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@ -152,6 +152,7 @@
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\end{figure}
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\begin{itemize}
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\item DAGP with $K=2$ processes, one white noise process and one GP with an RBF kernel
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\smallskip
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\item DAGP yields an explicit separation into outliers and signal for the training data
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\end{itemize}
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\end{block}
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@ -168,11 +169,12 @@
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\begin{itemize}
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\item Given a data association problem, DAGP simultaneously learns
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\begin{itemize}
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\normalsize
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\item independent models $(\mat{F}^{\pix{k}}, \mat{Y}^{\pix{k}})$ for the $K$ processes
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\item concrete assignments $\mat{A}$ of the training data to these processes
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\item a factorization of the input space with respect to the relative importance $\mat{\alpha}$ of these processes
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\end{itemize}
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% \smallskip
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\smallskip
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\item DAGP's marginal likelihood combines $K$ regression problems and a classification problem
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\begin{align}
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\Prob*{\mat{Y} \given \mat{X}} &=
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@ -191,6 +193,7 @@
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\end{align}
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\end{itemize}
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\end{block}
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\vspace*{-1ex}
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\begin{block}{Scalable inference}
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\begin{itemize}
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\item Learning based on doubly stochastic variational inference by \textcite{salimbeni_doubly_2017}
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@ -202,7 +205,9 @@
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\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}}}}
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\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}}}}.
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\end{align}
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\item We use a continuous relaxation of the assignment problem using concrete random variables in $\Variat{\mat{A}}$
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\smallskip
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\item We use a continuous relaxation of the assignment problem with concrete random variables in $\Variat{\mat{A}}$
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\smallskip
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\item The joint variational bound is given by
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\begin{align}
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\Ell_{\text{DAGP}}
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@ -212,6 +217,7 @@
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&\quad - \sum_{k=1}^K \KL*{\Variat*{\mat{u^{\pix{k}}}}}{\Prob*{\mat{u^{\pix{k}}} \given \mat{Z^{\pix{k}}}}}
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- \sum_{k=1}^K \KL*{\Variat*{\mat{u_\alpha^{\pix{k}}}}}{\Prob*{\mat{u_\alpha^{\pix{k}}} \given \mat{Z_\alpha^{\pix{k}}}}}
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\end{align}
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\smallskip
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\item This bound can be sampled efficiently and factorizes along the data allowing for mini-batches
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\smallskip
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\item The predictive posterior can be efficiently approximated via sampling
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@ -227,7 +233,7 @@
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\separatorcolumn
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%
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\begin{column}{\colwidth}
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\begin{block}{Wet-Chicken RL benchmark}
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\begin{block}{Reinforcement Learning}
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\centering
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\includestandalonewithpath{figures/wetchicken}
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\end{block}
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