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update week 11
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‎doc/pub/week11/ipynb/ipynb-week11-src.tar.gz‎

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‎doc/pub/week11/ipynb/week11.ipynb‎

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‎doc/pub/week11/pdf/week11.pdf‎

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‎doc/src/week11/_minted/2F94C7C8030AA1854BB403778B0F2084.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{c+c1}{\PYGZsh{} Set up the conditional probability distribution for each dimension}
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\PYG{c+c1}{\PYGZsh{} For example, I can sample p(a | b) using sample\PYGZus{}for\PYGZus{}dim[0].}
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\PYG{n}{univariate\PYGZus{}conditionals} \PYG{o}{=} \PYG{p}{[}
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\PYG{n}{get\PYGZus{}conditional\PYGZus{}dist}\PYG{p}{(}\PYG{n}{joint\PYGZus{}mu}\PYG{p}{,} \PYG{n}{joint\PYGZus{}cov}\PYG{p}{,} \PYG{n}{d}\PYG{p}{)}
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\PYG{k}{for} \PYG{n}{d} \PYG{o+ow}{in} \PYG{n+nb}{range}\PYG{p}{(}\PYG{n}{D}\PYG{p}{)}
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\PYG{p}{]}
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\end{MintedVerbatim}

‎doc/src/week11/_minted/43267A0395131F82B3FEF654B556A0B9.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{get\PYGZus{}conditional\PYGZus{}dist}\PYG{p}{(}\PYG{n}{joint\PYGZus{}mu}\PYG{p}{,} \PYG{n}{joint\PYGZus{}cov}\PYG{p}{,} \PYG{n}{var\PYGZus{}index}\PYG{p}{)}\PYG{p}{:}
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\PYG{+w}{ }\PYG{l+s+sd}{\PYGZsq{}\PYGZsq{}\PYGZsq{}Returns the conditional distribution given the joint distribution and which variable}
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\PYG{l+s+sd}{ the conditional probability should use.}
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\PYG{l+s+sd}{ Right now this only works for 2\PYGZhy{}variable joint distributions.}
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\PYG{l+s+sd}{ joint\PYGZus{}mu: joint distribution\PYGZsq{}s mu}
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\PYG{l+s+sd}{ joint\PYGZus{}cov: joint distribution\PYGZsq{}s covariance}
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\PYG{l+s+sd}{ var\PYGZus{}index: index of the variable in the joint distribution. Everything else will be}
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\PYG{l+s+sd}{ conditioned on. For example, if the joint distribution p(a, b, c) has mu [mu\PYGZus{}a, mu\PYGZus{}b, mu\PYGZus{}c],}
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\PYG{l+s+sd}{ to get p(c | a, b), use var\PYGZus{}index = 2.}
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\PYG{l+s+sd}{ returns:}
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\PYG{l+s+sd}{ a function that can sample from the univariate conditional distribution}
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\PYG{l+s+sd}{ \PYGZsq{}\PYGZsq{}\PYGZsq{}}
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\PYG{k}{assert} \PYG{n}{joint\PYGZus{}mu}\PYG{o}{.}\PYG{n}{shape}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]} \PYG{o}{==} \PYG{l+m+mi}{2}\PYG{p}{,} \PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{Sorry, this function only works for 2\PYGZhy{}dimensional joint distributions right now}\PYG{l+s+s1}{\PYGZsq{}}
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\PYG{n}{a} \PYG{o}{=} \PYG{n}{joint\PYGZus{}mu}\PYG{p}{[}\PYG{n}{var\PYGZus{}index}\PYG{p}{]}
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\PYG{n}{b} \PYG{o}{=} \PYG{n}{joint\PYGZus{}mu}\PYG{p}{[}\PYG{o}{\PYGZti{}}\PYG{n}{var\PYGZus{}index}\PYG{p}{]}
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\PYG{n}{A} \PYG{o}{=} \PYG{n}{joint\PYGZus{}cov}\PYG{p}{[}\PYG{n}{var\PYGZus{}index}\PYG{p}{,} \PYG{n}{var\PYGZus{}index}\PYG{p}{]}
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\PYG{n}{B} \PYG{o}{=} \PYG{n}{joint\PYGZus{}cov}\PYG{p}{[}\PYG{o}{\PYGZti{}}\PYG{n}{var\PYGZus{}index}\PYG{p}{,} \PYG{o}{\PYGZti{}}\PYG{n}{var\PYGZus{}index}\PYG{p}{]}
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\PYG{n}{C} \PYG{o}{=} \PYG{n}{joint\PYGZus{}cov}\PYG{p}{[}\PYG{n}{var\PYGZus{}index}\PYG{p}{,} \PYG{o}{\PYGZti{}}\PYG{n}{var\PYGZus{}index}\PYG{p}{]}
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\PYG{c+c1}{\PYGZsh{} we\PYGZsq{}re dealing with one dimension so}
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\PYG{n}{B\PYGZus{}inv} \PYG{o}{=} \PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{B}
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\PYG{c+c1}{\PYGZsh{} Return a function that can sample given a value of g}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{dist}\PYG{p}{(}\PYG{n}{g}\PYG{p}{)}\PYG{p}{:}
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\PYG{c+c1}{\PYGZsh{} a + C*B\PYGZca{}\PYGZob{}\PYGZhy{}1\PYGZcb{}(g \PYGZhy{} b)}
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\PYG{n}{mu} \PYG{o}{=} \PYG{n}{a} \PYG{o}{+} \PYG{n}{C} \PYG{o}{*} \PYG{n}{B\PYGZus{}inv} \PYG{o}{*} \PYG{p}{(}\PYG{n}{g} \PYG{o}{\PYGZhy{}} \PYG{n}{b}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} A \PYGZhy{} C * B\PYGZca{}\PYGZob{}\PYGZhy{}1\PYGZcb{} * C\PYGZca{}T}
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\PYG{n}{cov} \PYG{o}{=} \PYG{n}{A} \PYG{o}{\PYGZhy{}} \PYG{n}{B\PYGZus{}inv} \PYG{o}{*} \PYG{n}{C} \PYG{o}{*} \PYG{n}{C}
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\PYG{k}{return} \PYG{n}{np}\PYG{o}{.}\PYG{n}{sqrt}\PYG{p}{(}\PYG{n}{cov}\PYG{p}{)} \PYG{o}{*} \PYG{n}{np}\PYG{o}{.}\PYG{n}{random}\PYG{o}{.}\PYG{n}{randn}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{p}{)} \PYG{o}{+} \PYG{n}{mu}
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\PYG{k}{return} \PYG{n}{dist}
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\end{MintedVerbatim}

‎doc/src/week11/_minted/6E30EEDCA6E4F0B63088422FCFB9AE8A.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{n}{N} \PYG{o}{=} \PYG{l+m+mi}{10000}
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\PYG{n}{L} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{linalg}\PYG{o}{.}\PYG{n}{cholesky}\PYG{p}{(}\PYG{n}{joint\PYGZus{}cov}\PYG{p}{)}
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\PYG{n}{samples\PYGZus{}from\PYGZus{}true\PYGZus{}distribution} \PYG{o}{=} \PYG{n}{L} \PYG{o}{@} \PYG{n}{np}\PYG{o}{.}\PYG{n}{random}\PYG{o}{.}\PYG{n}{randn}\PYG{p}{(}\PYG{n}{D}\PYG{p}{,} \PYG{n}{N}\PYG{p}{)} \PYG{o}{+} \PYG{n}{joint\PYGZus{}mu}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{o}{*}\PYG{n}{samples\PYGZus{}from\PYGZus{}true\PYGZus{}distribution}\PYG{p}{,} \PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{.}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{,} \PYG{n}{alpha}\PYG{o}{=}\PYG{l+m+mf}{0.1}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{axis}\PYG{p}{(}\PYG{p}{[}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{4}\PYG{p}{,} \PYG{l+m+mi}{4}\PYG{p}{,} \PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{4}\PYG{p}{,} \PYG{l+m+mi}{4}\PYG{p}{]}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{show}\PYG{p}{(}\PYG{p}{)}
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\end{MintedVerbatim}

‎doc/src/week11/_minted/791C9439E969965404265CEA26262C75.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{numpy}\PYG{+w}{ }\PYG{k}{as}\PYG{+w}{ }\PYG{n+nn}{np}
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{torch}
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{torch}\PYG{n+nn}{.}\PYG{n+nn}{utils}\PYG{n+nn}{.}\PYG{n+nn}{data}
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{torch}\PYG{n+nn}{.}\PYG{n+nn}{nn}\PYG{+w}{ }\PYG{k}{as}\PYG{+w}{ }\PYG{n+nn}{nn}
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{torch}\PYG{n+nn}{.}\PYG{n+nn}{nn}\PYG{n+nn}{.}\PYG{n+nn}{functional}\PYG{+w}{ }\PYG{k}{as}\PYG{+w}{ }\PYG{n+nn}{F}
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{torch}\PYG{n+nn}{.}\PYG{n+nn}{optim}\PYG{+w}{ }\PYG{k}{as}\PYG{+w}{ }\PYG{n+nn}{optim}
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\PYG{k+kn}{from}\PYG{+w}{ }\PYG{n+nn}{torch}\PYG{n+nn}{.}\PYG{n+nn}{autograd}\PYG{+w}{ }\PYG{k+kn}{import} \PYG{n}{Variable}
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\PYG{k+kn}{from}\PYG{+w}{ }\PYG{n+nn}{torchvision}\PYG{+w}{ }\PYG{k+kn}{import} \PYG{n}{datasets}\PYG{p}{,} \PYG{n}{transforms}
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\PYG{k+kn}{from}\PYG{+w}{ }\PYG{n+nn}{torchvision}\PYG{n+nn}{.}\PYG{n+nn}{utils}\PYG{+w}{ }\PYG{k+kn}{import} \PYG{n}{make\PYGZus{}grid} \PYG{p}{,} \PYG{n}{save\PYGZus{}image}
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{matplotlib}\PYG{n+nn}{.}\PYG{n+nn}{pyplot}\PYG{+w}{ }\PYG{k}{as}\PYG{+w}{ }\PYG{n+nn}{plt}
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\PYG{n}{batch\PYGZus{}size} \PYG{o}{=} \PYG{l+m+mi}{64}
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\PYG{n}{train\PYGZus{}loader} \PYG{o}{=} \PYG{n}{torch}\PYG{o}{.}\PYG{n}{utils}\PYG{o}{.}\PYG{n}{data}\PYG{o}{.}\PYG{n}{DataLoader}\PYG{p}{(}
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\PYG{n}{datasets}\PYG{o}{.}\PYG{n}{MNIST}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{./data}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{,}
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\PYG{n}{train}\PYG{o}{=}\PYG{k+kc}{True}\PYG{p}{,}
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\PYG{n}{download} \PYG{o}{=} \PYG{k+kc}{True}\PYG{p}{,}
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\PYG{n}{transform} \PYG{o}{=} \PYG{n}{transforms}\PYG{o}{.}\PYG{n}{Compose}\PYG{p}{(}
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\PYG{p}{[}\PYG{n}{transforms}\PYG{o}{.}\PYG{n}{ToTensor}\PYG{p}{(}\PYG{p}{)}\PYG{p}{]}\PYG{p}{)}
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\PYG{p}{)}\PYG{p}{,}
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\PYG{n}{batch\PYGZus{}size}\PYG{o}{=}\PYG{n}{batch\PYGZus{}size}
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\PYG{p}{)}
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\PYG{n}{test\PYGZus{}loader} \PYG{o}{=} \PYG{n}{torch}\PYG{o}{.}\PYG{n}{utils}\PYG{o}{.}\PYG{n}{data}\PYG{o}{.}\PYG{n}{DataLoader}\PYG{p}{(}
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\PYG{n}{datasets}\PYG{o}{.}\PYG{n}{MNIST}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{./data}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{,}
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\PYG{n}{train}\PYG{o}{=}\PYG{k+kc}{False}\PYG{p}{,}
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\PYG{n}{transform}\PYG{o}{=}\PYG{n}{transforms}\PYG{o}{.}\PYG{n}{Compose}\PYG{p}{(}
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\PYG{p}{[}\PYG{n}{transforms}\PYG{o}{.}\PYG{n}{ToTensor}\PYG{p}{(}\PYG{p}{)}\PYG{p}{]}\PYG{p}{)}
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\PYG{p}{)}\PYG{p}{,}
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\PYG{n}{batch\PYGZus{}size}\PYG{o}{=}\PYG{n}{batch\PYGZus{}size}\PYG{p}{)}
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\PYG{k}{class}\PYG{+w}{ }\PYG{n+nc}{RBM}\PYG{p}{(}\PYG{n}{nn}\PYG{o}{.}\PYG{n}{Module}\PYG{p}{)}\PYG{p}{:}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf+fm}{\PYGZus{}\PYGZus{}init\PYGZus{}\PYGZus{}}\PYG{p}{(}\PYG{n+nb+bp}{self}\PYG{p}{,}
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\PYG{n}{n\PYGZus{}vis}\PYG{o}{=}\PYG{l+m+mi}{784}\PYG{p}{,}
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\PYG{n}{n\PYGZus{}hin}\PYG{o}{=}\PYG{l+m+mi}{500}\PYG{p}{,}
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\PYG{n}{k}\PYG{o}{=}\PYG{l+m+mi}{5}\PYG{p}{)}\PYG{p}{:}
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\PYG{n+nb}{super}\PYG{p}{(}\PYG{n}{RBM}\PYG{p}{,} \PYG{n+nb+bp}{self}\PYG{p}{)}\PYG{o}{.}\PYG{n+nf+fm}{\PYGZus{}\PYGZus{}init\PYGZus{}\PYGZus{}}\PYG{p}{(}\PYG{p}{)}
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\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{W} \PYG{o}{=} \PYG{n}{nn}\PYG{o}{.}\PYG{n}{Parameter}\PYG{p}{(}\PYG{n}{torch}\PYG{o}{.}\PYG{n}{randn}\PYG{p}{(}\PYG{n}{n\PYGZus{}hin}\PYG{p}{,}\PYG{n}{n\PYGZus{}vis}\PYG{p}{)}\PYG{o}{*}\PYG{l+m+mf}{1e\PYGZhy{}2}\PYG{p}{)}
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\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{v\PYGZus{}bias} \PYG{o}{=} \PYG{n}{nn}\PYG{o}{.}\PYG{n}{Parameter}\PYG{p}{(}\PYG{n}{torch}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{(}\PYG{n}{n\PYGZus{}vis}\PYG{p}{)}\PYG{p}{)}
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\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{h\PYGZus{}bias} \PYG{o}{=} \PYG{n}{nn}\PYG{o}{.}\PYG{n}{Parameter}\PYG{p}{(}\PYG{n}{torch}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{(}\PYG{n}{n\PYGZus{}hin}\PYG{p}{)}\PYG{p}{)}
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\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{k} \PYG{o}{=} \PYG{n}{k}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{sample\PYGZus{}from\PYGZus{}p}\PYG{p}{(}\PYG{n+nb+bp}{self}\PYG{p}{,}\PYG{n}{p}\PYG{p}{)}\PYG{p}{:}
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\PYG{k}{return} \PYG{n}{F}\PYG{o}{.}\PYG{n}{relu}\PYG{p}{(}\PYG{n}{torch}\PYG{o}{.}\PYG{n}{sign}\PYG{p}{(}\PYG{n}{p} \PYG{o}{\PYGZhy{}} \PYG{n}{Variable}\PYG{p}{(}\PYG{n}{torch}\PYG{o}{.}\PYG{n}{rand}\PYG{p}{(}\PYG{n}{p}\PYG{o}{.}\PYG{n}{size}\PYG{p}{(}\PYG{p}{)}\PYG{p}{)}\PYG{p}{)}\PYG{p}{)}\PYG{p}{)}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{v\PYGZus{}to\PYGZus{}h}\PYG{p}{(}\PYG{n+nb+bp}{self}\PYG{p}{,}\PYG{n}{v}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{p\PYGZus{}h} \PYG{o}{=} \PYG{n}{F}\PYG{o}{.}\PYG{n}{sigmoid}\PYG{p}{(}\PYG{n}{F}\PYG{o}{.}\PYG{n}{linear}\PYG{p}{(}\PYG{n}{v}\PYG{p}{,}\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{W}\PYG{p}{,}\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{h\PYGZus{}bias}\PYG{p}{)}\PYG{p}{)}
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\PYG{n}{sample\PYGZus{}h} \PYG{o}{=} \PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{sample\PYGZus{}from\PYGZus{}p}\PYG{p}{(}\PYG{n}{p\PYGZus{}h}\PYG{p}{)}
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\PYG{k}{return} \PYG{n}{p\PYGZus{}h}\PYG{p}{,}\PYG{n}{sample\PYGZus{}h}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{h\PYGZus{}to\PYGZus{}v}\PYG{p}{(}\PYG{n+nb+bp}{self}\PYG{p}{,}\PYG{n}{h}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{p\PYGZus{}v} \PYG{o}{=} \PYG{n}{F}\PYG{o}{.}\PYG{n}{sigmoid}\PYG{p}{(}\PYG{n}{F}\PYG{o}{.}\PYG{n}{linear}\PYG{p}{(}\PYG{n}{h}\PYG{p}{,}\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{W}\PYG{o}{.}\PYG{n}{t}\PYG{p}{(}\PYG{p}{)}\PYG{p}{,}\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{v\PYGZus{}bias}\PYG{p}{)}\PYG{p}{)}
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\PYG{n}{sample\PYGZus{}v} \PYG{o}{=} \PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{sample\PYGZus{}from\PYGZus{}p}\PYG{p}{(}\PYG{n}{p\PYGZus{}v}\PYG{p}{)}
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\PYG{k}{return} \PYG{n}{p\PYGZus{}v}\PYG{p}{,}\PYG{n}{sample\PYGZus{}v}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{forward}\PYG{p}{(}\PYG{n+nb+bp}{self}\PYG{p}{,}\PYG{n}{v}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{pre\PYGZus{}h1}\PYG{p}{,}\PYG{n}{h1} \PYG{o}{=} \PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{v\PYGZus{}to\PYGZus{}h}\PYG{p}{(}\PYG{n}{v}\PYG{p}{)}
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\PYG{n}{h\PYGZus{}} \PYG{o}{=} \PYG{n}{h1}
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\PYG{k}{for} \PYG{n}{\PYGZus{}} \PYG{o+ow}{in} \PYG{n+nb}{range}\PYG{p}{(}\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{k}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{pre\PYGZus{}v\PYGZus{}}\PYG{p}{,}\PYG{n}{v\PYGZus{}} \PYG{o}{=} \PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{h\PYGZus{}to\PYGZus{}v}\PYG{p}{(}\PYG{n}{h\PYGZus{}}\PYG{p}{)}
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\PYG{n}{pre\PYGZus{}h\PYGZus{}}\PYG{p}{,}\PYG{n}{h\PYGZus{}} \PYG{o}{=} \PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{v\PYGZus{}to\PYGZus{}h}\PYG{p}{(}\PYG{n}{v\PYGZus{}}\PYG{p}{)}
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\PYG{k}{return} \PYG{n}{v}\PYG{p}{,}\PYG{n}{v\PYGZus{}}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{free\PYGZus{}energy}\PYG{p}{(}\PYG{n+nb+bp}{self}\PYG{p}{,}\PYG{n}{v}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{vbias\PYGZus{}term} \PYG{o}{=} \PYG{n}{v}\PYG{o}{.}\PYG{n}{mv}\PYG{p}{(}\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{v\PYGZus{}bias}\PYG{p}{)}
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\PYG{n}{wx\PYGZus{}b} \PYG{o}{=} \PYG{n}{F}\PYG{o}{.}\PYG{n}{linear}\PYG{p}{(}\PYG{n}{v}\PYG{p}{,}\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{W}\PYG{p}{,}\PYG{n+nb+bp}{self}\PYG{o}{.}\PYG{n}{h\PYGZus{}bias}\PYG{p}{)}
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\PYG{n}{hidden\PYGZus{}term} \PYG{o}{=} \PYG{n}{wx\PYGZus{}b}\PYG{o}{.}\PYG{n}{exp}\PYG{p}{(}\PYG{p}{)}\PYG{o}{.}\PYG{n}{add}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{o}{.}\PYG{n}{log}\PYG{p}{(}\PYG{p}{)}\PYG{o}{.}\PYG{n}{sum}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{p}{)}
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\PYG{k}{for} \PYG{n}{\PYGZus{}}\PYG{p}{,} \PYG{p}{(}\PYG{n}{data}\PYG{p}{,}\PYG{n}{target}\PYG{p}{)} \PYG{o+ow}{in} \PYG{n+nb}{enumerate}\PYG{p}{(}\PYG{n}{train\PYGZus{}loader}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{data} \PYG{o}{=} \PYG{n}{Variable}\PYG{p}{(}\PYG{n}{data}\PYG{o}{.}\PYG{n}{view}\PYG{p}{(}\PYG{o}{\PYGZhy{}}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{784}\PYG{p}{)}\PYG{p}{)}
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\PYG{n}{train\PYGZus{}op}\PYG{o}{.}\PYG{n}{step}\PYG{p}{(}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Training loss for }\PYG{l+s+si}{\PYGZob{}\PYGZcb{}}\PYG{l+s+s2}{ epoch: }\PYG{l+s+si}{\PYGZob{}\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{o}{.}\PYG{n}{format}\PYG{p}{(}\PYG{n}{epoch}\PYG{p}{,} \PYG{n}{np}\PYG{o}{.}\PYG{n}{mean}\PYG{p}{(}\PYG{n}{loss\PYGZus{}}\PYG{p}{)}\PYG{p}{)}\PYG{p}{)}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{show\PYGZus{}adn\PYGZus{}save}\PYG{p}{(}\PYG{n}{file\PYGZus{}name}\PYG{p}{,}\PYG{n}{img}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{npimg} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{transpose}\PYG{p}{(}\PYG{n}{img}\PYG{o}{.}\PYG{n}{numpy}\PYG{p}{(}\PYG{p}{)}\PYG{p}{,}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{2}\PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{)}\PYG{p}{)}
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\PYG{n}{f} \PYG{o}{=} \PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{./}\PYG{l+s+si}{\PYGZpc{}s}\PYG{l+s+s2}{.png}\PYG{l+s+s2}{\PYGZdq{}} \PYG{o}{\PYGZpc{}} \PYG{n}{file\PYGZus{}name}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{imshow}\PYG{p}{(}\PYG{n}{npimg}\PYG{p}{)}
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\PYG{n}{plt}\PYG{o}{.}\PYG{n}{imsave}\PYG{p}{(}\PYG{n}{f}\PYG{p}{,}\PYG{n}{npimg}\PYG{p}{)}
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\PYG{n}{show\PYGZus{}adn\PYGZus{}save}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{real}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,}\PYG{n}{make\PYGZus{}grid}\PYG{p}{(}\PYG{n}{v}\PYG{o}{.}\PYG{n}{view}\PYG{p}{(}\PYG{l+m+mi}{32}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{28}\PYG{p}{,}\PYG{l+m+mi}{28}\PYG{p}{)}\PYG{o}{.}\PYG{n}{data}\PYG{p}{)}\PYG{p}{)}
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\PYG{n}{show\PYGZus{}adn\PYGZus{}save}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{generate}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,}\PYG{n}{make\PYGZus{}grid}\PYG{p}{(}\PYG{n}{v1}\PYG{o}{.}\PYG{n}{view}\PYG{p}{(}\PYG{l+m+mi}{32}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{28}\PYG{p}{,}\PYG{l+m+mi}{28}\PYG{p}{)}\PYG{o}{.}\PYG{n}{data}\PYG{p}{)}\PYG{p}{)}
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\end{MintedVerbatim}

‎doc/src/week11/_minted/A3E61CC5AEB9A07789FE9BD2AD9F8010.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{o}{*}\PYG{n}{samples\PYGZus{}from\PYGZus{}true\PYGZus{}distribution}\PYG{p}{,} \PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{.}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{,} \PYG{n}{alpha}\PYG{o}{=}\PYG{l+m+mf}{0.1}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{plot}\PYG{p}{(}\PYG{o}{*}\PYG{n}{samples}\PYG{p}{,} \PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{.r}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{)}
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\PYG{n}{ax}\PYG{o}{.}\PYG{n}{axis}\PYG{p}{(}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{square}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{)}
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‎doc/src/week11/_minted/D2DFF7AAB78247C1D4D2B10B41895007.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{numpy}\PYG{+w}{ }\PYG{k}{as}\PYG{+w}{ }\PYG{n+nn}{np}
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{matplotlib}\PYG{n+nn}{.}\PYG{n+nn}{pyplot}\PYG{+w}{ }\PYG{k}{as}\PYG{+w}{ }\PYG{n+nn}{plt}
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\PYG{c+c1}{\PYGZsh{} two dimensions}
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\PYG{n}{D} \PYG{o}{=} \PYG{l+m+mi}{2}
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\PYG{c+c1}{\PYGZsh{} set up the means (standard normal distribution}
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\PYG{n}{a\PYGZus{}mu} \PYG{o}{=} \PYG{l+m+mi}{0}
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\PYG{n}{b\PYGZus{}mu} \PYG{o}{=} \PYG{l+m+mi}{0}
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\PYG{c+c1}{\PYGZsh{} and the variances and covariances}
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\PYG{n}{a\PYGZus{}sigma} \PYG{o}{=} \PYG{l+m+mi}{1}
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\PYG{n}{joint\PYGZus{}mu} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{vstack}\PYG{p}{(}\PYG{p}{(}\PYG{n}{a\PYGZus{}mu}\PYG{p}{,} \PYG{n}{b\PYGZus{}mu}\PYG{p}{)}\PYG{p}{)}
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\end{MintedVerbatim}

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