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| author | jeanpouget-abadie <jean.pougetabadie@gmail.com> | 2015-12-03 12:04:59 -0500 |
|---|---|---|
| committer | jeanpouget-abadie <jean.pougetabadie@gmail.com> | 2015-12-03 12:04:59 -0500 |
| commit | 80a683b0b879be707b8d8b92e5e73fb1d887d842 (patch) | |
| tree | 0aa1ed9da54ea0da70dd881d01d15b2ab21bde84 | |
| parent | 5f82a47d7ad642b05d089ca43811aba3a233b224 (diff) | |
| download | cascades-80a683b0b879be707b8d8b92e5e73fb1d887d842.tar.gz | |
more poster
| -rw-r--r-- | poster/Finale_poster/poster.tex | 97 |
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} |
