notes.lyx 13 KB

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  60. \pdf_title "Notes for \"An Introduction to Statistical Learning\""
  61. \pdf_author "Zelphir Kaltstahl"
  62. \pdf_subject "statistical learning"
  63. \pdf_keywords "statistical learning"
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  95. \index Index
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  122. \end_header
  123. \begin_body
  124. \begin_layout Title
  125. Notes for
  126. \begin_inset Quotes eld
  127. \end_inset
  128. An Introduction to Statistical Learning
  129. \begin_inset Quotes erd
  130. \end_inset
  131. \end_layout
  132. \begin_layout Standard
  133. \begin_inset CommandInset toc
  134. LatexCommand tableofcontents
  135. \end_inset
  136. \begin_inset Newpage pagebreak
  137. \end_inset
  138. \end_layout
  139. \begin_layout Section
  140. macros (ignore this section in PDF)
  141. \end_layout
  142. \begin_layout Itemize
  143. bold math symbol:
  144. \begin_inset FormulaMacro
  145. \newcommand{\mathbold}[1]{\bm{{#1}}}
  146. {\bm{#1}}
  147. \end_inset
  148. \end_layout
  149. \begin_layout Itemize
  150. big parentheses wrapping an expression:
  151. \begin_inset FormulaMacro
  152. \newcommand{\paren}[1]{\left(#1\right)}
  153. {\left(#1\right)}
  154. \end_inset
  155. \end_layout
  156. \begin_layout Itemize
  157. \begin_inset Formula $\paren{\frac{\frac{1}{2}}{3}}$
  158. \end_inset
  159. \end_layout
  160. \begin_layout Section
  161. Definitions
  162. \end_layout
  163. \begin_layout Description
  164. Supervised
  165. \begin_inset space \space{}
  166. \end_inset
  167. Learning analyzing an input to output relationship to make predictions or
  168. estimations about future outputs
  169. \end_layout
  170. \begin_layout Description
  171. Unsupervised
  172. \begin_inset space \space{}
  173. \end_inset
  174. Learning learn structures and relationships from data
  175. \end_layout
  176. \begin_layout Description
  177. Regression prediction of continuous or quantitative values
  178. \end_layout
  179. \begin_layout Description
  180. Classification prediction of categorical or qualitative values
  181. \end_layout
  182. \begin_layout Description
  183. Clustering grouping input data points, without predicting an output value
  184. \end_layout
  185. \begin_layout Description
  186. Principal
  187. \begin_inset space \space{}
  188. \end_inset
  189. component todo
  190. \end_layout
  191. \begin_layout Description
  192. Dimension todo
  193. \end_layout
  194. \begin_layout Description
  195. Observation (see data point)
  196. \end_layout
  197. \begin_layout Description
  198. Input
  199. \begin_inset space \space{}
  200. \end_inset
  201. variable one attribute of a data set
  202. \end_layout
  203. \begin_layout Description
  204. Data
  205. \begin_inset space \space{}
  206. \end_inset
  207. point tuple of all input variables
  208. \end_layout
  209. \begin_layout Section
  210. Mathematical notation of the book
  211. \end_layout
  212. \begin_layout Itemize
  213. \begin_inset Formula $n$
  214. \end_inset
  215. : number of (distinct) data points
  216. \end_layout
  217. \begin_layout Itemize
  218. \begin_inset Formula $p$
  219. \end_inset
  220. : number of input variables
  221. \end_layout
  222. \begin_layout Itemize
  223. \begin_inset Formula $x_{ij}$
  224. \end_inset
  225. : row-major interpretation: select from the data set
  226. \begin_inset Formula $\mathbold X$
  227. \end_inset
  228. the
  229. \begin_inset Formula $i$
  230. \end_inset
  231. -th data point,
  232. \begin_inset Formula $j$
  233. \end_inset
  234. -th variable, indexing starting at
  235. \begin_inset Formula $1$
  236. \end_inset
  237. \end_layout
  238. \begin_layout Itemize
  239. \begin_inset Formula $x_{i}$
  240. \end_inset
  241. : select from the data set
  242. \begin_inset Formula $\mathbold X$
  243. \end_inset
  244. the
  245. \begin_inset Formula $i$
  246. \end_inset
  247. -th data point, which will be a vector:
  248. \begin_inset Formula $x_{i}=\paren{\begin{array}{c}
  249. x_{i1}\\
  250. x_{i2}\\
  251. \vdots\\
  252. x_{ip}
  253. \end{array}}$
  254. \end_inset
  255. \end_layout
  256. \begin_layout Itemize
  257. \begin_inset Formula $\mathbold{x_{j}}$
  258. \end_inset
  259. : (note the bold in contrast to
  260. \begin_inset Formula $x_{i}$
  261. \end_inset
  262. !) column
  263. \begin_inset Formula $j$
  264. \end_inset
  265. of data set
  266. \begin_inset Formula $\mathbold X$
  267. \end_inset
  268. \end_layout
  269. \begin_layout Itemize
  270. \begin_inset Formula $x^{T}$
  271. \end_inset
  272. : transpose
  273. \begin_inset Formula $x$
  274. \end_inset
  275. \end_layout
  276. \begin_layout Itemize
  277. \begin_inset Formula $\mathbold X$
  278. \end_inset
  279. : matrix of
  280. \begin_inset Formula $n$
  281. \end_inset
  282. rows and
  283. \begin_inset Formula $p$
  284. \end_inset
  285. columns:
  286. \begin_inset Formula
  287. \begin{align*}
  288. \mathbold{X=\paren{\begin{array}{cccc}
  289. x_{11} & x_{12} & \dots & x_{1p}\\
  290. x_{21} & x_{22} & \dots & x_{2p}\\
  291. \vdots & \vdots & \ddots & \vdots\\
  292. x_{n1} & x_{n2} & \dots & x_{np}
  293. \end{array}}} & =(\mathbold{x_{1}},\mathbold{x_{2}},\dots,\mathbold{x_{p}})=\begin{pmatrix}x_{1}^{T}\\
  294. x_{2}^{T}\\
  295. \vdots\\
  296. x_{n}^{T}
  297. \end{pmatrix}
  298. \end{align*}
  299. \end_inset
  300. \end_layout
  301. \begin_layout Section
  302. Formulas and so on
  303. \end_layout
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