aboutsummaryrefslogtreecommitdiffstats
diff options
context:
space:
mode:
Diffstat
-rw-r--r--finale/bayes.tex107
-rw-r--r--finale/def.tex97
-rw-r--r--finale/mid_report.tex52
-rw-r--r--finale/mle.tex163
-rw-r--r--simulation/main.py28
5 files changed, 418 insertions, 29 deletions
diff --git a/finale/bayes.tex b/finale/bayes.tex
new file mode 100644
index 0000000..82cb732
--- /dev/null
+++ b/finale/bayes.tex
@@ -0,0 +1,107 @@
+\begin{Verbatim}[commandchars=\\\{\}]
+\PY{k+kn}{import} \PY{n+nn}{pymc}
+\PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k+kn}{as} \PY{n+nn}{np}
+
+\PY{k}{def} \PY{n+nf}{glm\PYZus{}node\PYZus{}setup}\PY{p}{(}\PY{n}{cascade}\PY{p}{,} \PY{n}{y\PYZus{}obs}\PY{p}{,} \PY{n}{prior}\PY{o}{=}\PY{n+nb+bp}{None}\PY{p}{,} \PY{o}{*}\PY{n}{args}\PY{p}{,} \PY{o}{*}\PY{o}{*}\PY{n}{kwargs}\PY{p}{)}\PY{p}{:}
+ \PY{l+s+sd}{\PYZdq{}\PYZdq{}\PYZdq{}}
+\PY{l+s+sd}{ Build an IC PyMC node\PYZhy{}level model from:}
+\PY{l+s+sd}{ \PYZhy{}observed cascades: cascade}
+\PY{l+s+sd}{ \PYZhy{}outcome vector: y\PYZus{}obs}
+\PY{l+s+sd}{ \PYZhy{}desired PyMC prior and parameters: prior, *args}
+\PY{l+s+sd}{ Note: we use the glm formulation: y = Bernoulli[f(x.dot(theta))]}
+\PY{l+s+sd}{ \PYZdq{}\PYZdq{}\PYZdq{}}
+ \PY{n}{n\PYZus{}nodes} \PY{o}{=} \PY{n+nb}{len}\PY{p}{(}\PY{n}{cascade}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
+
+ \PY{c}{\PYZsh{} Container class for node\PYZsq{}s parents}
+ \PY{n}{theta} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{empty}\PY{p}{(}\PY{n}{n\PYZus{}nodes}\PY{p}{,} \PY{n}{dtype}\PY{o}{=}\PY{n+nb}{object}\PY{p}{)}
+ \PY{k}{for} \PY{n}{j} \PY{o+ow}{in} \PY{n+nb}{xrange}\PY{p}{(}\PY{n}{n\PYZus{}nodes}\PY{p}{)}\PY{p}{:}
+ \PY{k}{if} \PY{n}{prior} \PY{o+ow}{is} \PY{n+nb+bp}{None}\PY{p}{:}
+ \PY{n}{theta}\PY{p}{[}\PY{n}{j}\PY{p}{]} \PY{o}{=} \PY{n}{pymc}\PY{o}{.}\PY{n}{Beta}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{theta\PYZus{}\PYZob{}\PYZcb{}}\PY{l+s}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{j}\PY{p}{)}\PY{p}{,} \PY{n}{alpha}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{,} \PY{n}{beta}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)}
+ \PY{k}{else}\PY{p}{:}
+ \PY{n}{theta}\PY{p}{[}\PY{n}{j}\PY{p}{]} \PY{o}{=} \PY{n}{prior}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{theta\PYZus{}\PYZob{}\PYZcb{}}\PY{l+s}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{j}\PY{p}{)}\PY{p}{,} \PY{o}{*}\PY{n}{args}\PY{p}{,} \PY{o}{*}\PY{o}{*}\PY{n}{kwargs}\PY{p}{)}
+
+ \PY{c}{\PYZsh{} Observed container class for cascade realization}
+ \PY{n}{x} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{empty}\PY{p}{(}\PY{n}{n\PYZus{}nodes}\PY{p}{,} \PY{n}{dtype}\PY{o}{=}\PY{n+nb}{object}\PY{p}{)}
+ \PY{k}{for} \PY{n}{i}\PY{p}{,} \PY{n}{val} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{cascade}\PY{o}{.}\PY{n}{T}\PY{p}{)}\PY{p}{:}
+ \PY{n}{x}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{pymc}\PY{o}{.}\PY{n}{Normal}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{x\PYZus{}\PYZob{}\PYZcb{}}\PY{l+s}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{i}\PY{p}{)}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,} \PY{n}{value}\PY{o}{=}\PY{n}{val}\PY{p}{,} \PY{n}{observed}\PY{o}{=}\PY{n+nb+bp}{True}\PY{p}{)}
+
+ \PY{n+nd}{@pymc.deterministic}
+ \PY{k}{def} \PY{n+nf}{glm\PYZus{}p}\PY{p}{(}\PY{n}{x}\PY{o}{=}\PY{n}{x}\PY{p}{,} \PY{n}{theta}\PY{o}{=}\PY{n}{theta}\PY{p}{)}\PY{p}{:}
+ \PY{k}{return} \PY{l+m+mf}{1.} \PY{o}{\PYZhy{}} \PY{n}{np}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{n}{x}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{theta}\PY{p}{)}\PY{p}{)}
+
+ \PY{n+nd}{@pymc.observed}
+ \PY{k}{def} \PY{n+nf}{y}\PY{p}{(}\PY{n}{glm\PYZus{}p}\PY{o}{=}\PY{n}{glm\PYZus{}p}\PY{p}{,} \PY{n}{value}\PY{o}{=}\PY{n}{y\PYZus{}obs}\PY{p}{)}\PY{p}{:}
+ \PY{k}{return} \PY{n}{pymc}\PY{o}{.}\PY{n}{bernoulli\PYZus{}like}\PY{p}{(}\PY{n}{value}\PY{p}{,} \PY{n}{glm\PYZus{}p}\PY{p}{)}
+
+ \PY{k}{return} \PY{n}{pymc}\PY{o}{.}\PY{n}{Model}\PY{p}{(}\PY{p}{[}\PY{n}{y}\PY{p}{,} \PY{n}{pymc}\PY{o}{.}\PY{n}{Container}\PY{p}{(}\PY{n}{theta}\PY{p}{)}\PY{p}{,} \PY{n}{pymc}\PY{o}{.}\PY{n}{Container}\PY{p}{(}\PY{n}{x}\PY{p}{)}\PY{p}{]}\PY{p}{)}
+
+
+\PY{k}{def} \PY{n+nf}{mc\PYZus{}graph\PYZus{}setup}\PY{p}{(}\PY{n}{infected}\PY{p}{,} \PY{n}{susceptible}\PY{p}{,} \PY{n}{prior}\PY{o}{=}\PY{n+nb+bp}{None}\PY{p}{,} \PY{o}{*}\PY{n}{args}\PY{p}{,} \PY{o}{*}\PY{o}{*}\PY{n}{kwargs}\PY{p}{)}\PY{p}{:}
+ \PY{l+s+sd}{\PYZdq{}\PYZdq{}\PYZdq{}}
+\PY{l+s+sd}{ Build an IC PyMC graph\PYZhy{}level model from:}
+\PY{l+s+sd}{ \PYZhy{}infected nodes over time: list/tuple of list/tuple of np.array}
+\PY{l+s+sd}{ \PYZhy{}susceptible nodes over time: same format as above}
+\PY{l+s+sd}{ Note: we use the Markov Chain formulation: X\PYZus{}\PYZob{}t+1\PYZcb{}|X\PYZus{}t,theta = f(X\PYZus{}t.theta)}
+\PY{l+s+sd}{ \PYZdq{}\PYZdq{}\PYZdq{}}
+ \PY{c}{\PYZsh{} Container class for graph parameters}
+ \PY{n}{n\PYZus{}nodes} \PY{o}{=} \PY{n+nb}{len}\PY{p}{(}\PY{n}{infected}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
+ \PY{n}{theta} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{empty}\PY{p}{(}\PY{p}{(}\PY{n}{n\PYZus{}nodes}\PY{p}{,}\PY{n}{n\PYZus{}nodes}\PY{p}{)}\PY{p}{,} \PY{n}{dtype}\PY{o}{=}\PY{n+nb}{object}\PY{p}{)}
+ \PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{xrange}\PY{p}{(}\PY{n}{n\PYZus{}nodes}\PY{p}{)}\PY{p}{:}
+ \PY{k}{for} \PY{n}{j} \PY{o+ow}{in} \PY{n+nb}{xrange}\PY{p}{(}\PY{n}{n\PYZus{}nodes}\PY{p}{)}\PY{p}{:}
+ \PY{k}{if} \PY{n}{prior} \PY{o+ow}{is} \PY{n+nb+bp}{None}\PY{p}{:}
+ \PY{n}{theta}\PY{p}{[}\PY{n}{i}\PY{p}{,} \PY{n}{j}\PY{p}{]} \PY{o}{=} \PY{n}{pymc}\PY{o}{.}\PY{n}{Beta}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{theta\PYZus{}\PYZob{}\PYZcb{}\PYZob{}\PYZcb{}}\PY{l+s}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{i}\PY{p}{,} \PY{n}{j}\PY{p}{)}\PY{p}{,} \PY{n}{alpha}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{,}
+ \PY{n}{beta}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)}
+ \PY{k}{else}\PY{p}{:}
+ \PY{n}{theta}\PY{p}{[}\PY{n}{i}\PY{p}{,} \PY{n}{j}\PY{p}{]} \PY{o}{=} \PY{n}{prior}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{theta\PYZus{}\PYZob{}\PYZcb{}\PYZob{}\PYZcb{}}\PY{l+s}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{i}\PY{p}{,} \PY{n}{j}\PY{p}{)}\PY{p}{,} \PY{o}{*}\PY{n}{args}\PY{p}{,} \PY{o}{*}\PY{o}{*}\PY{n}{kwargs}\PY{p}{)}
+
+ \PY{c}{\PYZsh{} Container class for cascade realization}
+ \PY{n}{x} \PY{o}{=} \PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}
+ \PY{k}{for} \PY{n}{i}\PY{p}{,} \PY{n}{cascade} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{infected}\PY{p}{)}\PY{p}{:}
+ \PY{k}{for} \PY{n}{j}\PY{p}{,} \PY{n}{step} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{cascade}\PY{p}{)}\PY{p}{:}
+ \PY{k}{for} \PY{n}{k}\PY{p}{,} \PY{n}{node} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{step}\PY{p}{)}\PY{p}{:}
+ \PY{k}{if} \PY{n}{j} \PY{o+ow}{and} \PY{n}{susceptible}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{[}\PY{n}{j}\PY{p}{]}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{:}
+ \PY{n}{p} \PY{o}{=} \PY{l+m+mf}{1.} \PY{o}{\PYZhy{}} \PY{n}{pymc}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{n}{cascade}\PY{p}{[}\PY{n}{j}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{theta}\PY{p}{[}\PY{n}{k}\PY{p}{]}\PY{p}{)}\PY{p}{)}
+ \PY{k}{else}\PY{p}{:}
+ \PY{n}{p} \PY{o}{=} \PY{o}{.}\PY{l+m+mi}{5}
+ \PY{n}{x}\PY{p}{[}\PY{n}{i}\PY{p}{,} \PY{n}{j}\PY{p}{,} \PY{n}{k}\PY{p}{]} \PY{o}{=} \PY{n}{pymc}\PY{o}{.}\PY{n}{Bernoulli}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{x\PYZus{}\PYZob{}\PYZcb{}\PYZob{}\PYZcb{}\PYZob{}\PYZcb{}}\PY{l+s}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{i}\PY{p}{,} \PY{n}{j}\PY{p}{,} \PY{n}{k}\PY{p}{)}\PY{p}{,} \PY{n}{p}\PY{o}{=}\PY{n}{p}\PY{p}{,}
+ \PY{n}{value}\PY{o}{=}\PY{n}{node}\PY{p}{,} \PY{n}{observed}\PY{o}{=}\PY{n+nb+bp}{True}\PY{p}{)}
+
+ \PY{k}{return} \PY{n}{pymc}\PY{o}{.}\PY{n}{Model}\PY{p}{(}\PY{p}{[}\PY{n}{pymc}\PY{o}{.}\PY{n}{Container}\PY{p}{(}\PY{n}{theta}\PY{p}{)}\PY{p}{,} \PY{n}{pymc}\PY{o}{.}\PY{n}{Container}\PY{p}{(}\PY{n}{x}\PY{p}{)}\PY{p}{]}\PY{p}{)}
+
+
+\PY{k}{if} \PY{n}{\PYZus{}\PYZus{}name\PYZus{}\PYZus{}}\PY{o}{==}\PY{l+s}{\PYZdq{}}\PY{l+s}{\PYZus{}\PYZus{}main\PYZus{}\PYZus{}}\PY{l+s}{\PYZdq{}}\PY{p}{:}
+ \PY{k+kn}{import} \PY{n+nn}{main}
+ \PY{k+kn}{import} \PY{n+nn}{matplotlib.pyplot} \PY{k+kn}{as} \PY{n+nn}{plt}
+ \PY{k+kn}{import} \PY{n+nn}{seaborn}
+ \PY{n}{seaborn}\PY{o}{.}\PY{n}{set\PYZus{}style}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{whitegrid}\PY{l+s}{\PYZsq{}}\PY{p}{)}
+ \PY{n}{g} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{]}\PY{p}{)}
+ \PY{n}{p} \PY{o}{=} \PY{l+m+mf}{0.5}
+ \PY{n}{g} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{log}\PY{p}{(}\PY{l+m+mf}{1.} \PY{o}{/} \PY{p}{(}\PY{l+m+mi}{1} \PY{o}{\PYZhy{}} \PY{n}{p} \PY{o}{*} \PY{n}{g}\PY{p}{)}\PY{p}{)}
+
+ \PY{k}{print}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{running the graph\PYZhy{}level MC set\PYZhy{}up}\PY{l+s}{\PYZsq{}}\PY{p}{)}
+ \PY{n}{cascades} \PY{o}{=} \PY{n}{main}\PY{o}{.}\PY{n}{simulate\PYZus{}cascades}\PY{p}{(}\PY{l+m+mi}{1000}\PY{p}{,} \PY{n}{g}\PY{p}{)}
+ \PY{n}{infected}\PY{p}{,} \PY{n}{susc} \PY{o}{=} \PY{n}{main}\PY{o}{.}\PY{n}{build\PYZus{}cascade\PYZus{}list}\PY{p}{(}\PY{n}{cascades}\PY{p}{)}
+ \PY{n}{model} \PY{o}{=} \PY{n}{mc\PYZus{}graph\PYZus{}setup}\PY{p}{(}\PY{n}{infected}\PY{p}{,} \PY{n}{susc}\PY{p}{)}
+ \PY{n}{mcmc} \PY{o}{=} \PY{n}{pymc}\PY{o}{.}\PY{n}{MCMC}\PY{p}{(}\PY{n}{model}\PY{p}{)}
+ \PY{n}{mcmc}\PY{o}{.}\PY{n}{sample}\PY{p}{(}\PY{l+m+mi}{10}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{4}\PY{p}{,} \PY{l+m+mi}{1000}\PY{p}{)}
+ \PY{n}{fig}\PY{p}{,} \PY{n}{ax} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{g}\PY{p}{)}\PY{p}{,} \PY{n+nb}{len}\PY{p}{(}\PY{n}{g}\PY{p}{)}\PY{p}{)}
+ \PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{xrange}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{g}\PY{p}{)}\PY{p}{)}\PY{p}{:}
+ \PY{k}{for} \PY{n}{j} \PY{o+ow}{in} \PY{n+nb}{xrange}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{g}\PY{p}{)}\PY{p}{)}\PY{p}{:}
+ \PY{n}{ax}\PY{p}{[}\PY{n}{i}\PY{p}{,}\PY{n}{j}\PY{p}{]}\PY{o}{.}\PY{n}{locator\PYZus{}params}\PY{p}{(}\PY{n}{nbins}\PY{o}{=}\PY{l+m+mi}{3}\PY{p}{,} \PY{n}{axis}\PY{o}{=}\PY{l+s}{\PYZsq{}}\PY{l+s}{x}\PY{l+s}{\PYZsq{}}\PY{p}{)}
+ \PY{n}{ax}\PY{p}{[}\PY{n}{i}\PY{p}{,}\PY{n}{j}\PY{p}{]}\PY{o}{.}\PY{n}{hist}\PY{p}{(}\PY{n}{mcmc}\PY{o}{.}\PY{n}{trace}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{theta\PYZus{}\PYZob{}\PYZcb{}\PYZob{}\PYZcb{}}\PY{l+s}{\PYZsq{}}\PY{o}{.}\PY{n}{format}\PY{p}{(}\PY{n}{i}\PY{p}{,}\PY{n}{j}\PY{p}{)}\PY{p}{)}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{normed}\PY{o}{=}\PY{n+nb+bp}{True}\PY{p}{)}
+ \PY{n}{ax}\PY{p}{[}\PY{n}{i}\PY{p}{,} \PY{n}{j}\PY{p}{]}\PY{o}{.}\PY{n}{set\PYZus{}xlim}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}
+ \PY{n}{ax}\PY{p}{[}\PY{n}{i}\PY{p}{,} \PY{n}{j}\PY{p}{]}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{p}{[}\PY{n}{g}\PY{p}{[}\PY{n}{i}\PY{p}{,} \PY{n}{j}\PY{p}{]}\PY{p}{]}\PY{o}{*}\PY{l+m+mi}{2}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,} \PY{n}{ax}\PY{p}{[}\PY{n}{i}\PY{p}{,}\PY{n}{j}\PY{p}{]}\PY{o}{.}\PY{n}{get\PYZus{}ylim}\PY{p}{(}\PY{p}{)}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{]}\PY{p}{,} \PY{n}{color}\PY{o}{=}\PY{l+s}{\PYZsq{}}\PY{l+s}{red}\PY{l+s}{\PYZsq{}}\PY{p}{)}
+ \PY{n}{plt}\PY{o}{.}\PY{n}{tight\PYZus{}layout}\PY{p}{(}\PY{n}{pad}\PY{o}{=}\PY{l+m+mf}{0.4}\PY{p}{,} \PY{n}{w\PYZus{}pad}\PY{o}{=}\PY{l+m+mf}{0.5}\PY{p}{,} \PY{n}{h\PYZus{}pad}\PY{o}{=}\PY{o}{.}\PY{l+m+mi}{1}\PY{p}{)}
+ \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
+
+
+ \PY{k}{print}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{running the node level set\PYZhy{}up}\PY{l+s}{\PYZsq{}}\PY{p}{)}
+ \PY{n}{node} \PY{o}{=} \PY{l+m+mi}{0}
+ \PY{n}{cascades} \PY{o}{=} \PY{n}{main}\PY{o}{.}\PY{n}{simulate\PYZus{}cascades}\PY{p}{(}\PY{l+m+mi}{100}\PY{p}{,} \PY{n}{g}\PY{p}{)}
+ \PY{n}{cascade}\PY{p}{,} \PY{n}{y\PYZus{}obs} \PY{o}{=} \PY{n}{main}\PY{o}{.}\PY{n}{build\PYZus{}matrix}\PY{p}{(}\PY{n}{cascades}\PY{p}{,} \PY{n}{node}\PY{p}{)}
+ \PY{n}{model} \PY{o}{=} \PY{n}{glm\PYZus{}node\PYZus{}setup}\PY{p}{(}\PY{n}{cascade}\PY{p}{,} \PY{n}{y\PYZus{}obs}\PY{p}{)}
+ \PY{n}{mcmc} \PY{o}{=} \PY{n}{pymc}\PY{o}{.}\PY{n}{MCMC}\PY{p}{(}\PY{n}{model}\PY{p}{)}
+ \PY{n}{mcmc}\PY{o}{.}\PY{n}{sample}\PY{p}{(}\PY{l+m+mf}{1e5}\PY{p}{,} \PY{l+m+mf}{1e4}\PY{p}{)}
+ \PY{n}{plt}\PY{o}{.}\PY{n}{hist}\PY{p}{(}\PY{n}{mcmc}\PY{o}{.}\PY{n}{trace}\PY{p}{(}\PY{l+s}{\PYZsq{}}\PY{l+s}{theta\PYZus{}1}\PY{l+s}{\PYZsq{}}\PY{p}{)}\PY{p}{[}\PY{p}{:}\PY{p}{]}\PY{p}{,} \PY{n}{bins}\PY{o}{=}\PY{l+m+mf}{1e2}\PY{p}{)}
+ \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
+\end{Verbatim}
diff --git a/finale/def.tex b/finale/def.tex
new file mode 100644
index 0000000..7262705
--- /dev/null
+++ b/finale/def.tex
@@ -0,0 +1,97 @@
+\usepackage{fancyvrb}
+\usepackage{color}
+\usepackage[UTF-8]{inputenc}
+
+\makeatletter
+\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax%
+ \let\PY@ul=\relax \let\PY@tc=\relax%
+ \let\PY@bc=\relax \let\PY@ff=\relax}
+\def\PY@tok#1{\csname PY@tok@#1\endcsname}
+\def\PY@toks#1+{\ifx\relax#1\empty\else%
+ \PY@tok{#1}\expandafter\PY@toks\fi}
+\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{%
+ \PY@it{\PY@bf{\PY@ff{#1}}}}}}}
+\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}}
+
+\expandafter\def\csname PY@tok@nt\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##1}}}
+\expandafter\def\csname PY@tok@se\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.13}{##1}}}
+\expandafter\def\csname PY@tok@gh\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
+\expandafter\def\csname PY@tok@ow\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}}
+\expandafter\def\csname PY@tok@kd\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@sx\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
+\expandafter\def\csname PY@tok@nb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}}
+\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}}
+\expandafter\def\csname PY@tok@vg\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf}
+\expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@na\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.49,0.56,0.16}{##1}}}
+\expandafter\def\csname PY@tok@sr\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}}
+\expandafter\def\csname PY@tok@ni\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.60,0.60,0.60}{##1}}}
+\expandafter\def\csname PY@tok@m\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@err\endcsname{\def\PY@bc##1{\setlength{\fboxsep}{0pt}\fcolorbox[rgb]{1.00,0.00,0.00}{1,1,1}{\strut ##1}}}
+\expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}}
+\expandafter\def\csname PY@tok@nf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
+\expandafter\def\csname PY@tok@si\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}}
+\expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@mb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+\expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}}
+\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+\expandafter\def\csname PY@tok@no\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.00,0.00}{##1}}}
+\expandafter\def\csname PY@tok@bp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@ne\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.82,0.25,0.23}{##1}}}
+\expandafter\def\csname PY@tok@nc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
+\expandafter\def\csname PY@tok@kp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}}
+\expandafter\def\csname PY@tok@sc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit}
+\expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+\expandafter\def\csname PY@tok@o\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@vc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}}
+\expandafter\def\csname PY@tok@nn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
+\expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@cp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.74,0.48,0.00}{##1}}}
+\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+\expandafter\def\csname PY@tok@nd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}}
+\expandafter\def\csname PY@tok@kr\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@kt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.69,0.00,0.25}{##1}}}
+\expandafter\def\csname PY@tok@nl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.63,0.00}{##1}}}
+\expandafter\def\csname PY@tok@vi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@mh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@kn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@s\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@sb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@nv\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+
+\def\PYZbs{\char`\\}
+\def\PYZus{\char`\_}
+\def\PYZob{\char`\{}
+\def\PYZcb{\char`\}}
+\def\PYZca{\char`\^}
+\def\PYZam{\char`\&}
+\def\PYZlt{\char`\<}
+\def\PYZgt{\char`\>}
+\def\PYZsh{\char`\#}
+\def\PYZpc{\char`\%}
+\def\PYZdl{\char`\$}
+\def\PYZhy{\char`\-}
+\def\PYZsq{\char`\'}
+\def\PYZdq{\char`\"}
+\def\PYZti{\char`\~}
+% for compatibility with earlier versions
+\def\PYZat{@}
+\def\PYZlb{[}
+\def\PYZrb{]}
+\makeatother
diff --git a/finale/mid_report.tex b/finale/mid_report.tex
index bd7f475..4abcd47 100644
--- a/finale/mid_report.tex
+++ b/finale/mid_report.tex
@@ -8,8 +8,9 @@
\usepackage{graphicx, subfig}
\usepackage{bbm}
\usepackage{fullpage}
-
+\input{def}
\DeclareMathOperator*{\argmax}{arg\,max}
+\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator{\E}{\mathbb{E}}
\let\P\relax
\DeclareMathOperator{\P}{\mathbb{P}}
@@ -457,42 +458,47 @@ with $\binom{4}{2}=6$ parameters to learn with the MCMC package PyMC\@. We plot
in Figure~\ref{betapriorbayeslearning} the progressive learning of $\Theta$ for
increasing numbers of observations. Of note, since the GLMC model does not
include self-loops, the diagonal terms are never properly learned, which is
-expected but not undesirable. We notice that the existence or not of an edge is
-(relatively) quickly learned, with the posterior on edges with no weight
-converging to $0$ after $100$ cascades. To get a concentrated posterior around
-the true non-zero edge weigth requires $1000$ cascades, which is unreasonably
-high considering the small number of parameters that we are learning in this
-experiment.
+expected but not undesirable. We notice that the absence of an edge is
+(relatively) quickly learned: the posterior on edges with no weight converges
+to $0$ after $100$ cascades. For existing edges though, the posterior visually
+concentrates only after $1000$ cascades, which is unreasonably high considering
+the small number of parameters that we are learning in this experiment.
\subsection{Active Learning}
-Finally, we propose an Active Learning formulation of Network Inference
+Finally, we propose an Active Learning formulation of the Network Inference
problem. In this setup, the source $x^0$ is no longer drawn from a random
distribution $p_s$ but a single source $i$ is chosen by the designer of the
experiment. Once a source is drawn, a cascade is drawn from the Markovian
-process, $\mathcal{D'}$. We wish to choose the source which maximises the
-information gain on the parameter $\Theta$, so as to speed up learning. We
-suggest to choose the source which maximises the mutual information between
-$\theta$ and $X$ at each time step. The mutual information can be computed
-node-by-node by sampling:
+process $\mathcal{D'}$ described in \eqref{eq:markov}.
+
+Our suggested selection stratgey is to select at each time step the source is
+to select the node which maximises the information gain (mutual information) on
+the parameter $\Theta$ resulting from observing the cascade $\bx$. The mutual
+information can be computed node-by-node by sampling:
\begin{equation*}
-I((x_t)_{t\geq 1} ,\Theta | x_0 = i) = \mathbb{E}_{\substack{\Theta \sim D_t \\
+I(\bx ,\Theta | x^0 = i) = \mathbb{E}_{\substack{\Theta \sim D_t \\
x | \Theta, i \sim D'}}\log p(x|\Theta) - \mathbb{E}_{\substack{\Theta \sim D_t
\\ x' | \Theta, i \sim D'}} \log p(x')
\end{equation*}
-The second term involves marginalizing over $\Theta$: $p(x') =
-\mathbb{E}_{\Theta \sim D_t} p(x'| \Theta)$.
+where $D_t$ denotes the posterior distribution on $\Theta$ after the first $t$
+cascades. Not that the second term involves marginalizing over $\Theta$:
+$p(x') = \mathbb{E}_{\Theta \sim D_t} p(x'| \Theta)$. The full specification of
+our Active Learning procedure is described in Algorithm 1. For the final
+version of this project, we plan to test experimentally the learning speedup
+induced by using Active Learning compared to independent observations from
+a random source.
\begin{algorithm}
\caption{Active Bayesian Learning through Cascades (ABC)}
\begin{algorithmic}[1]
-\State $\theta \sim \mathcal{D}_0 = \mathcal{D}$ \Comment{Initial prior on
-$\theta$}
+\State $\Theta \sim \mathcal{D}_0 = \mathcal{D}$ \Comment{Initial prior on
+$\Theta$}
\While{True}
-\State $i \leftarrow \arg\min_{i} I(\theta, (x_t)_{t \geq 1} | x_0 = i)$
+\State $i \leftarrow \argmin_{i} I(\Theta, \bx | x_0 = i)$
\Comment{Maximize mutual information}
\State Observe $(x_t)_{t\geq1} |x_0 = i$ \Comment{Observe cascade from source}
-\State $\mathcal{D}_{t+1} \gets \text{posterior of $\theta \sim \mathcal{D}_t$
+\State $\mathcal{D}_{t+1} \gets \text{posterior of $\Theta \sim \mathcal{D}_t$
given $(x_t)_{t\geq1}$}$ \Comment{Update posterior on $\theta$}
\EndWhile
\end{algorithmic}
@@ -500,5 +506,9 @@ given $(x_t)_{t\geq1}$}$ \Comment{Update posterior on $\theta$}
\bibliography{sparse}{}
\bibliographystyle{abbrv}
-
+\appendix
+\section{\textsf{mle.py}}
+\input{mle}
+\section{\textsf{bayes.py}}
+\input{bayes}
\end{document}
diff --git a/finale/mle.tex b/finale/mle.tex
new file mode 100644
index 0000000..70caa3e
--- /dev/null
+++ b/finale/mle.tex
@@ -0,0 +1,163 @@
+\begin{Verbatim}[commandchars=\\\{\}]
+\PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k+kn}{as} \PY{n+nn}{np}
+\PY{k+kn}{from} \PY{n+nn}{numpy.linalg} \PY{k+kn}{import} \PY{n}{norm}
+\PY{k+kn}{import} \PY{n+nn}{numpy.random} \PY{k+kn}{as} \PY{n+nn}{nr}
+\PY{k+kn}{from} \PY{n+nn}{scipy.optimize} \PY{k+kn}{import} \PY{n}{minimize}
+\PY{k+kn}{import} \PY{n+nn}{matplotlib.pyplot} \PY{k+kn}{as} \PY{n+nn}{plt}
+\PY{k+kn}{import} \PY{n+nn}{seaborn}
+\PY{k+kn}{from} \PY{n+nn}{random} \PY{k+kn}{import} \PY{n}{random}\PY{p}{,} \PY{n}{randint}
+
+\PY{n}{seaborn}\PY{o}{.}\PY{n}{set\PYZus{}style}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{white}\PY{l+s}{\PYZdq{}}\PY{p}{)}
+
+
+\PY{k}{def} \PY{n+nf}{likelihood}\PY{p}{(}\PY{n}{p}\PY{p}{,} \PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{p}{)}\PY{p}{:}
+ \PY{n}{a} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{p}\PY{p}{)}
+ \PY{k}{return} \PY{n}{np}\PY{o}{.}\PY{n}{log}\PY{p}{(}\PY{l+m+mf}{1.} \PY{o}{\PYZhy{}} \PY{n}{np}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{n}{a}\PY{p}{[}\PY{n}{y}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n}{a}\PY{p}{[}\PY{o}{\PYZti{}}\PY{n}{y}\PY{p}{]}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{p}{)}
+
+
+\PY{k}{def} \PY{n+nf}{likelihood\PYZus{}gradient}\PY{p}{(}\PY{n}{p}\PY{p}{,} \PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{p}{)}\PY{p}{:}
+ \PY{n}{a} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{p}\PY{p}{)}
+ \PY{n}{l} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{log}\PY{p}{(}\PY{l+m+mf}{1.} \PY{o}{\PYZhy{}} \PY{n}{np}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{n}{a}\PY{p}{[}\PY{n}{y}\PY{p}{]}\PY{p}{)}\PY{p}{)}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n}{a}\PY{p}{[}\PY{o}{\PYZti{}}\PY{n}{y}\PY{p}{]}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{p}{)}
+ \PY{n}{g1} \PY{o}{=} \PY{l+m+mf}{1.} \PY{o}{/} \PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{n}{a}\PY{p}{[}\PY{n}{y}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{l+m+mf}{1.}\PY{p}{)}
+ \PY{n}{g} \PY{o}{=} \PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{n}{y}\PY{p}{]} \PY{o}{*} \PY{n}{g1}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{n}{np}\PY{o}{.}\PY{n}{newaxis}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n}{x}\PY{p}{[}\PY{o}{\PYZti{}}\PY{n}{y}\PY{p}{]}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{)}
+ \PY{k}{return} \PY{n}{l}\PY{p}{,} \PY{n}{g}
+
+
+\PY{k}{def} \PY{n+nf}{test\PYZus{}gradient}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{p}{)}\PY{p}{:}
+ \PY{n}{eps} \PY{o}{=} \PY{l+m+mf}{1e\PYZhy{}10}
+ \PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{xrange}\PY{p}{(}\PY{n}{x}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{:}
+ \PY{n}{p} \PY{o}{=} \PY{l+m+mf}{0.5} \PY{o}{*} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n}{x}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}
+ \PY{n}{a} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{p}\PY{p}{)}
+ \PY{n}{g1} \PY{o}{=} \PY{l+m+mf}{1.} \PY{o}{/} \PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{n}{a}\PY{p}{[}\PY{n}{y}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{l+m+mf}{1.}\PY{p}{)}
+ \PY{n}{g} \PY{o}{=} \PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{n}{y}\PY{p}{]} \PY{o}{*} \PY{n}{g1}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{n}{np}\PY{o}{.}\PY{n}{newaxis}\PY{p}{]}\PY{p}{)}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n}{x}\PY{p}{[}\PY{o}{\PYZti{}}\PY{n}{y}\PY{p}{]}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{)}
+ \PY{n}{p}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{+}\PY{o}{=} \PY{n}{eps}
+ \PY{n}{f1} \PY{o}{=} \PY{n}{likelihood}\PY{p}{(}\PY{n}{p}\PY{p}{,} \PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{p}{)}
+ \PY{n}{p}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{\PYZhy{}}\PY{o}{=} \PY{l+m+mi}{2} \PY{o}{*} \PY{n}{eps}
+ \PY{n}{f2} \PY{o}{=} \PY{n}{likelihood}\PY{p}{(}\PY{n}{p}\PY{p}{,} \PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{p}{)}
+ \PY{k}{print} \PY{n}{g}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{,} \PY{p}{(}\PY{n}{f1} \PY{o}{\PYZhy{}} \PY{n}{f2}\PY{p}{)} \PY{o}{/} \PY{p}{(}\PY{l+m+mi}{2} \PY{o}{*} \PY{n}{eps}\PY{p}{)}
+
+
+\PY{k}{def} \PY{n+nf}{infer}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{p}{)}\PY{p}{:}
+ \PY{k}{def} \PY{n+nf}{f}\PY{p}{(}\PY{n}{p}\PY{p}{)}\PY{p}{:}
+ \PY{n}{l}\PY{p}{,} \PY{n}{g} \PY{o}{=} \PY{n}{likelihood\PYZus{}gradient}\PY{p}{(}\PY{n}{p}\PY{p}{,} \PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{p}{)}
+ \PY{k}{return} \PY{o}{\PYZhy{}}\PY{n}{l}\PY{p}{,} \PY{o}{\PYZhy{}}\PY{n}{g}
+ \PY{n}{x0} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n}{x}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}
+ \PY{n}{bounds} \PY{o}{=} \PY{p}{[}\PY{p}{(}\PY{l+m+mf}{1e\PYZhy{}10}\PY{p}{,} \PY{n+nb+bp}{None}\PY{p}{)}\PY{p}{]} \PY{o}{*} \PY{n}{x}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}
+ \PY{k}{return} \PY{n}{minimize}\PY{p}{(}\PY{n}{f}\PY{p}{,} \PY{n}{x0}\PY{p}{,} \PY{n}{jac}\PY{o}{=}\PY{n+nb+bp}{True}\PY{p}{,} \PY{n}{bounds}\PY{o}{=}\PY{n}{bounds}\PY{p}{,} \PY{n}{method}\PY{o}{=}\PY{l+s}{\PYZdq{}}\PY{l+s}{L\PYZhy{}BFGS\PYZhy{}B}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{o}{.}\PY{n}{x}
+
+
+\PY{k}{def} \PY{n+nf}{bootstrap}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{p}{,} \PY{n}{n\PYZus{}iter}\PY{o}{=}\PY{l+m+mi}{100}\PY{p}{)}\PY{p}{:}
+ \PY{n}{rval} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{p}{(}\PY{n}{n\PYZus{}iter}\PY{p}{,} \PY{n}{x}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{p}{)}
+ \PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{xrange}\PY{p}{(}\PY{n}{n\PYZus{}iter}\PY{p}{)}\PY{p}{:}
+ \PY{n}{indices} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{random}\PY{o}{.}\PY{n}{choice}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{y}\PY{p}{)}\PY{p}{,} \PY{n}{replace}\PY{o}{=}\PY{n+nb+bp}{False}\PY{p}{,} \PY{n}{size}\PY{o}{=}\PY{n+nb}{int}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{y}\PY{p}{)}\PY{o}{*}\PY{o}{.}\PY{l+m+mi}{9}\PY{p}{)}\PY{p}{)}
+ \PY{n}{rval}\PY{p}{[}\PY{n}{i}\PY{p}{]} \PY{o}{=} \PY{n}{infer}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{n}{indices}\PY{p}{]}\PY{p}{,} \PY{n}{y}\PY{p}{[}\PY{n}{indices}\PY{p}{]}\PY{p}{)}
+ \PY{k}{return} \PY{n}{rval}
+
+
+\PY{k}{def} \PY{n+nf}{confidence\PYZus{}interval}\PY{p}{(}\PY{n}{counts}\PY{p}{,} \PY{n}{bins}\PY{p}{)}\PY{p}{:}
+ \PY{n}{k} \PY{o}{=} \PY{l+m+mi}{0}
+ \PY{k}{while} \PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{n}{counts}\PY{p}{[}\PY{n+nb}{len}\PY{p}{(}\PY{n}{counts}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{o}{\PYZhy{}}\PY{n}{k}\PY{p}{:}\PY{n+nb}{len}\PY{p}{(}\PY{n}{counts}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{o}{+}\PY{n}{k}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZlt{}}\PY{o}{=} \PY{o}{.}\PY{l+m+mi}{95}\PY{o}{*}\PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{n}{counts}\PY{p}{)}\PY{p}{:}
+ \PY{n}{k} \PY{o}{+}\PY{o}{=} \PY{l+m+mi}{1}
+ \PY{k}{return} \PY{n}{bins}\PY{p}{[}\PY{n+nb}{len}\PY{p}{(}\PY{n}{bins}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{o}{\PYZhy{}}\PY{n}{k}\PY{p}{]}\PY{p}{,} \PY{n}{bins}\PY{p}{[}\PY{n+nb}{len}\PY{p}{(}\PY{n}{bins}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{o}{+}\PY{n}{k}\PY{p}{]}
+
+
+\PY{k}{def} \PY{n+nf}{build\PYZus{}matrix}\PY{p}{(}\PY{n}{cascades}\PY{p}{,} \PY{n}{node}\PY{p}{)}\PY{p}{:}
+
+ \PY{k}{def} \PY{n+nf}{aux}\PY{p}{(}\PY{n}{cascade}\PY{p}{,} \PY{n}{node}\PY{p}{)}\PY{p}{:}
+ \PY{n}{xlist}\PY{p}{,} \PY{n}{slist} \PY{o}{=} \PY{n+nb}{zip}\PY{p}{(}\PY{o}{*}\PY{n}{cascade}\PY{p}{)}
+ \PY{n}{indices} \PY{o}{=} \PY{p}{[}\PY{n}{i} \PY{k}{for} \PY{n}{i}\PY{p}{,} \PY{n}{s} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{slist}\PY{p}{)} \PY{k}{if} \PY{n}{s}\PY{p}{[}\PY{n}{node}\PY{p}{]} \PY{o+ow}{and} \PY{n}{i} \PY{o}{\PYZgt{}}\PY{o}{=} \PY{l+m+mi}{1}\PY{p}{]}
+ \PY{k}{if} \PY{n}{indices}\PY{p}{:}
+ \PY{n}{x} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{vstack}\PY{p}{(}\PY{n}{xlist}\PY{p}{[}\PY{n}{i}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]} \PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n}{indices}\PY{p}{)}
+ \PY{n}{y} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{n}{xlist}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{[}\PY{n}{node}\PY{p}{]} \PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n}{indices}\PY{p}{]}\PY{p}{)}
+ \PY{k}{return} \PY{n}{x}\PY{p}{,} \PY{n}{y}
+ \PY{k}{else}\PY{p}{:}
+ \PY{k}{return} \PY{n+nb+bp}{None}
+
+ \PY{n}{pairs} \PY{o}{=} \PY{p}{(}\PY{n}{aux}\PY{p}{(}\PY{n}{cascade}\PY{p}{,} \PY{n}{node}\PY{p}{)} \PY{k}{for} \PY{n}{cascade} \PY{o+ow}{in} \PY{n}{cascades}\PY{p}{)}
+ \PY{n}{xs}\PY{p}{,} \PY{n}{ys} \PY{o}{=} \PY{n+nb}{zip}\PY{p}{(}\PY{o}{*}\PY{p}{(}\PY{n}{pair} \PY{k}{for} \PY{n}{pair} \PY{o+ow}{in} \PY{n}{pairs} \PY{k}{if} \PY{n}{pair}\PY{p}{)}\PY{p}{)}
+ \PY{n}{x} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{vstack}\PY{p}{(}\PY{n}{xs}\PY{p}{)}
+ \PY{n}{y} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{concatenate}\PY{p}{(}\PY{n}{ys}\PY{p}{)}
+ \PY{k}{return} \PY{n}{x}\PY{p}{,} \PY{n}{y}
+
+
+\PY{k}{def} \PY{n+nf}{build\PYZus{}cascade\PYZus{}list}\PY{p}{(}\PY{n}{cascades}\PY{p}{)}\PY{p}{:}
+ \PY{n}{x}\PY{p}{,} \PY{n}{s} \PY{o}{=} \PY{p}{[}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{p}{]}
+ \PY{k}{for} \PY{n}{cascade} \PY{o+ow}{in} \PY{n}{cascades}\PY{p}{:}
+ \PY{n}{xlist}\PY{p}{,} \PY{n}{slist} \PY{o}{=} \PY{n+nb}{zip}\PY{p}{(}\PY{o}{*}\PY{n}{cascade}\PY{p}{)}
+ \PY{n}{x}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{xlist}\PY{p}{)}
+ \PY{n}{s}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{slist}\PY{p}{)}
+ \PY{k}{return} \PY{n}{x}\PY{p}{,} \PY{n}{s}
+
+
+\PY{k}{def} \PY{n+nf}{simulate\PYZus{}cascade}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{graph}\PY{p}{)}\PY{p}{:}
+ \PY{l+s+sd}{\PYZdq{}\PYZdq{}\PYZdq{}}
+\PY{l+s+sd}{ Simulate an IC cascade given a graph and initial state.}
+
+\PY{l+s+sd}{ For each time step we yield:}
+\PY{l+s+sd}{ \PYZhy{} susc: the nodes susceptible at the beginning of this time step}
+\PY{l+s+sd}{ \PYZhy{} x: the subset of susc who became infected}
+\PY{l+s+sd}{ \PYZdq{}\PYZdq{}\PYZdq{}}
+ \PY{n}{susc} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{n}{graph}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{n}{dtype}\PY{o}{=}\PY{n+nb}{bool}\PY{p}{)} \PY{c}{\PYZsh{} t=0, everyone is susceptible}
+ \PY{k}{yield} \PY{n}{x}\PY{p}{,} \PY{n}{susc}
+ \PY{k}{while} \PY{n}{np}\PY{o}{.}\PY{n}{any}\PY{p}{(}\PY{n}{x}\PY{p}{)}\PY{p}{:}
+ \PY{n}{susc} \PY{o}{=} \PY{n}{susc} \PY{o}{\PYZca{}} \PY{n}{x} \PY{c}{\PYZsh{} nodes infected at previous step are now inactive}
+ \PY{k}{if} \PY{o+ow}{not} \PY{n}{np}\PY{o}{.}\PY{n}{any}\PY{p}{(}\PY{n}{susc}\PY{p}{)}\PY{p}{:}
+ \PY{k}{break}
+ \PY{n}{x} \PY{o}{=} \PY{l+m+mi}{1} \PY{o}{\PYZhy{}} \PY{n}{np}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{n}{np}\PY{o}{.}\PY{n}{dot}\PY{p}{(}\PY{n}{graph}\PY{o}{.}\PY{n}{T}\PY{p}{,} \PY{n}{x}\PY{p}{)}\PY{p}{)}
+ \PY{n}{y} \PY{o}{=} \PY{n}{nr}\PY{o}{.}\PY{n}{random}\PY{p}{(}\PY{n}{x}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
+ \PY{n}{x} \PY{o}{=} \PY{p}{(}\PY{n}{x} \PY{o}{\PYZgt{}}\PY{o}{=} \PY{n}{y}\PY{p}{)} \PY{o}{\PYZam{}} \PY{n}{susc}
+ \PY{k}{yield} \PY{n}{x}\PY{p}{,} \PY{n}{susc}
+
+
+\PY{k}{def} \PY{n+nf}{uniform\PYZus{}source}\PY{p}{(}\PY{n}{graph}\PY{p}{)}\PY{p}{:}
+ \PY{n}{x0} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{graph}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{n}{dtype}\PY{o}{=}\PY{n+nb}{bool}\PY{p}{)}
+ \PY{n}{x0}\PY{p}{[}\PY{n}{nr}\PY{o}{.}\PY{n}{randint}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{n}{graph}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}\PY{p}{]} \PY{o}{=} \PY{n+nb+bp}{True}
+ \PY{k}{return} \PY{n}{x0}
+
+
+\PY{k}{def} \PY{n+nf}{simulate\PYZus{}cascades}\PY{p}{(}\PY{n}{n}\PY{p}{,} \PY{n}{graph}\PY{p}{,} \PY{n}{source}\PY{o}{=}\PY{n}{uniform\PYZus{}source}\PY{p}{)}\PY{p}{:}
+ \PY{k}{for} \PY{n}{\PYZus{}} \PY{o+ow}{in} \PY{n+nb}{xrange}\PY{p}{(}\PY{n}{n}\PY{p}{)}\PY{p}{:}
+ \PY{n}{x0} \PY{o}{=} \PY{n}{source}\PY{p}{(}\PY{n}{graph}\PY{p}{)}
+ \PY{k}{yield} \PY{n}{simulate\PYZus{}cascade}\PY{p}{(}\PY{n}{x0}\PY{p}{,} \PY{n}{graph}\PY{p}{)}
+
+
+\PY{k}{if} \PY{n}{\PYZus{}\PYZus{}name\PYZus{}\PYZus{}} \PY{o}{==} \PY{l+s}{\PYZdq{}}\PY{l+s}{\PYZus{}\PYZus{}main\PYZus{}\PYZus{}}\PY{l+s}{\PYZdq{}}\PY{p}{:}
+ \PY{c}{\PYZsh{} g = np.array([[0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 0]])}
+ \PY{n}{g} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mf}{0.5}\PY{p}{]}\PY{p}{,} \PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{]}\PY{p}{]}\PY{p}{)}
+ \PY{n}{p} \PY{o}{=} \PY{l+m+mf}{0.5}
+ \PY{n}{g} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{log}\PY{p}{(}\PY{l+m+mf}{1.} \PY{o}{/} \PY{p}{(}\PY{l+m+mi}{1} \PY{o}{\PYZhy{}} \PY{n}{p} \PY{o}{*} \PY{n}{g}\PY{p}{)}\PY{p}{)}
+ \PY{c}{\PYZsh{} error = []}
+
+ \PY{k}{def} \PY{n+nf}{source}\PY{p}{(}\PY{n}{graph}\PY{p}{,} \PY{n}{t}\PY{p}{)}\PY{p}{:}
+ \PY{n}{x0} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{graph}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{n}{dtype}\PY{o}{=}\PY{n+nb}{bool}\PY{p}{)}
+ \PY{n}{a} \PY{o}{=} \PY{n}{randint}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
+ \PY{n}{x0}\PY{p}{[}\PY{n}{a}\PY{p}{]} \PY{o}{=} \PY{n+nb+bp}{True}
+ \PY{k}{if} \PY{n}{random}\PY{p}{(}\PY{p}{)} \PY{o}{\PYZgt{}} \PY{n}{t}\PY{p}{:}
+ \PY{n}{x0}\PY{p}{[}\PY{l+m+mi}{1}\PY{o}{\PYZhy{}}\PY{n}{a}\PY{p}{]} \PY{o}{=} \PY{n+nb+bp}{True}
+ \PY{k}{return} \PY{n}{x0}
+
+ \PY{n}{thresh} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{arange}\PY{p}{(}\PY{l+m+mf}{0.}\PY{p}{,} \PY{l+m+mf}{1.1}\PY{p}{,} \PY{n}{step}\PY{o}{=}\PY{l+m+mf}{0.2}\PY{p}{)}
+ \PY{n}{sizes} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{arange}\PY{p}{(}\PY{l+m+mi}{10}\PY{p}{,} \PY{l+m+mi}{100}\PY{p}{,} \PY{n}{step}\PY{o}{=}\PY{l+m+mi}{10}\PY{p}{)}
+ \PY{n}{nsimul} \PY{o}{=} \PY{l+m+mi}{10}
+ \PY{n}{r} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{sizes}\PY{p}{)}\PY{p}{,} \PY{n+nb}{len}\PY{p}{(}\PY{n}{thresh}\PY{p}{)}\PY{p}{)}
+ \PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{thresh}\PY{p}{:}
+ \PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n}{nsimul}\PY{p}{:}
+ \PY{n}{cascades} \PY{o}{=} \PY{n}{simulate\PYZus{}cascades}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{n}{sizes}\PY{p}{)}\PY{p}{,} \PY{n}{g}\PY{p}{,}
+ \PY{n}{source}\PY{o}{=}\PY{k}{lambda} \PY{n}{graph}\PY{p}{:} \PY{n}{source}\PY{p}{(}\PY{n}{graph}\PY{p}{,} \PY{n}{t}\PY{p}{)}\PY{p}{)}
+ \PY{n}{e} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{g}\PY{o}{.}\PY{n}{shape}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{)}
+ \PY{k}{for} \PY{n}{j}\PY{p}{,} \PY{n}{s} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{sizes}\PY{p}{)}\PY{p}{:}
+ \PY{n}{x}\PY{p}{,} \PY{n}{y} \PY{o}{=} \PY{n}{build\PYZus{}matrix}\PY{p}{(}\PY{n}{cascades}\PY{p}{,} \PY{l+m+mi}{2}\PY{p}{)}
+ \PY{n}{e} \PY{o}{+}\PY{o}{=} \PY{n}{infer}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{p}{:}\PY{n}{s}\PY{p}{]}\PY{p}{,} \PY{n}{y}\PY{p}{[}\PY{p}{:}\PY{n}{s}\PY{p}{]}\PY{p}{)}
+
+ \PY{k}{for} \PY{n}{i}\PY{p}{,} \PY{n}{t} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{thresh}\PY{p}{)}\PY{p}{:}
+ \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{sizes}\PY{p}{,} \PY{n}{m}\PY{p}{[}\PY{p}{:}\PY{p}{,} \PY{n}{i}\PY{p}{]}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{n+nb}{str}\PY{p}{(}\PY{n}{t}\PY{p}{)}\PY{p}{)}
+ \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{)}
+ \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)}
+
+
+ \PY{c}{\PYZsh{} conf = bootstrap(x, y, n\PYZus{}iter=100)}
+ \PY{c}{\PYZsh{} estimand = np.linalg.norm(np.delete(conf \PYZhy{} g[0], 0, axis=1), axis=1)}
+ \PY{c}{\PYZsh{} error.append(confidence\PYZus{}interval(*np.histogram(estimand, bins=50)))}
+ \PY{c}{\PYZsh{} plt.semilogx(sizes, error)}
+ \PY{c}{\PYZsh{} plt.show()}
+\end{Verbatim}
diff --git a/simulation/main.py b/simulation/main.py
index bdc5c97..e4b30f2 100644
--- a/simulation/main.py
+++ b/simulation/main.py
@@ -125,22 +125,34 @@ if __name__ == "__main__":
g = np.array([[0, 0, 1], [0, 0, 0.5], [0, 0, 0]])
p = 0.5
g = np.log(1. / (1 - p * g))
- sizes = [100, 500, 1000, 5000, 10000]
# error = []
- def source(graph):
+ def source(graph, t):
x0 = np.zeros(graph.shape[0], dtype=bool)
a = randint(0, 1)
x0[a] = True
- if random() > 0.01:
+ if random() > t:
x0[1-a] = True
return x0
- for i in sizes:
- cascades = simulate_cascades(i, g, source=source)
- x, y = build_matrix(cascades, 2)
- e = infer(x, y)
- print e
+ thresh = np.arange(0., 1.1, step=0.2)
+ sizes = np.arange(10, 100, step=10)
+ nsimul = 10
+ r = np.zeros(len(sizes), len(thresh))
+ for t in thresh:
+ for i in nsimul:
+ cascades = simulate_cascades(np.max(sizes), g,
+ source=lambda graph: source(graph, t))
+ e = np.zeros(g.shape[0])
+ for j, s in enumerate(sizes):
+ x, y = build_matrix(cascades, 2)
+ e += infer(x[:s], y[:s])
+
+ for i, t in enumerate(thresh):
+ plt.plot(sizes, m[:, i], label=str(t))
+ plt.legend()
+ plt.show()
+
# conf = bootstrap(x, y, n_iter=100)
# estimand = np.linalg.norm(np.delete(conf - g[0], 0, axis=1), axis=1)
generated by cgit v1.2.3-70-g09d2 (git 2.52.0) at 2025-12-21 13:14:11 +0000