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#unonight #sffamily (at ตลาดนัดเลียบด่วน รามอินทรา) https://www.instagram.com/p/ClJfd0ghhkW/?igshid=NGJjMDIxMWI=
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Celebration meal #SFfamily❤️ https://www.instagram.com/p/BunM_mXhVY7/?utm_source=ig_tumblr_share&igshid=1p0apnq3pd1k1
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Stay tuned: We will tell you all about our new #cardgame tomorrow Fogust 1st 🌁 . . #sanfrancisco #sflandmarks #haightashbury #castro #chinatown #unionsquare #lombardstreet #goldengatebridge #SF #🌁 #preview #sftravel #sfsightseeing #fogaholics #foglife #fogust #onlyinsf #digitalpainting #kickstarter #illustration #kidsgames #sffamily #sfmom #familygame #unplugandplay #jogojoy #sfetsy (at San Francisco, California) https://www.instagram.com/p/Bl6VGF5lg7i/?utm_source=ig_tumblr_share&igshid=18m4n6qzzc2h4
#sfetsy#sftravel#onlyinsf#digitalpainting#kickstarter#sf#unionsquare#fogaholics#sanfrancisco#sflandmarks#cardgame#🌁#fogust#sfmom#preview#haightashbury#lombardstreet#unplugandplay#sffamily#familygame#chinatown#kidsgames#foglife#illustration#castro#goldengatebridge#jogojoy#sfsightseeing
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\title{04.01.2017}
% A subtitle is optional and this may be deleted
\subtitle{Vector LBP with aggregation via DD: results}
\author{Gorodnitskii Oleg: [email protected]}
\AtBeginSubsection[GaBP preconditioned conjugate gradient method]
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%----------------------------------------------------------------------------------------------------------
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\titlepage
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\begin{frame}{Short description:}
Consider \textbf{Vector LBP}. It is known that the \textbf{Vector} version of LBP has significantly stronger convergence properties under correct choice of separation onto blocks, compared to the \textbf{Scalar} version. \cite{mal08}\\
Optimal and correct (in sense that it will lead to the convergence of Vector LBP) choice of separation onto blocks is unknown for arbitrary case.\\
Here we propose separation via DD properties of each node.\\
We examine each individual node $\pmb{i}$ and set of its neighbors $\mathcal{N}(\pmb{i})$:
\begin{enumerate}
\item If $\mathcal{N}(\pmb{i})$ is such that $J_{ii} \leq \sum_{j \in \mathcal{N}(\pmb{i})}|J_{ij}|$ (DD is violated in i-th row) then we replace $\pmb{i}$ and $\mathcal{N}(\pmb{i})$ with supernode $\mathcal{S}_i = \{\pmb{i}\} \cup \mathcal{N}(\pmb{i})$
\item If $\pmb{j} \in \mathcal{N}(\pmb{i})$ and $J_{jj} \leq \sum_{k \in \mathcal{N}(\pmb{j})}|J_{jk}|$ (DD is violated both in i-th and j-th row) we put $\pmb{j}$ in $\mathcal{S}_i$
\item If $\pmb{j} \notin \mathcal{N}(\pmb{i})$ and $J_{jj} \leq \sum_{k \in \mathcal{N}(\pmb{j})}|J_{jk}|$, and $\mathcal{N}(\pmb{i}) \cap \mathcal{N}(\pmb{j}) \neq \emptyset$ we put $\pmb{k} \in \mathcal{N}(\pmb{i}) \cap \mathcal{N}(\pmb{j}) $ randomly into $\mathcal{S}_i$ or $\mathcal{S}_j$
\end{enumerate}\\
Thus we eliminate all nodes and it's neighbors which violate DD, replacing them with supernodes.
\end{frame}
%-----------------------------------------------------------------------------------------------------
\begin{frame}{Results: Case 1}
\begin{center}
\includegraphics[scale = 0.35]{graph_1}
\end{center} (28 nodes, p = 0.35, Non-Walksummable)\\
\end{frame}
%-----------------------------------------------------------------------------------------------------
\begin{frame}{Results: Case 1, convergence}
\begin{center}
\includegraphics[scale = 0.42]{Means_err_vec_1}
\includegraphics[scale = 0.42]{Means_err_scalar_1}
\end{center} (Vector LBP and Scalar LBP convergence - x-axis - number of iteration, y-axis - $\text{Norm}_2$ error for means)\\
\end{frame}
%-----------------------------------------------------------------------------------------------------
\begin{frame}{Results: Case 2}
\begin{center}
\includegraphics[scale = 0.33]{graph_2}
\end{center} (80 nodes, p = 0.32, Non-Walksummable)\\
\end{frame}
%-----------------------------------------------------------------------------------------------------
\begin{frame}{Results: Case 2, convergence}
\begin{center}
\includegraphics[scale = 0.42]{Means_err_vec_2}
\includegraphics[scale = 0.42]{Means_err_scalar_2}
\end{center} (x-axis - number of iteration, y-axis - $\text{Norm}_2$ error for means)\\
\end{frame}
%-----------------------------------------------------------------------------------------------------
\begin{frame}{Results: Case 3}
\begin{center}
\includegraphics[scale = 0.35]{graph_3}
\end{center} (90 nodes, p = 0.29, Non-Walksummable)\\
\end{frame}
%-----------------------------------------------------------------------------------------------------
\begin{frame}{Results: Case 3, convergence}
\begin{center}
\includegraphics[scale = 0.42]{Means_err_vec_3}
\includegraphics[scale = 0.42]{Means_err_scalar_3}
\end{center} (x-axis - number of iteration, y-axis - $\text{Norm}_2$ error for means)\\
\end{frame}
\printbibliography
\end{document}
[ @taylorswift ]* 💜💜♾️♾️
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It’s that time of year again San Francisco families when we come to forest on the weekend to greet new and perspective students. Please come out to one of our open house events to meet our staff. There will be music and an art activity as well. Please RSVP first, at [email protected]
#SFForestschool#Forestpreschool#SFkids#SFfamilies#wildroootssf
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Reminder of blogs!
This is a side Blog for this account! While NSFW it is non-explicit.
@corabryn-blog is the primary for this account! It is very NSFW and very sexually explicit!
@sfwbabygirlcora is 100% SFW and SFFamily. Few words, mostly cute or aesthetic stuff that is not sexual. I don’t mention either this or the explicit Blog there at all in order to keep it that way!
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Last night was epic, to say the least. Congrats to Mr. and Mrs. Annear! Love you both so, so much. ❤️🍖 #anneartoeternity #hentzforthannear #sffamily http://ift.tt/2yHk8zK
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Happy birthday Zack!!! #goodfriends #sffamily #bfam (at Stones Throw)
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#sfmeeting #sffamily (at Bangkok, Thailand) https://www.instagram.com/p/ClJLVqVh0XY/?igshid=NGJjMDIxMWI=
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#aboutlastnight #sffamily #wifeysbday (em Hops & Hominy) https://www.instagram.com/p/BqIYmZKAjQj/?utm_source=ig_tumblr_share&igshid=l0b9318bkup9
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Stay tuned: We’ll tell you all about our new #cardgame tomorrow Fogust 1st 🌁 . . . #sanfrancisco #sflandmarks #haightashbury #castro #chinatown #unionsquare #lombardstreet #goldengatebridge #SF #🌁 #wip #preview #sftravel #sfsightseeing #sffog #sfsummer #sfmom #sffamily #sanfranciscobay #sanfranciscoart #fog #karlthefog #fogaholics #foglife #fogust #onlyinsf #digitalpainting #kickstarter #photoshop #illustration #kidsgames #familygame #unplugandplay #sffun #jogojoy #sfetsy (at San Francisco, California) https://www.instagram.com/p/Bl6UaejFZRw/?utm_source=ig_tumblr_share&igshid=15icmygi4v9fu
#sfsummer#kidsgames#sffog#sf#sffamily#cardgame#sfetsy#sffun#unplugandplay#kickstarter#sftravel#haightashbury#foglife#illustration#jogojoy#familygame#photoshop#chinatown#castro#sfmom#digitalpainting#preview#🌁#goldengatebridge#fogaholics#wip#sanfranciscobay#lombardstreet#sanfrancisco#karlthefog
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\date{}
\title{02.24.2017}
%----------------------------------------------------------------------------------------------------------
\begin{document}
%-----------------------------------------------------------------------------------------------------
\begin{frame}{Convergence of GaBP beliefs to delta functions for $\beta \rightarrow \infty$:}
For Gaussian probability density function: $p(x) \sim \mathcal{N}(\mu, A^{-1}), \ \mu = A^{-1}b$ marginal densities are also Gaussian \cite{bic} (page 9) $$p_i(x_i) \sim \mathcal{N}(\mu_i = \{A^{-1}b\}_i,\{A^{-1}\}_{ii})$$
In case of GaBP beliefs converge to true marginals for walk-summable model.\\
Consider inverse temperature $\beta = T^{-1}$ and substitution $A \rightarrow \beta A, b \rightarrow \beta b$
After substitution we get:
$$p_i(x_i) \sim \mathcal{N}(\mu_i = \{A^{-1}b\}_i,\{\frac{A^{-1}}{\beta}\}_{ii})$$\\
Letting $\beta \rightarrow \infty$ we get:\\
$$p_i(x_i) \sim \mathcal{N}(\mu_i = \{A^{-1}b\}_i,\{\frac{A^{-1}}{\beta}\}_{ii} \rightarrow 0) \rightarrow \mu_i \times \delta(x_i - \mu_i) \text{ - Dirac delta function}$$\\
\end{frame}
%-----------------------------------------------------------------------------------------------------
\begin{frame}{}
\textbf{Conclusion}: Gaussian BP is derived from \textbf{integral-product} rule, via direct integration. If we apply $A \rightarrow \beta A, b \rightarrow \beta b, \beta \rightarrow \infty$ substitution we get max-product algorithm from integral-product algorithm.\\
In this case, as showed above, beliefs always converge to delta functions in case of walk-summable models.\\
\bibliographystyle{plain}
\bibliography{references}
\end{frame}
%-----------------------------------------------------------------------------------------------------
[ @taylorswift ]* 💜💜♾️♾️
\end{document}
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Bateman & Fua Christmas! #SFFamily #dentalschoolbesties (at San Francisco, California)
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It feels like a perfect night to dress up like hipsters and make fun of our exes 💋 #tswift #sfadventures #sffamily #bestfriends #HailSatanFtCats #TaylorSwiftNight
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MASHing this weekend away in Chicago presenting at NCA! Wish me luck fellow MASHers and thanks for all the support!#SFfamily (at Amtrak)
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#sffamily (em AT&T Park) https://www.instagram.com/p/BnnDWDmlI8f/?utm_source=ig_tumblr_share&igshid=e5p61r6b27uq
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