### Move new refrences to own bib file; Fix broken equation

arxiv-v1
Markus Kaiser 1 년 전
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054ae720de
3개의 변경된 파일29개의 추가작업 그리고 41개의 파일을 삭제
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dynamic_dirichlet_deep_gp.tex
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zotero_export.bib

#### + 17 - 0 additional.bib파일 보기

 @@ -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.tex파일 보기

 @@ -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.bib파일 보기

 @@ -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} }