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authorjeanpouget-abadie <jean.pougetabadie@gmail.com>2015-12-03 12:04:59 -0500
committerjeanpouget-abadie <jean.pougetabadie@gmail.com>2015-12-03 12:04:59 -0500
commit80a683b0b879be707b8d8b92e5e73fb1d887d842 (patch)
tree0aa1ed9da54ea0da70dd881d01d15b2ab21bde84
parent5f82a47d7ad642b05d089ca43811aba3a233b224 (diff)
downloadcascades-80a683b0b879be707b8d8b92e5e73fb1d887d842.tar.gz
more poster
-rw-r--r--poster/Finale_poster/poster.tex97
1 files changed, 16 insertions, 81 deletions
diff --git a/poster/Finale_poster/poster.tex b/poster/Finale_poster/poster.tex
index 63219a7..5da0c80 100644
--- a/poster/Finale_poster/poster.tex
+++ b/poster/Finale_poster/poster.tex
@@ -1,4 +1,4 @@
-\documentclass[final, 10]{beamer}
+\documentclass[final, 12]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[scale=1.6]{beamerposter} % Use the beamerposter package for laying
\usetheme{confposter} % Use the confposter theme supplied with this template
@@ -101,9 +101,13 @@
\centering
\includegraphics[scale=3]{graphical.pdf}
\end{figure}
+\begin{itemize}
+ \item $\phi$: fixed source distribution
+ \item capture uncertainty on each edge
+ \item encode expressive graph priors (tied parameters)
+\end{itemize}
\end{block}
-
\end{column} % End of the first column
%-----------------------------------------------------------------------------
@@ -111,91 +115,22 @@
%-----------------------------------------------------------------------------
\begin{column}{\onecolwid} % The first column
+\begin{block}{Active Learning}
+ \emph{Can we gain by choosing the source node? If so, how to best choose the
+ source node?}
-\end{column}
-%-----------------------------------------------------------------------------
-\begin{column}{\sepwid}\end{column}
-%-----------------------------------------------------------------------------
-
-\begin{column}{\onecolwid}
-
-\begin{block}{Sparse Recovery}
-
-\begin{itemize}
- \item Solving for $A x = b$ when $A$ is non-degenerate is possible if
- \begin{itemize}
- \item $A$ is {\bf almost invertible}
- \item $x$ is {\bf sparse}
- \end{itemize}
- \item If $x$ is solution to $\min L(x)$ where
- $L$ is convex, then~\cite{Negahban:2009}~solve for:
- \begin{equation*}
- \min_x L(x) + \lambda \| x\|
- \end{equation*}
-\end{itemize}
-\end{block}
-
-\begin{theorem}
- {\bf Assumptions}:
- \begin{itemize}
- \item $f$ and $1-f$ are log-concave with log-gradient bounded by
- $\frac{1}{\alpha}$
- \item $\nabla^2 {\cal L}$ verifies the $(S,\gamma)$-{\bf
- RE} condition
- \vspace{1cm}
-\end{itemize} {\bf Algorithm}:
- \begin{itemize}
- \item Solve MLE program with $\lambda = 2\sqrt{\frac{\log m}{\alpha n}}$
- \begin{framed}
- \begin{equation*}
- \hat \theta_i \in \arg \max_{\theta} {\cal L}_i(\theta_i | x^1,
- \dots x^n) - \lambda \|\theta_i\|_1
- \end{equation*}
- \end{framed}
- \end{itemize}
- \vspace{1cm}
- {\bf Guarantee}
- With high probability:
- \begin{framed}
- \begin{equation*}
- \|\hat \theta - \theta^*\|_2 \leq \frac{6}{\gamma} \sqrt{\frac{s \log
- m}{\alpha n}}
- \end{equation*}
- \end{framed}
- where $s$ is degree of node, $m$ is number of nodes, $n$ is the number of
- observations
-\end{theorem}
-
-\begin{block}{Restricted Eigenvalue Condition}
- {\bf Definition}
- \begin{itemize}
- \item $C(S) \equiv \{ X :\|X_{\bar S}\|_1 \leq 3 \|X\|_1\}$
- \item Matrix $A$ verifies the $(\gamma, S)$-{(\bf RE)} condition if:
- $$\forall X \in C({\cal S}), X^T A X \geq \gamma \|X\|_2^2$$
- \end{itemize}
-
- \vspace{1cm}
- {\bf Hessian $\mapsto$ Gram Matrix}
- \begin{itemize}
- \item If $f$ and $1-f$ are $c$-strictly log-convex, we can replace the
- condition on the $\nabla^2 {\cal L}$ by the same condition on the Gram
- matrix $X^T X$.
- \end{itemize}
- \vspace{1cm}
- {\bf Hessian $\mapsto$ Expected Hessian}
- \begin{itemize}
- \item If $\mathbb{E}[A]$ verifies the $(S, \gamma)$-{(\bf RE)} condition,
- then $A$ verifies the $(S, \gamma/2)$-{(\bf RE)}
- condition~\cite{vandegeer:2009}
- \end{itemize}
+ \begin{block}{Heuristic 1 (Baseline)}
+ \end{block}
+ \begin{block}{Heuristic 2}
+ \end{block}
\end{block}
-\end{column} % End of the second column
-
+\end{column}
%-----------------------------------------------------------------------------
-\begin{column}{\sepwid}\end{column} % Empty spacer column
+\begin{column}{\sepwid}\end{column}
%-----------------------------------------------------------------------------
+
\begin{column}{\onecolwid} % The third column
\begin{block}{Experimental validation}
\begin{figure}