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Move new refrences to own bib file; Fix broken equation

arxiv-v1
Markus Kaiser 7 months ago
parent
commit
054ae720de
3 changed files with 29 additions and 41 deletions
  1. 17
    0
      additional.bib
  2. 12
    24
      dynamic_dirichlet_deep_gp.tex
  3. 0
    17
      zotero_export.bib

+ 17
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additional.bib View File

@@ -0,0 +1,17 @@
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+@book{Bar-Shalom:1987,
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+ author = {Bar-Shalom, Y.},
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+ title = {Tracking and Data Association},
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+ year = {1987},
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+ isbn = {0-120-79760-7},
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+ publisher = {Academic Press Professional, Inc.},
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+ address = {San Diego, CA, USA},
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+}
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+
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+@ARTICLE{Cox93areview,
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+    author = {Ingemar J. Cox},
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+    title = {A Review of Statistical Data Association Techniques for Motion Correspondence},
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+    journal = {International Journal of Computer Vision},
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+    year = {1993},
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+    volume = {10},
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+    pages = {53--66}
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+}

+ 12
- 24
dynamic_dirichlet_deep_gp.tex View File

@@ -15,6 +15,7 @@
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 % \overfullrule=5pt
16 16
 
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 \addbibresource{zotero_export.bib}
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+\addbibresource{additional.bib}
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 % We set this for hyperref
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 \title{Multimodal Deep Gaussian Processes}
@@ -65,34 +66,21 @@ We further denote the evaluation of the $\nth{k}$ latent function associated wit
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 For consistency, we refer to the $\nth{k}$ entry in $\mat{a_n}$ as $a_n^{\pix{k}}$ and also collect these values as $\mat{A} = \left(\mat{a_1}, \ldots, \mat{a_N}\right)$.
66 67
 
67 68
 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,
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-%% \begin{align}
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-%% \begin{split}
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-%%     \label{eq:true_marginal_likelihood}
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-%%     \Prob*{\mat{Y} \given \mat{X}} &= \\
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-%%     \MoveEqLeft\int
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-%%     \Prob*{\mat{Y} \given \mat{F}, \mat{A}}
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-%%     \Prob*{\mat{F} \given \mat{X}}
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-%%     \Prob*{\mat{A} \given \mat{X}}
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-%%     \diff \mat{A} \diff \mat{F}\text{,} \\
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-%%     \Prob*{\mat{Y} \given \mat{F}, \mat{A}} &= \\
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-%%     \MoveEqLeft\prod_{n=1}^N\prod_{k=1}^K
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-%%     \Gaussian*{\mat{y_n} \given \given \mat{f_n^{\pix{k}}}, \left(\sigma^{\pix{k}}\right)^2}^{\Fun{\Ind}{a_n^{\pix{k}} = 1}},
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-%% \end{split}
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-%% \end{align}
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-
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-\begin{multiline}\label{eq:true_marginal_likelihood}
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-    \Prob*{\mat{Y} \given \mat{X}} =
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+\begin{align}
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+\begin{split}
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+    \label{eq:true_marginal_likelihood}
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+    \Prob*{\mat{Y} \given \mat{X}} &= \\
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+    \MoveEqLeft\int
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     \Prob*{\mat{Y} \given \mat{F}, \mat{A}}
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     \Prob*{\mat{F} \given \mat{X}}
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     \Prob*{\mat{A} \given \mat{X}}
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-    \diff \mat{A} \diff \mat{F}\text{,}
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-    \\
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-    \Prob*{\mat{Y} \given \mat{F}, \mat{A}} =
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+    \diff \mat{A} \diff \mat{F}\text{,} \\
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+    \Prob*{\mat{Y} \given \mat{F}, \mat{A}} &= \\
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     \MoveEqLeft\prod_{n=1}^N\prod_{k=1}^K
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-    \Gaussian*{\mat{y_n} \given \given \mat{f_n^{\pix{k}}}, \left(\sigma^{\pix{k}}\right)^2}^{\Fun{\Ind}{a_n^{\pix{k}} = 1}},
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-\end{multiline}
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-
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-where $\sigma^{\pix{k}}$ is the noise level of the $\nth{k}$ Gaussian likelihood and $\Fun{\Ind}$ is the indicator function.
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+    \Gaussian*{\mat{y_n} \given \mat{f_n^{\pix{k}}}, \left(\sigma^{\pix{k}}\right)^2}^{\Fun{\Ind}{a_n^{\pix{k}} = 1}},
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+\end{split}
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+\end{align}
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+where $\sigma^{\pix{k}}$ is the noise level of the $\nth{k}$ Gaussian likelihood and $\Ind$ is the indicator function.
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 Since we assume the $K$ modes to be independent given the data and assignments, we place independent GP priors on the latent functions,
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 \begin{align}

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- 17
zotero_export.bib View File

@@ -296,20 +296,3 @@
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   url = {http://papers.nips.cc/paper/1900-mixtures-of-gaussian-processes.pdf},
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   urldate = {2018-09-26}
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 }
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-
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-@book{Bar-Shalom:1987,
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- author = {Bar-Shalom, Y.},
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- title = {Tracking and Data Association},
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- year = {1987},
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- isbn = {0-120-79760-7},
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- publisher = {Academic Press Professional, Inc.},
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- address = {San Diego, CA, USA},
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-}
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-@ARTICLE{Cox93areview,
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-    author = {Ingemar J. Cox},
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-    title = {A Review of Statistical Data Association Techniques for Motion Correspondence},
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-    journal = {International Journal of Computer Vision},
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-    year = {1993},
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-    volume = {10},
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-    pages = {53--66}
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-}

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