Small fixes

Markus Kaiser 4 years ago
parent 334dd31194
commit 4ad2efa9bb

@ -45,7 +45,7 @@
\node[text width=25em] at (3.5, 0.6) {
\item[Dynamics] Agent in a flowing river
\item[Dynamics] Wet-Chicken 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 $\R^2$

@ -152,6 +152,7 @@
\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
@ -168,11 +169,12 @@
\item Given a data association problem, DAGP simultaneously learns
\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
% \smallskip
\item DAGP's marginal likelihood combines $K$ regression problems and a classification problem
\Prob*{\mat{Y} \given \mat{X}} &=
@ -191,6 +193,7 @@
\begin{block}{Scalable inference}
\item Learning based on doubly stochastic variational inference by \textcite{salimbeni_doubly_2017}
@ -202,7 +205,9 @@
\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}}}}.
\item We use a continuous relaxation of the assignment problem using concrete random variables in $\Variat{\mat{A}}$
\item We use a continuous relaxation of the assignment problem with concrete random variables in $\Variat{\mat{A}}$
\item The joint variational bound is given by
@ -212,6 +217,7 @@
&\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}}}}}
\item This bound can be sampled efficiently and factorizes along the data allowing for mini-batches
\item The predictive posterior can be efficiently approximated via sampling
@ -227,7 +233,7 @@
\begin{block}{Wet-Chicken RL benchmark}
\begin{block}{Reinforcement Learning}