Browse Source

Fix typos

icml
Markus Kaiser 3 years ago
parent
commit
2b8351c113
  1. BIN
      dynamic_dirichlet_deep_gp.pdf
  2. 14
      dynamic_dirichlet_deep_gp.tex

BIN
dynamic_dirichlet_deep_gp.pdf

Binary file not shown.

14
dynamic_dirichlet_deep_gp.tex

@ -18,13 +18,13 @@
\addbibresource{additional.bib}
% We set this for hyperref
\title{Data Assocication using Gaussian Processes}
\title{Data Association using Gaussian Processes}
% \author{\href{mailto:markus.kaiser@siemens.com}{Markus Kaiser}}
\author{Anonymous}
\begin{document}
\twocolumn[
\icmltitle{Data Assocication using Gaussian Processes}
\icmltitle{Data Association using Gaussian Processes}
% NOTE(mrksr): We leave anonymous information here for now.
\begin{icmlauthorlist}
@ -92,12 +92,12 @@ We describe this non-stationary structure using additional Gaussian process prio
This leads to a flexible yet interpretable model with a principled treatment of uncertainty.
The paper has the following contributions:
In \cref{sec:model}, we propose the data assocication using Gaussian Processes model (DAGP).
In \cref{sec:model}, we propose the data association using Gaussian Processes model (DAGP).
In \cref{sec:variational_approximation}, we present an efficient learning scheme via a variational approximation which allows us to simultaneously train all parts of our model via stochastic optimization and how the same learning scheme can be applied to deep Gaussian process priors.
We demonstrate our model on a noise separation problem, an artificial multimodal data set, and a multimodal regression problem based on the cart-pole benchmark in \cref{sec:experiments}.
We demonstrate our model on a noise separation problem, an artificial multimodal data set, and a multi-regime regression problem based on the cart-pole benchmark in \cref{sec:experiments}.
\section{Data Assocication using Gaussian Processes}
\section{Data Association using Gaussian Processes}
\label{sec:model}
\begin{figure}[t]
\centering
@ -478,9 +478,9 @@ While the function has still been identified well, some of the noise is also exp
\subsection{Multimodal Data}
\label{subsec:semi_bimodal}
Our second experiment applies DAGP to a multimadal data set.
Our second experiment applies DAGP to a multimodal data set.
The data, together with recovered posterior attributions, can be seen in \cref{fig:semi_bimodal}.
We uniformly sample 350 data points in the interval $x \in [-2\pi, 2\pi]$ and obtaine $y_1 = \Fun{\sin}{x} + \epsilon$, $y_2 = \Fun{\sin}{x} - 2 \Fun{\exp}{-\sfrac{1}{2} \cdot (x-2)^2} + \epsilon$ and $y_3 = -1 - \sfrac{3}{8\pi} \cdot x + \sfrac{3}{10} \cdot \Fun*{\sin}{2x} + \epsilon$ with additive independent noise $\epsilon \sim \Gaussian*{0, 0.005^2}$.
We uniformly sample 350 data points in the interval $x \in [-2\pi, 2\pi]$ and obtain $y_1 = \Fun{\sin}{x} + \epsilon$, $y_2 = \Fun{\sin}{x} - 2 \Fun{\exp}{-\sfrac{1}{2} \cdot (x-2)^2} + \epsilon$ and $y_3 = -1 - \sfrac{3}{8\pi} \cdot x + \sfrac{3}{10} \cdot \Fun*{\sin}{2x} + \epsilon$ with additive independent noise $\epsilon \sim \Gaussian*{0, 0.005^2}$.
The resulting data set $\D = \Set{\left( x, y_1 \right), \left( x, y_2 \right), \left( x, y_3 \right)}$ is trimodal in the interval $[0, 5]$ and is otherwise bimodal with one mode containing double the amount of data than the other.
We use squared exponential kernels as priors for both the $f^{\pix{k}}$ and $\alpha^{\pix{k}}$ and $25$ inducing points in every GP.

Loading…
Cancel
Save