{y}$ as" ] }, { "cell_type": "markdown", - "id": "93125b69", - "metadata": {}, + "id": "6a5e7573", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\bar{y} = \\frac{1}{n} \\sum_{i=0}^{n - 1} y_i.\n", @@ -5699,8 +5664,10 @@ }, { "cell_type": "markdown", - "id": "973a4d1a", - "metadata": {}, + "id": "f304109e", + "metadata": { + "editable": true + }, "source": [ "You should split your data in train and test and also consider scaling the data.\n", "\n", @@ -5710,8 +5677,11 @@ { "cell_type": "code", "execution_count": 34, - "id": "b173966c", - "metadata": {}, + "id": "e401828b", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "def FrankeFunction(x,y):\n", @@ -5750,8 +5720,10 @@ }, { "cell_type": "markdown", - "id": "59c6410f", - "metadata": {}, + "id": "813839cb", + "metadata": { + "editable": true + }, "source": [ "Write then your own code for the Ridge method or use **Scikit-Learn**.\n", "Perform the same analysis as you did for ordinary Least Squares (for the same polynomials) but now for different values of $\\lambda$. Compare and\n", @@ -5767,25 +5739,7 @@ ] } ], - "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": "3.9.7" - } - }, + "metadata": {}, "nbformat": 4, "nbformat_minor": 5 } diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt index 973434693..13f23d4b1 100644 --- a/doc/src/week35/week35.do.txt +++ b/doc/src/week35/week35.do.txt @@ -4,18 +4,16 @@ DATE: today !split -===== Plans for week 35, August 30 -September 3 ===== +===== Plans for week 35 ===== * Thursday: Review of ordinary Least Squares with applications and discussion of Ridge Regression and Singular Value Decomposition -* "Video of lecture Thursday":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember2.mp4?vrtx=view-as-webpage". * Friday: Analysis of Ridge and Lasso Regression and links with Singular Value Decomposition -* "Video of lecture Friday":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember3.mp4?vrtx=view-as-webpage" * "Video series on the SVD":"http://databookuw.com/page-2/page-4/". Highly recommended. !split -===== Thursday September 2 ===== +===== Thursday September 1 ===== The main topics on Thursday are: o Repetition from last week on linear regression @@ -1566,11 +1564,8 @@ example !split -===== Friday September 3 ===== +===== Friday September 2 ===== -"Video of Lecture from 2020":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureSeptember11.mp4?vrtx=view-as-webpage" and "handwritten notes":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesSeptember11.pdf" - -More material will be added here, see handwritten notes also. Note that this material will be cleaned up after the lecture of Friday September 3. See the handwritten notes from Friday's lecture at URL:"https://github.com/CompPhysics/MachineLearning/tree/master/doc/HandWrittenNotes/2021". !split