The Nonparametric Kernel Bayes Smoother

Yu Nishiyama, Amir Afsharinejad, Shunsuke Naruse, Byron Boots, Le Song
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:547-555, 2016.

Abstract

Recently, significant progress has been made developing kernel mean expressions for Bayesian inference. An important success in this domain is the nonparametric kernel Bayes’ filter (nKB-filter), which can be used for sequential inference in state space models. We expand upon this work by introducing a smoothing algorithm, the nonparametric kernel Bayes’ smoother (nKB-smoother) which relies on kernel Bayesian inference through the kernel sum rule and kernel Bayes’ rule. We derive the smoothing equations, analyze the computational cost, and show smoothing consistency. We summarize the algorithm, which is simple to implement, requiring only matrix multiplications and the output of the nKB-filter. Finally, we report experimental results that compare the nKB-smoother to previous parametric and nonparametric approaches to Bayesian filtering and smoothing. In the supplementary materials, we show that the combination of the nKB-filter and the nKB-smoother allows marginal kernel mean computation, which gives an alternative to kernel belief propagation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v51-nishiyama16, title = {The Nonparametric Kernel Bayes Smoother}, author = {Nishiyama, Yu and Afsharinejad, Amir and Naruse, Shunsuke and Boots, Byron and Song, Le}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {547--555}, year = {2016}, editor = {Gretton, Arthur and Robert, Christian C.}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/nishiyama16.pdf}, url = {https://proceedings.mlr.press/v51/nishiyama16.html}, abstract = {Recently, significant progress has been made developing kernel mean expressions for Bayesian inference. An important success in this domain is the nonparametric kernel Bayes’ filter (nKB-filter), which can be used for sequential inference in state space models. We expand upon this work by introducing a smoothing algorithm, the nonparametric kernel Bayes’ smoother (nKB-smoother) which relies on kernel Bayesian inference through the kernel sum rule and kernel Bayes’ rule. We derive the smoothing equations, analyze the computational cost, and show smoothing consistency. We summarize the algorithm, which is simple to implement, requiring only matrix multiplications and the output of the nKB-filter. Finally, we report experimental results that compare the nKB-smoother to previous parametric and nonparametric approaches to Bayesian filtering and smoothing. In the supplementary materials, we show that the combination of the nKB-filter and the nKB-smoother allows marginal kernel mean computation, which gives an alternative to kernel belief propagation.} }
Endnote
%0 Conference Paper %T The Nonparametric Kernel Bayes Smoother %A Yu Nishiyama %A Amir Afsharinejad %A Shunsuke Naruse %A Byron Boots %A Le Song %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-nishiyama16 %I PMLR %P 547--555 %U https://proceedings.mlr.press/v51/nishiyama16.html %V 51 %X Recently, significant progress has been made developing kernel mean expressions for Bayesian inference. An important success in this domain is the nonparametric kernel Bayes’ filter (nKB-filter), which can be used for sequential inference in state space models. We expand upon this work by introducing a smoothing algorithm, the nonparametric kernel Bayes’ smoother (nKB-smoother) which relies on kernel Bayesian inference through the kernel sum rule and kernel Bayes’ rule. We derive the smoothing equations, analyze the computational cost, and show smoothing consistency. We summarize the algorithm, which is simple to implement, requiring only matrix multiplications and the output of the nKB-filter. Finally, we report experimental results that compare the nKB-smoother to previous parametric and nonparametric approaches to Bayesian filtering and smoothing. In the supplementary materials, we show that the combination of the nKB-filter and the nKB-smoother allows marginal kernel mean computation, which gives an alternative to kernel belief propagation.
RIS
TY - CPAPER TI - The Nonparametric Kernel Bayes Smoother AU - Yu Nishiyama AU - Amir Afsharinejad AU - Shunsuke Naruse AU - Byron Boots AU - Le Song BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-nishiyama16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 547 EP - 555 L1 - http://proceedings.mlr.press/v51/nishiyama16.pdf UR - https://proceedings.mlr.press/v51/nishiyama16.html AB - Recently, significant progress has been made developing kernel mean expressions for Bayesian inference. An important success in this domain is the nonparametric kernel Bayes’ filter (nKB-filter), which can be used for sequential inference in state space models. We expand upon this work by introducing a smoothing algorithm, the nonparametric kernel Bayes’ smoother (nKB-smoother) which relies on kernel Bayesian inference through the kernel sum rule and kernel Bayes’ rule. We derive the smoothing equations, analyze the computational cost, and show smoothing consistency. We summarize the algorithm, which is simple to implement, requiring only matrix multiplications and the output of the nKB-filter. Finally, we report experimental results that compare the nKB-smoother to previous parametric and nonparametric approaches to Bayesian filtering and smoothing. In the supplementary materials, we show that the combination of the nKB-filter and the nKB-smoother allows marginal kernel mean computation, which gives an alternative to kernel belief propagation. ER -
APA
Nishiyama, Y., Afsharinejad, A., Naruse, S., Boots, B. & Song, L.. (2016). The Nonparametric Kernel Bayes Smoother. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:547-555 Available from https://proceedings.mlr.press/v51/nishiyama16.html.

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