Timezone: »
Poster
Graph Zeta Function in the Bethe Free Energy and Loopy Belief Propagation
Yusuke Watanabe · Kenji Fukumizu
We propose a new approach to the analysis of Loopy Belief Propagation (LBP) by establishing a formula that connects the Hessian of the Bethe free energy with the edge zeta function. The formula has a number of theoretical implications on LBP. It is applied to give a sufficient condition that the Hessian of the Bethe free energy is positive definite, which shows non-convexity for graphs with multiple cycles. The formula clarifies the relation between the local stability of a fixed point of LBP and local minima of the Bethe free energy. We also propose a new approach to the uniqueness of LBP fixed point, and show various conditions of uniqueness.
Author Information
Yusuke Watanabe (The Institute of Statistical Mathematics)
Kenji Fukumizu (Institute of Statistical Mathematics / Preferred Networks / RIKEN AIP)
Related Events (a corresponding poster, oral, or spotlight)
-
2009 Spotlight: Graph Zeta Function in the Bethe Free Energy and Loopy Belief Propagation »
Tue. Dec 8th 11:33 -- 11:34 PM Room
More from the Same Authors
-
2023 : Optimal Transport for Measures with Noisy Tree Metric »
Tam Le · Truyen Nguyen · Kenji Fukumizu -
2023 Poster: Transfer Learning with Affine Model Transformation »
Shunya Minami · Kenji Fukumizu · Yoshihiro Hayashi · Ryo Yoshida -
2022 Poster: Invariance Learning based on Label Hierarchy »
Shoji Toyota · Kenji Fukumizu -
2022 Poster: Unsupervised Learning of Equivariant Structure from Sequences »
Takeru Miyato · Masanori Koyama · Kenji Fukumizu -
2020 Poster: Robust Persistence Diagrams using Reproducing Kernels »
Siddharth Vishwanath · Kenji Fukumizu · Satoshi Kuriki · Bharath Sriperumbudur -
2019 Poster: Semi-flat minima and saddle points by embedding neural networks to overparameterization »
Kenji Fukumizu · Shoichiro Yamaguchi · Yoh-ichi Mototake · Mirai Tanaka -
2019 Poster: Tree-Sliced Variants of Wasserstein Distances »
Tam Le · Makoto Yamada · Kenji Fukumizu · Marco Cuturi -
2018 Poster: Variational Learning on Aggregate Outputs with Gaussian Processes »
Ho Chung Law · Dino Sejdinovic · Ewan Cameron · Tim Lucas · Seth Flaxman · Katherine Battle · Kenji Fukumizu -
2017 : Learning on topological and geometrical structures of data. »
Kenji Fukumizu -
2017 Poster: A Linear-Time Kernel Goodness-of-Fit Test »
Wittawat Jitkrittum · Wenkai Xu · Zoltan Szabo · Kenji Fukumizu · Arthur Gretton -
2017 Oral: A Linear-Time Kernel Goodness-of-Fit Test »
Wittawat Jitkrittum · Wenkai Xu · Zoltan Szabo · Kenji Fukumizu · Arthur Gretton -
2017 Poster: Trimmed Density Ratio Estimation »
Song Liu · Akiko Takeda · Taiji Suzuki · Kenji Fukumizu -
2016 Poster: Convergence guarantees for kernel-based quadrature rules in misspecified settings »
Motonobu Kanagawa · Bharath Sriperumbudur · Kenji Fukumizu -
2012 Poster: Learning from Distributions via Support Measure Machines »
Krikamol Muandet · Kenji Fukumizu · Francesco Dinuzzo · Bernhard Schölkopf -
2012 Poster: Gradient-based kernel method for feature extraction and variable selection »
Kenji Fukumizu · Chenlei Leng -
2012 Spotlight: Learning from Distributions via Support Measure Machines »
Krikamol Muandet · Kenji Fukumizu · Francesco Dinuzzo · Bernhard Schölkopf -
2012 Poster: Optimal kernel choice for large-scale two-sample tests »
Arthur Gretton · Bharath Sriperumbudur · Dino Sejdinovic · Heiko Strathmann · Sivaraman Balakrishnan · Massimiliano Pontil · Kenji Fukumizu -
2011 Poster: Kernel Bayes' Rule »
Kenji Fukumizu · Le Song · Arthur Gretton -
2011 Poster: Learning in Hilbert vs. Banach Spaces: A Measure Embedding Viewpoint »
Bharath Sriperumbudur · Kenji Fukumizu · Gert Lanckriet -
2011 Poster: Uniqueness of Belief Propagation on Signed Graphs »
Yusuke Watanabe -
2011 Spotlight: Uniqueness of Belief Propagation on Signed Graphs »
Yusuke Watanabe -
2009 Poster: Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions »
Bharath Sriperumbudur · Kenji Fukumizu · Arthur Gretton · Gert Lanckriet · Bernhard Schölkopf -
2009 Oral: Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions »
Bharath Sriperumbudur · Kenji Fukumizu · Arthur Gretton · Gert Lanckriet · Bernhard Schölkopf -
2009 Poster: A Fast, Consistent Kernel Two-Sample Test »
Arthur Gretton · Kenji Fukumizu · Zaid Harchaoui · Bharath Sriperumbudur -
2009 Spotlight: A Fast, Consistent Kernel Two-Sample Test »
Arthur Gretton · Kenji Fukumizu · Zaid Harchaoui · Bharath Sriperumbudur -
2008 Poster: Characteristic Kernels on Groups and Semigroups »
Kenji Fukumizu · Bharath Sriperumbudur · Arthur Gretton · Bernhard Schölkopf -
2008 Oral: Characteristic Kernels on Groups and Semigroups »
Kenji Fukumizu · Bharath Sriperumbudur · Arthur Gretton · Bernhard Schölkopf -
2007 Workshop: Representations and Inference on Probability Distributions »
Kenji Fukumizu · Arthur Gretton · Alexander Smola -
2007 Spotlight: Kernel Measures of Conditional Dependence »
Kenji Fukumizu · Arthur Gretton · Xiaohai Sun · Bernhard Schölkopf -
2007 Poster: Kernel Measures of Conditional Dependence »
Kenji Fukumizu · Arthur Gretton · Xiaohai Sun · Bernhard Schölkopf -
2007 Spotlight: A Kernel Statistical Test of Independence »
Arthur Gretton · Kenji Fukumizu · Choon Hui Teo · Le Song · Bernhard Schölkopf · Alexander Smola -
2007 Poster: A Kernel Statistical Test of Independence »
Arthur Gretton · Kenji Fukumizu · Choon Hui Teo · Le Song · Bernhard Schölkopf · Alexander Smola -
2006 Poster: Kernels on Structured Objects Through Nested Histograms »
Marco Cuturi · Kenji Fukumizu