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Add text to the poster

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Markus Kaiser 2 years ago
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  1. 4
      ecml-poster/figures/dynamics_posterior.tex
  2. 9
      ecml-poster/figures/wetchicken.tex
  3. 77
      ecml-poster/poster.tex

4
ecml-poster/figures/dynamics_posterior.tex

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\draw [very thick, dashed, sStoneLight, fill=sStone, fill opacity=.2]
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9
ecml-poster/figures/wetchicken.tex

@ -7,7 +7,7 @@
\begin{document}
\begin{tikzpicture}[
x=5.5em, y=7em,
x=5.5em, y=6.75em,
]
\tikzstyle{river} = [
@ -37,18 +37,19 @@
\includegraphics[height=2.5em]{\figurepath/chicken/hyper_chicken_standing.png}
}
\begin{scope}[shift={(1.25, 0)}]
\begin{scope}[shift={(1, 0)}]
\addriver
\node at (0.5, 0.5) {
\hyperchicken
};
\node[text width=15em] at (2.75, 0.5) {
\begin{description}[Dynamics]
\node[text width=25em] at (3.5, 0.6) {
\begin{description}[Challenges]
\item[Dynamics] Agent in a flowing river
\item[Goal] Get close to the waterfall
\item[State] $(x, y)$-position in $\R^2$
\item[Action] $(x, y)$-movement in $\R^2$
\item[Challenges] Multimodality and heteroskedasticity
\end{description}
};
\end{scope}

77
ecml-poster/poster.tex

@ -89,69 +89,70 @@
\separatorcolumn
%
\begin{column}{\colwidth}
\begin{block}{Multimodal Data}
\begin{block}{Multimodal data}
\begin{figure}
\centering
\begin{subfigure}{\textwidth}
\centering
\includestandalonewithpath{figures/semi_bimodal_data}
\caption{
Data
Multimodal dataset
}
\end{subfigure}\\[2ex]
\begin{subfigure}{\textwidth}
\centering
\includestandalonewithpath{figures/semi_bimodal_attribution}
\caption{
Attribution
Concrete assignments $\mat{A}$ learned for the training data
}
\end{subfigure}\\[2ex]
\begin{subfigure}{\textwidth}
\centering
\includestandalonewithpath{figures/semi_bimodal_joint}
\caption{
Joint
Joint predictions $\mat{Y}^{\pix{k}}$ of $K=4$ processes
}
\end{subfigure}\\[2ex]
\begin{subfigure}{\textwidth}
\centering
\includestandalonewithpath{figures/semi_bimodal_predictive_attribution}
\caption{
Attribution predictions
Assignment probabilities $\mat{\alpha}$ associated with these processes
}
\end{subfigure}
\end{figure}
\begin{itemize}
\item AMO-GP correctly recovers the latent shared function, warping and alignment
\item DAGP identifies the that three modes are sufficient, one of which is only relevant around $[0, 5]$
\end{itemize}
\end{block}
\begin{block}{Noise Separation}
\begin{block}{Noise separation}
\begin{figure}
\centering
\begin{subfigure}{\textwidth}
\centering
\includestandalonewithpath{figures/noise_separation_data}
\caption{
Data
Noise separation problem with 60\% outliers
}
\end{subfigure}\\[2ex]
\begin{subfigure}{\textwidth}
\centering
\includestandalonewithpath{figures/noise_separation_attribution}
\caption{
Attribution
Concrete assignments $\mat{A}$ learned for the training data
}
\end{subfigure}\\[2ex]
\begin{subfigure}{\textwidth}
\centering
\includestandalonewithpath{figures/noise_separation_joint}
\caption{
Joint
Joint predictions $\mat{Y}^{\pix{k}}$ of $K=2$ processes
}
\end{subfigure}
\end{figure}
\begin{itemize}
\item AMO-GP correctly recovers the latent shared function, warping and alignment
\item DAGP with $K=2$ processes, one white noise process and one GP with an RBF kernel
\item DAGP yields an explicit separation into outliers and signal for the training data
\end{itemize}
\end{block}
\end{column}
@ -159,15 +160,20 @@
\separatorcolumn
%
\begin{column}{\colwidth}
\begin{block}{Modelling Assumptions of DAGP}
\begin{block}{Modelling assumptions of DAGP}
\begin{figure}
\centering
\includestandalonewithpath{figures/graphical_model}
\end{figure}
\begin{itemize}
\item AMO-GP connects multiple deep GPs via a shared layer which is a multi-output GP
\smallskip
\item Marginal Likelihood
\item Given a data association problem, DAGP simultaneously learns
\begin{itemize}
\item independent models $(\mat{F}^{\pix{k}}, \mat{Y}^{\pix{k}})$ for the $K$ processes
\item concrete assignments $\mat{A}$ of the training data to these processes
\item a factorization of the input space with respect to the relative importance $\mat{\alpha}$ of these processes
\end{itemize}
% \smallskip
\item DAGP's marginal likelihood combines $K$ regression problems and a classification problem
\begin{align}
\Prob*{\mat{Y} \given \mat{X}} &=
\int
@ -185,29 +191,19 @@
\end{align}
\end{itemize}
\end{block}
\begin{block}{Scalable Inference}
\begin{block}{Scalable inference}
\begin{itemize}
\item Application to non-linear time series alignment with very noisy observations
\item Learning based on doubly stochastic variational inference by \textcite{salimbeni_doubly_2017}
\smallskip
\item Variational distribution
\item We add variational inducing variables $\Variat*{\rv{u} \given \mat{Z}} \sim \Gaussian*{\rv{u} \given \mat{m}, \mat{S}}$ with the factorization
\begin{align}
\Variat*{\mat{F}, \mat{\alpha}, \mat{U}}
&= \Variat*{\mat{\alpha}, \Set*{\mat{F^{\pix{k}}}, \mat{u^{\pix{k}}}, \mat{u_\alpha^{\pix{k}}}}_{k=1}^K} \\
\MoveEqLeft = \prod_{k=1}^K\prod_{n=1}^N \Prob*{\mat{\alpha_n^{\pix{k}}} \given \mat{u_\alpha^{\pix{k}}}, \mat{x_n}}\Variat*{\mat{u_\alpha^{\pix{k}}}}
\prod_{k=1}^K \prod_{n=1}^N \Prob*{\mat{f_n^{\pix{k}}} \given \mat{u^{\pix{k}}}, \mat{x_n}}\Variat*{\mat{u^{\pix{k}}}}.
\end{align}
\smallskip
\item Variational joint
\begin{align}
\Variat*{\mat{Y}, \mat{A}} &=
\int
\Prob*{\mat{Y} \given \mat{F}, \mat{A}}
\Prob*{\mat{A} \given \mat{\alpha}}
\Variat*{\mat{F}, \mat{\alpha}}
\diff \mat{F} \diff \mat{\alpha},
\end{align}
\smallskip
\item Variational bound
\item We use a continuous relaxation of the assignment problem using concrete random variables in $\Variat{\mat{A}}$
\item The joint variational bound is given by
\begin{align}
\Ell_{\text{DAGP}}
&= \Moment*{\E_{\Variat*{\mat{F}, \mat{\alpha}, \mat{U}}}}{\log\frac{\Prob*{\mat{Y}, \mat{A}, \mat{F}, \mat{\alpha}, \mat{U} \given \mat{X}}}{\Variat*{\mat{F}, \mat{\alpha}, \mat{U}}}} \\
@ -216,8 +212,9 @@
&\quad - \sum_{k=1}^K \KL*{\Variat*{\mat{u^{\pix{k}}}}}{\Prob*{\mat{u^{\pix{k}}} \given \mat{Z^{\pix{k}}}}}
- \sum_{k=1}^K \KL*{\Variat*{\mat{u_\alpha^{\pix{k}}}}}{\Prob*{\mat{u_\alpha^{\pix{k}}} \given \mat{Z_\alpha^{\pix{k}}}}}
\end{align}
\item This bound can be sampled efficiently and factorizes along the data allowing for mini-batches
\smallskip
\item Predictive posterior
\item The predictive posterior can be efficiently approximated via sampling
\begin{align}
\Variat*{\mat{f_\ast} \given \mat{x_\ast}}
&= \int \sum_{k=1}^K \Variat*{a_\ast^{\pix{k}} \given \mat{x_\ast}} \Variat*{\mat{f_\ast^{\pix{k}}} \given \mat{x_\ast}} \diff \mat{a_\ast^{\pix{k}}} \\
@ -230,27 +227,28 @@
\separatorcolumn
%
\begin{column}{\colwidth}
\begin{block}{Wet-Chicken RL Benchmark}
\begin{block}{Wet-Chicken RL benchmark}
\centering
\includestandalonewithpath{figures/wetchicken}
\end{block}
\begin{block}{Interpretable Transition Model}
\begin{block}{Interpretable transition model}
\begin{figure}
\centering
\includestandalonewithpath{figures/dynamics_posterior}
\end{figure}
\begin{itemize}
\item AMO-GP correctly recovers the latent shared function, warping and alignment
\item DAGP's model structure yields interpretable sub-models using only abstract prior knowledge
\end{itemize}
\end{block}
\begin{block}{Conservative Policy}
\vspace*{-1ex}
\begin{block}{Conservative policy}
\begin{figure}
\centering
\begin{subfigure}{.475\textwidth}
\centering
\includestandalonewithpath{figures/policy_quiver}
\caption{
$\Fun*{R}{x, y} = x$
Policy using standard reward
}
\end{subfigure}
\hfill
@ -258,12 +256,15 @@
\centering
\includestandalonewithpath{figures/conservative_policy_quiver}
\caption{
$\Fun*{R^\prime}{x, y} = \Fun*{R}{x, y} - 5 \cdot \Prob{\text{drop} \given x, y}$
Policy using conservative reward
}
\end{subfigure}
\end{figure}
\begin{itemize}
\item AMO-GP correctly recovers the latent shared function, warping and alignment
\item The sub-models of the DAGP transition model can be used for reward shaping to avoid drops
\begin{align}
\Fun*{R_{\text{conservative}}}{x, y} = \Fun*{R_{\text{original}}}{x, y} - 5 \cdot \Prob{\text{drop} \given x, y}
\end{align}
\end{itemize}
\end{block}
\end{column}

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