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Move new refrences to own bib file; Fix broken equation

arxiv-v1
Markus Kaiser 10 meses atrás
pai
commit
054ae720de
3 arquivos alterados com 29 adições e 41 exclusões
  1. 17
    0
      additional.bib
  2. 12
    24
      dynamic_dirichlet_deep_gp.tex
  3. 0
    17
      zotero_export.bib

+ 17
- 0
additional.bib Ver arquivo

@@ -0,0 +1,17 @@
@book{Bar-Shalom:1987,
author = {Bar-Shalom, Y.},
title = {Tracking and Data Association},
year = {1987},
isbn = {0-120-79760-7},
publisher = {Academic Press Professional, Inc.},
address = {San Diego, CA, USA},
}

@ARTICLE{Cox93areview,
author = {Ingemar J. Cox},
title = {A Review of Statistical Data Association Techniques for Motion Correspondence},
journal = {International Journal of Computer Vision},
year = {1993},
volume = {10},
pages = {53--66}
}

+ 12
- 24
dynamic_dirichlet_deep_gp.tex Ver arquivo

@@ -15,6 +15,7 @@
% \overfullrule=5pt

\addbibresource{zotero_export.bib}
\addbibresource{additional.bib}

% We set this for hyperref
\title{Multimodal Deep Gaussian Processes}
@@ -65,34 +66,21 @@ We further denote the evaluation of the $\nth{k}$ latent function associated wit
For consistency, we refer to the $\nth{k}$ entry in $\mat{a_n}$ as $a_n^{\pix{k}}$ and also collect these values as $\mat{A} = \left(\mat{a_1}, \ldots, \mat{a_N}\right)$.

Given the notation above, the marginal likelihood of the MDGP can be separated in the likelihood, the latent function processes and the assignment process and is given by,
%% \begin{align}
%% \begin{split}
%% \label{eq:true_marginal_likelihood}
%% \Prob*{\mat{Y} \given \mat{X}} &= \\
%% \MoveEqLeft\int
%% \Prob*{\mat{Y} \given \mat{F}, \mat{A}}
%% \Prob*{\mat{F} \given \mat{X}}
%% \Prob*{\mat{A} \given \mat{X}}
%% \diff \mat{A} \diff \mat{F}\text{,} \\
%% \Prob*{\mat{Y} \given \mat{F}, \mat{A}} &= \\
%% \MoveEqLeft\prod_{n=1}^N\prod_{k=1}^K
%% \Gaussian*{\mat{y_n} \given \given \mat{f_n^{\pix{k}}}, \left(\sigma^{\pix{k}}\right)^2}^{\Fun{\Ind}{a_n^{\pix{k}} = 1}},
%% \end{split}
%% \end{align}

\begin{multiline}\label{eq:true_marginal_likelihood}
\Prob*{\mat{Y} \given \mat{X}} =
\begin{align}
\begin{split}
\label{eq:true_marginal_likelihood}
\Prob*{\mat{Y} \given \mat{X}} &= \\
\MoveEqLeft\int
\Prob*{\mat{Y} \given \mat{F}, \mat{A}}
\Prob*{\mat{F} \given \mat{X}}
\Prob*{\mat{A} \given \mat{X}}
\diff \mat{A} \diff \mat{F}\text{,}
\\
\Prob*{\mat{Y} \given \mat{F}, \mat{A}} =
\diff \mat{A} \diff \mat{F}\text{,} \\
\Prob*{\mat{Y} \given \mat{F}, \mat{A}} &= \\
\MoveEqLeft\prod_{n=1}^N\prod_{k=1}^K
\Gaussian*{\mat{y_n} \given \given \mat{f_n^{\pix{k}}}, \left(\sigma^{\pix{k}}\right)^2}^{\Fun{\Ind}{a_n^{\pix{k}} = 1}},
\end{multiline}
where $\sigma^{\pix{k}}$ is the noise level of the $\nth{k}$ Gaussian likelihood and $\Fun{\Ind}$ is the indicator function.
\Gaussian*{\mat{y_n} \given \mat{f_n^{\pix{k}}}, \left(\sigma^{\pix{k}}\right)^2}^{\Fun{\Ind}{a_n^{\pix{k}} = 1}},
\end{split}
\end{align}
where $\sigma^{\pix{k}}$ is the noise level of the $\nth{k}$ Gaussian likelihood and $\Ind$ is the indicator function.

Since we assume the $K$ modes to be independent given the data and assignments, we place independent GP priors on the latent functions,
\begin{align}

+ 0
- 17
zotero_export.bib Ver arquivo

@@ -296,20 +296,3 @@
url = {http://papers.nips.cc/paper/1900-mixtures-of-gaussian-processes.pdf},
urldate = {2018-09-26}
}

@book{Bar-Shalom:1987,
author = {Bar-Shalom, Y.},
title = {Tracking and Data Association},
year = {1987},
isbn = {0-120-79760-7},
publisher = {Academic Press Professional, Inc.},
address = {San Diego, CA, USA},
}
@ARTICLE{Cox93areview,
author = {Ingemar J. Cox},
title = {A Review of Statistical Data Association Techniques for Motion Correspondence},
journal = {International Journal of Computer Vision},
year = {1993},
volume = {10},
pages = {53--66}
}

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