From 84e4aee102ae08e3581c1a81e7ab01960edbdb59 Mon Sep 17 00:00:00 2001 From: Andreaierardi Date: Sun, 12 Apr 2020 11:38:30 +0200 Subject: [PATCH] up --- .../Machine Learning/main.aux | 15 - .../Machine Learning/main.log | 1133 +++++++++++++++-- .../Machine Learning/main.pdf | Bin 0 -> 9915 bytes .../Machine Learning/main.synctex(busy) | Bin 0 -> 24576 bytes .../Machine Learning/main.tex | 114 +- 5 files changed, 1154 insertions(+), 108 deletions(-) create mode 100644 1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.pdf create mode 100644 1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.synctex(busy) diff --git a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.aux b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.aux index f9d19dd4d..e69de29bb 100644 --- a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.aux +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.aux @@ -1,15 +0,0 @@ -\relax -\@writefile{toc}{\contentsline {section}{\numberline {1}Lecture 1 - 09-03-2020}{1}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Introduction}{1}\protected@file@percent } -\@writefile{toc}{\contentsline {paragraph}{Outline}{3}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {2}Lecture 10 - 07-04-2020}{4}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}TO BE DEFINE}{4}\protected@file@percent } -\citation{Gil:02} -\bibstyle{abbrv} -\bibdata{main} -\@writefile{toc}{\contentsline {section}{\numberline {3}Previous work}{6}\protected@file@percent } -\newlabel{previous work}{{3}{6}} -\@writefile{toc}{\contentsline {section}{\numberline {4}Results}{6}\protected@file@percent } -\newlabel{results}{{4}{6}} -\@writefile{toc}{\contentsline {section}{\numberline {5}Conclusions}{6}\protected@file@percent } -\newlabel{conclusions}{{5}{6}} diff --git a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.log b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.log index e162cdb69..5fbcbe299 100644 --- a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.log +++ b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.log @@ -1,12 +1,12 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 2.9.7380 64-bit) (preloaded format=latex 2020.4.11) 11 APR 2020 23:48 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 2.9.7300 64-bit) (preloaded format=pdflatex 2020.4.12) 12 APR 2020 11:36 entering extended mode **./main.tex (main.tex -LaTeX2e <2020-02-02> patch level 5 -L3 programming layer <2020-04-06> -("C:\Program Files\MiKTeX 2.9\tex/latex/base\article.cls" +LaTeX2e <2020-02-02> patch level 2 +L3 programming layer <2020-02-14> +("E:\Program Files\MiKTeX 2.9\tex/latex/base\article.cls" Document Class: article 2019/12/20 v1.4l Standard LaTeX document class -("C:\Program Files\MiKTeX 2.9\tex/latex/base\size12.clo" +("E:\Program Files\MiKTeX 2.9\tex/latex/base\size12.clo" File: size12.clo 2019/12/20 v1.4l Standard LaTeX file (size option) ) \c@part=\count167 @@ -21,24 +21,24 @@ File: size12.clo 2019/12/20 v1.4l Standard LaTeX file (size option) \belowcaptionskip=\skip48 \bibindent=\dimen134 ) -("C:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amsmath.sty" +("E:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amsmath.sty" Package: amsmath 2020/01/20 v2.17e AMS math features \@mathmargin=\skip49 For additional information on amsmath, use the `?' option. -("C:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amstext.sty" +("E:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amstext.sty" Package: amstext 2000/06/29 v2.01 AMS text -("C:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amsgen.sty" +("E:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amsgen.sty" File: amsgen.sty 1999/11/30 v2.0 generic functions -\@emptytoks=\toks15 +\@emptytoks=\toks14 \ex@=\dimen135 )) -("C:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amsbsy.sty" +("E:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amsbsy.sty" Package: amsbsy 1999/11/29 v1.2d Bold Symbols \pmbraise@=\dimen136 ) -("C:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amsopn.sty" +("E:\Program Files\MiKTeX 2.9\tex/latex/amsmath\amsopn.sty" Package: amsopn 2016/03/08 v2.02 operator names ) \inf@bad=\count175 @@ -61,43 +61,43 @@ LaTeX Font Info: Redeclaring font encoding OMS on input line 734. \dotsspace@=\muskip16 \c@parentequation=\count182 \dspbrk@lvl=\count183 -\tag@help=\toks16 +\tag@help=\toks15 \row@=\count184 \column@=\count185 \maxfields@=\count186 -\andhelp@=\toks17 +\andhelp@=\toks16 \eqnshift@=\dimen138 \alignsep@=\dimen139 \tagshift@=\dimen140 \tagwidth@=\dimen141 \totwidth@=\dimen142 \lineht@=\dimen143 -\@envbody=\toks18 +\@envbody=\toks17 \multlinegap=\skip50 \multlinetaggap=\skip51 -\mathdisplay@stack=\toks19 +\mathdisplay@stack=\toks18 LaTeX Info: Redefining \[ on input line 2859. LaTeX Info: Redefining \] on input line 2860. ) -("C:\Program Files\MiKTeX 2.9\tex/latex/systeme\systeme.sty" -("C:\Program Files\MiKTeX 2.9\tex/latex/xstring\xstring.sty" -("C:\Program Files\MiKTeX 2.9\tex/generic/xstring\xstring.tex" +("E:\Program Files\MiKTeX 2.9\tex/latex/systeme\systeme.sty" +("E:\Program Files\MiKTeX 2.9\tex/latex/xstring\xstring.sty" +("E:\Program Files\MiKTeX 2.9\tex/generic/xstring\xstring.tex" \integerpart=\count187 \decimalpart=\count188 ) Package: xstring 2019/02/06 v1.83 String manipulations (CT) ) -("C:\Program Files\MiKTeX 2.9\tex/generic/systeme\systeme.tex" -\SYS_systemecode=\toks20 -\SYS_systempreamble=\toks21 +("E:\Program Files\MiKTeX 2.9\tex/generic/systeme\systeme.tex" +\SYS_systemecode=\toks19 +\SYS_systempreamble=\toks20 \SYSeqnum=\count189 ) Package: systeme 2019/01/13 v0.32 Mise en forme de systemes d'equations (CT) ) -("C:\Program Files\MiKTeX 2.9\tex/latex/amsfonts\amssymb.sty" +("E:\Program Files\MiKTeX 2.9\tex/latex/amsfonts\amssymb.sty" Package: amssymb 2013/01/14 v3.01 AMS font symbols -("C:\Program Files\MiKTeX 2.9\tex/latex/amsfonts\amsfonts.sty" +("E:\Program Files\MiKTeX 2.9\tex/latex/amsfonts\amsfonts.sty" Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 @@ -105,15 +105,10 @@ LaTeX Font Info: Redeclaring math symbol \hbar on input line 98. LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 106. )) -("C:\Program Files\MiKTeX 2.9\tex/latex/l3backend\l3backend-dvips.def" -File: l3backend-dvips.def 2020-03-12 L3 backend support: dvips +("E:\Program Files\MiKTeX 2.9\tex/latex/l3backend\l3backend-pdfmode.def" +File: l3backend-pdfmode.def 2020-02-03 L3 backend support: PDF mode +\l__kernel_color_stack_int=\count190 \l__pdf_internal_box=\box47 -\g__pdf_backend_object_int=\count190 -\l__pdf_backend_content_box=\box48 -\l__pdf_backend_model_box=\box49 -\g__pdf_backend_annotation_int=\count191 -\g__pdf_backend_link_int=\count192 -\g__pdf_backend_link_sf_int=\count193 ) (main.aux) \openout1 = `main.aux'. @@ -134,13 +129,13 @@ LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 16. LaTeX Font Info: ... okay on input line 16. LaTeX Font Info: Trying to load font information for U+msa on input line 17. - ("C:\Program Files\MiKTeX 2.9\tex/latex/amsfonts\umsa.fd" + ("E:\Program Files\MiKTeX 2.9\tex/latex/amsfonts\umsa.fd" File: umsa.fd 2013/01/14 v3.01 AMS symbols A ) LaTeX Font Info: Trying to load font information for U+msb on input line 17. -("C:\Program Files\MiKTeX 2.9\tex/latex/amsfonts\umsb.fd" +("E:\Program Files\MiKTeX 2.9\tex/latex/amsfonts\umsb.fd" File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) Underfull \hbox (badness 10000) in paragraph at lines 29--116 @@ -154,111 +149,1067 @@ Underfull \hbox (badness 10000) in paragraph at lines 29--116 [1 -] [2] -Underfull \hbox (badness 10000) in paragraph at lines 119--157 +{C:/Users/AndreDany/AppData/Local/MiKTeX/2.9/pdftex/config/pdftex.map}] +[2] +Underfull \hbox (badness 10000) in paragraph at lines 119--158 [] -Underfull \hbox (badness 10000) in paragraph at lines 119--157 +Underfull \hbox (badness 10000) in paragraph at lines 119--158 [] -Underfull \hbox (badness 10000) in paragraph at lines 119--157 +Underfull \hbox (badness 10000) in paragraph at lines 119--158 [] -LaTeX Font Warning: Command \small invalid in math mode on input line 172. +LaTeX Warning: Reference `previous work' on page 3 undefined on input line 162. -Underfull \hbox (badness 10000) in paragraph at lines 170--187 - [] +LaTeX Warning: Reference `results' on page 3 undefined on input line 163. -Underfull \hbox (badness 10000) in paragraph at lines 170--187 +LaTeX Warning: Reference `conclusions' on page 3 undefined on input line 164. + + +Underfull \hbox (badness 10000) in paragraph at lines 170--179 [] [3] -Underfull \hbox (badness 10000) in paragraph at lines 188--190 +Underfull \hbox (badness 10000) in paragraph at lines 180--193 [] -Underfull \hbox (badness 10000) in paragraph at lines 188--190 +Underfull \hbox (badness 10000) in paragraph at lines 180--193 [] -Underfull \hbox (badness 10000) in paragraph at lines 191--197 +Underfull \hbox (badness 10000) in paragraph at lines 195--198 [] [4] -Underfull \hbox (badness 10000) in paragraph at lines 200--213 +Underfull \hbox (badness 10000) in paragraph at lines 212--215 [] -Underfull \hbox (badness 10000) in paragraph at lines 200--213 +Underfull \hbox (badness 10000) in paragraph at lines 212--215 [] -Underfull \hbox (badness 10000) in paragraph at lines 215--217 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 215--217 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 218--224 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 226--259 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 226--259 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 226--259 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 226--259 +Underfull \hbox (badness 10000) in paragraph at lines 226--244 [] [5] +Underfull \hbox (badness 10000) in paragraph at lines 244--249 -LaTeX Warning: Citation `Gil:02' on page 6 undefined on input line 261. + [] -No file main.bbl. -[6] (main.aux) +Runaway argument? +{\hat {y}, & \mbox {if } y = 1 \textit {(rain)} \\ ln \frac {1}{1-\hat \ETC. +! Paragraph ended before \@genfrac was complete. + + \par +l.262 + +I suspect you've forgotten a `}', causing me to apply this +control sequence to too much text. How can we recover? +My plan is to forget the whole thing and hope for the best. -LaTeX Warning: There were undefined references. +! Undefined control sequence. +l.264 \lim_{\hat{y}\to\0 + ^+} \ell(1,\hat{y}) = + \inf +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. - ) -Here is how much of TeX's memory you used: - 1950 strings out of 480934 - 25924 string characters out of 2909674 - 271852 words of memory out of 3000000 - 17841 multiletter control sequences out of 15000+200000 - 542046 words of font info for 61 fonts, out of 3000000 for 9000 - 1141 hyphenation exceptions out of 8191 - 30i,9n,31p,268b,200s stack positions out of 5000i,500n,10000p,200000b,50000s -Output written on main.dvi (6 pages, 14028 bytes). +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.268 \section + {Lecture 3 - 07-04-2020} +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.268 \section + {Lecture 3 - 07-04-2020} +Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing } inserted. + + } +l.268 \section{Lecture 3 - 07-04-2020} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing \cr inserted. + + \cr +l.268 \section{Lecture 3 - 07-04-2020} + +I'm guessing that you meant to end an alignment here. + +! Missing $ inserted. + + $ +l.268 \section{Lecture 3 - 07-04-2020} + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.281 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.281 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +LaTeX Font Warning: Command \small invalid in math mode on input line 282. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.284 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.284 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.287 \\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.288 $\mathbb{P}(Y_{\Pi(s,x)} = 1) = \\\\ + \mathbb{E}[\Pi { Y_{\Pi(s,x)} = 1... +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.288 $\mathbb{P}(Y_{\Pi(s,x)} = 1) = \\\\ + \mathbb{E}[\Pi { Y_{\Pi(s,x)} = 1... +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.288 ...thbb{E}[\Pi { Y_{\Pi(s,x)} = 1 } ] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.288 ...thbb{E}[\Pi { Y_{\Pi(s,x)} = 1 } ] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.289 ..._t = 1\} \cdot \Pi { Pi(s,x) = t}] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.289 ..._t = 1\} \cdot \Pi { Pi(s,x) = t}] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.290 ... \cdot \Pi\{\Pi(s,x) = t\} | X_t]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.290 ... \cdot \Pi\{\Pi(s,x) = t\} | X_t]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.291 ...a(X_t) \Rightarrow give me probability \\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.292 ...mathbb{E}[x] \ast \cdot \mathbb{E}[z]\\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.292 ...mathbb{E}[x] \ast \cdot \mathbb{E}[z]\\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.293 ...ot \barra{E} [ \Pi(s,x) = t | Xt]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.293 ...ot \barra{E} [ \Pi(s,x) = t | Xt]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.294 ...cdot \Pi \cdot \{\Pi (s,x) = t \}] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.294 ...cdot \Pi \cdot \{\Pi (s,x) = t \}] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +Overfull \hbox (71.26564pt too wide) in paragraph at lines 280--298 +$\OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 E\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 z\OT1/cm +r/m/n/12 ] = \OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 E\OT1/cmr/m/n/12 [\OMS/cmsy/m/n +/12 j\OML/cmm/m/it/12 E\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 z\OMS/cmsy/m/n/12 j\OM +L/cmm/m/it/12 x\OT1/cmr/m/n/12 ]]$ $[]$$[]$ $\OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 + E\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 X\OT1/cmr/m/n/12 ] = [][] \OMS/cmsy/m/n/12 +j\OML/cmm/m/it/12 E\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 (\OML/cm +m/m/it/12 At\OT1/cmr/m/n/12 )]$ $[]$$[]$ $\OML/cmm/m/it/12 x \OMS/cmsy/m/n/12 2 + \U/msb/m/n/12 R[]$ $[]$ $P\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 Y[] \OT1/cmr/m/n/1 +2 = 1) =$$[]$$[]\U/msb/m/n/12 E\OT1/cmr/m/n/12 [[]] =$$[]$$[] = + [] + + +Overfull \hbox (10.78996pt too wide) in paragraph at lines 280--298 +\OML/cmm/m/it/12 t\OMS/cmsy/m/n/12 gj\OML/cmm/m/it/12 X[]\OT1/cmr/m/n/12 ]] =$$ +[]$$[]\OML/cmm/m/it/12 giventhefactthatY[] \OMS/cmsy/m/n/12  \OML/cmm/m/it/12 +\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 X[]\OT1/cmr/m/n/12 ) \OMS/cmsy/m/n/12 ) \OML +/cmm/m/it/12 givemeprobability$$[]Y[] \OT1/cmr/m/n/12 = 1\OML/cmm/m/it/12 and\O +T1/cmr/m/n/12 (\OML/cmm/m/it/12 s; x\OT1/cmr/m/n/12 ) = + [] + + +Overfull \hbox (4.04996pt too wide) in paragraph at lines 280--298 +\OML/cmm/m/it/12 tareindependentgivenX[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 e:g:\ +U/msb/m/n/12 E\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 Zx\OT1/cmr/m/n/12 ] = \U/msb/m/ +n/12 E\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ] \OMS/cmsy/m/n/12   +\U/msb/m/n/12 E\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 z\OT1/cmr/m/n/12 ]$$[]$$[] = [ +][] \U/msb/m/n/12 E\OT1/cmr/m/n/12 [\U/msb/m/n/12 E\OT1/cmr/m/n/12 [\OMS/cmsy/ +m/n/12 f\OML/cmm/m/it/12 Y[] \OT1/cmr/m/n/12 = 1\OMS/cmsy/m/n/12 gj\OML/cmm/m/i +t/12 X[]\OT1/cmr/m/n/12 ] \OMS/cmsy/m/n/12  + [] + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.299 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.299 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.302 \barra{P} (Y_{\Pi(s,x)} = 1, y = -1 ) = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.302 \barra{P} (Y_{\Pi(s,x)} = 1, y = -1 ) = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.303 ...x) }= 1\} \dot \Pi\{Y= -1|X\} ]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.303 ...x) }= 1\} \dot \Pi\{Y= -1|X\} ]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.304 ...x)} = 1\} \cdot \Pi \{ y = -1 \} ] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.304 ...x)} = 1\} \cdot \Pi \{ y = -1 \} ] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.305 ... 1\} \cdot \Pi \{ y = -1 | X \} ]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.305 ... 1\} \cdot \Pi \{ y = -1 | X \} ]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.311 \\\\ + = \barra{E}[\barra{E}[\Pi \{Y_\Pi(s,x)\} = 1 | X] \cdot \barra{E}... +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.311 \\\\ + = \barra{E}[\barra{E}[\Pi \{Y_\Pi(s,x)\} = 1 | X] \cdot \barra{E}... +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.311 ...dot \barra{E}[\Pi \{y = -1\} |X ]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.311 ...dot \barra{E}[\Pi \{y = -1\} |X ]] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.312 ...\eta_{\Pi(s,x)} \cdot (1-\eta(x))] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.312 ...\eta_{\Pi(s,x)} \cdot (1-\eta(x))] = \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.313 ...barra{P}(Y_{\Pi(s,x)} = -1 , y = 1) = \\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.315 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.315 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.317 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.317 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.319 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.319 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.321 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.321 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.322 ...mptions on $D_x \quad and \quad \eta$: \\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.326 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.326 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.330 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.330 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.332 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.332 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.338 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.338 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.340 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.340 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.342 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.342 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.343 ...ta(x) \cdot (1- \eta(x)) + c||X-x'|| \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.343 ...ta(x) \cdot (1- \eta(x)) + c||X-x'|| \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.346 \\ + where $<=$ mean at most +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.347 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.347 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.349 \\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.352 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.352 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.354 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.354 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.356 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.356 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.358 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.358 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.361 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.361 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.363 \\\\ + --DISEGNO-- +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.363 \\\\- + -DISEGNO-- +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.364 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.364 \\\\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced \cr. +\reserved@b ->\ifnum 0=`{\fi }${}\cr + +l.367 \\ + +I can't figure out why you would want to use a tab mark +or \cr or \span just now. If something like a right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.370 \section + {Previous work}\label{previous work} +Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Something's wrong--perhaps a missing \item. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.370 \section + {Previous work}\label{previous work} +Try typing to proceed. +If that doesn' \ No newline at end of file diff --git a/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.pdf b/1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0a7928432161dc13f78eaf3578ff47080b997ad6 GIT binary patch literal 9915 zcmbuEV{~R+x~`LoZR<@cPAYcAwr#yZ#WpIoZQEwWwpp=lCw1!U?r-m}NB0@0_dfI2 zGuB#jK4bm4?`z%gc_edw-KEm1G}JC7xf=6%y2Z9DBt z`jVVuqoc*Vtz`AO*qFYbjYLE|L0b@omPth~1GI}x8=#gj(xFUpUQqS2vcs{oKG}Fk z%x@1*4EmO;TTu`iPP*MkbcP+Zkz8dhg<2+UycSlv1YB}%pG6oK4C9bd)<@ZUUu;Vz 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zO-@Tqx|dY=T5J;Y^}Q?TVhOFQ4h386VpQG5w>S4>3xub0t*Q}nJW)GeJ{nQ9$4RTq z8G@Sc*DRuOzUvkdQ)HzrBGUG(E)cu`e|+?BH;lPo&c1a9o3I0e15jMUvk@C z@|ywZ=YDx6zxrkNNj!lL`p2Veoo;LBWpB_&zf|ijy(#gcU(&lnnew^&8zdYQ%C{j&41cQjR})4!TpRCO0KQU)wuAObdXG(6R<<+)LNRO9Mp-Pba=qP@1W)42iV>h3 zOE@ykNDQkb-d9fs+qL`qVE(F{T;T91;5pJKnYLkCs9YXjjdaX7MLbC!$>pP?3{^bS z^_%|lN$;-Lnf~#hiycj}={pa67wP5xV^06u4gJeCeLs^harK0-ysTYxE} zcNcn-m7PjNj)eB~vz)I-C254ht2EOp@|K?g5p}bO-AeJ*BKXuT_i7r=aeB%7bd@!IBlp-z@Plh!8>^OWhAKe#V4NrCr zA5hcuJOk%B;ftonY~x}RnEA~tj; vBX+=WxDZ ..\\ +Binary classification\\ +Label space is Y = { -1, +1 }\\ +Zero-one loss\\ + +$ +\ell(y,\hat{y} = \begin{cases} 0, & \mbox{if } \hat{y} = y +\\ 1, & +\mbox{if }\hat{y} \neq y +\end{cases} +\\\\ +FP \quad \hat{y} = 1,\quad y = -1\\ +FN \quad \hat{y} = -1, \quad y = 1 +$ +\\\\ +Losses for regression?\\ +$y$, and $\hat{y} \in \barra{R}$, \\so they are numbers!\\ +One example of loss is the absolute loss: absolute difference between numbers\\ +\subsection{Loss} +\subsubsection{Absolute Loss} +$$\ell(y,\hat{y} = | y - \hat{y} | \Rightarrow absolute \quad loss\\ $$ +--- DISEGNO ---\\\\ +Some inconvenient properties: + +\begin{itemize} +\item ... +\item Derivative only two values (not much informations) +\end{itemize} + +\subsubsection{Square Loss} +$$ \ell(y,\hat{y} = ( y - \hat{y} )^2 \Rightarrow \textit{square loss}\\$$ +-- DISEGNO ---\\ +Derivative : +\begin{itemize} +\item more informative +\item and differentible +\end{itemize} +Real numbers as label $\rightarrow$ regression.\\ +Whenever taking difference between two prediction make sense (value are numbers) then we are talking about regression problem.\\ +Classification as categorization when we have small finite set.\\\\ + +\subsubsection{Example of information of square loss} + +$\ell(y,\hat{y}) = ( y - \hat{y} )^2 = F(y) +\\ +F'(\hat(y)) = -2 \cdot (y-\hat{y}) +$ +\begin{itemize} +\item I'm under sho or over and how much +\item How much far away from the truth +\end{itemize} +$ \ell(y,\hat{y}) = | y- \hat{y}| = F(y') \cdot F'(y) = Sign (y-\hat{y} )\\\\ $ +Question about the future\\ +Will it rain tomorrow?\\ +We have a label and this is a binary classification problem.\\ +My label space will be Y = { “rain”, “no rain” }\\ +We don’t get a binary prediction, we need another space called prediction space (or decision space). Z = [0,1]\\ +$ +Z = [0,1] +\hat{y} \in Z \qquad \hat{y} \textit{ is my prediction of rain tomorrow} +\\ +\hat{y} = \barra{P} (y = "rain") \quad \rightarrow \textit{my guess is tomorrow will rain (not sure)}\\\\ +y \in Y \qquad \hat{y} \in Z \\quad \textit{How can we manage loss?} +\\ +\textit{Put numbers in our space}\\ +\{1,0\} \quad \textit{where 1 is rain and 0 no rain}\\\\ +$ +I measure how much I’m far from reality.\\ +So loss behave like this and the punishment is gonna go linearly??\\ +\[26..\]\\ +However is pretty annoying. Sometime I prefer to punish more so i going quadratically instead of linearly.\\ +There are other way to punish this.\\ +I called \textbf{logarithmic loss}\\ +We are extending a lot the range of our loss function.\\ + +$$ +\ell(y,\hat{y}) = | y- \hat{y}| \in |0,1| \qquad \ell(y,\hat{y}) = ( y- \hat{y})^2 \in |0,1| +$$ +\\ +If i want to expand the punishment i use logarithmic loss\\ +\\ +$ \ell(y,\hat{y} = \begin{cases} ln \dfrac{1}{\hat{y}, & \mbox{if } y = 1 \textit{(rain)} +\\ ln \frac{1}{1-\hat{y}}, & +\mbox{if } y = 0 \textit{(no rain} +\end{cases} +\\\\ +F(\hat{y}) \rightarrow can be 0 if i predict with certainty + +\mbox{if} \hat{y} = 0.5 \qquad \ell(y, \dfrac{1}{2}) = ln 2 \quad \textit{costnat losses in each prediction}\\\\ +\lim_{\hat{y}\to\0^+} \ell(1,\hat{y}) = + \inf + +$ + +\section{Lecture 3 - 07-04-2020} +\section{Lecture 4 - 07-04-2020} +\section{Lecture 5 - 07-04-2020} +\section{Lecture 6 - 07-04-2020} +\section{Lecture 7 - 07-04-2020} +\section{Lecture 8 - 07-04-2020} +\section{Lecture 9 - 07-04-2020} + \section{Lecture 10 - 07-04-2020} \subsection{TO BE DEFINE}