Nonparametric Bayesian sparse graph linear dynamical systems

Rahi Kalantari, Joydeep Ghosh, Mingyuan Zhou
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1952-1960, 2018.

Abstract

A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional sparse random graph to model state transitions. Depending on the sparsity pattern of the corresponding row and column of the graph affinity matrix, a latent state of SGLDS can be categorized as either a non-dynamic state or a dynamic one. A normal-gamma construction is used to shrink the energy captured by the non-dynamic states, while the dynamic states can be further categorized into live, absorbing, or noise-injection states, which capture different types of dynamical components of the underlying time series. The state-of-the-art performance of SGLDS is demonstrated with experiments on both synthetic and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-kalantari18a, title = {Nonparametric Bayesian sparse graph linear dynamical systems}, author = {Kalantari, Rahi and Ghosh, Joydeep and Zhou, Mingyuan}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1952--1960}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/kalantari18a/kalantari18a.pdf}, url = {https://proceedings.mlr.press/v84/kalantari18a.html}, abstract = {A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional sparse random graph to model state transitions. Depending on the sparsity pattern of the corresponding row and column of the graph affinity matrix, a latent state of SGLDS can be categorized as either a non-dynamic state or a dynamic one. A normal-gamma construction is used to shrink the energy captured by the non-dynamic states, while the dynamic states can be further categorized into live, absorbing, or noise-injection states, which capture different types of dynamical components of the underlying time series. The state-of-the-art performance of SGLDS is demonstrated with experiments on both synthetic and real data.} }
Endnote
%0 Conference Paper %T Nonparametric Bayesian sparse graph linear dynamical systems %A Rahi Kalantari %A Joydeep Ghosh %A Mingyuan Zhou %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-kalantari18a %I PMLR %P 1952--1960 %U https://proceedings.mlr.press/v84/kalantari18a.html %V 84 %X A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional sparse random graph to model state transitions. Depending on the sparsity pattern of the corresponding row and column of the graph affinity matrix, a latent state of SGLDS can be categorized as either a non-dynamic state or a dynamic one. A normal-gamma construction is used to shrink the energy captured by the non-dynamic states, while the dynamic states can be further categorized into live, absorbing, or noise-injection states, which capture different types of dynamical components of the underlying time series. The state-of-the-art performance of SGLDS is demonstrated with experiments on both synthetic and real data.
APA
Kalantari, R., Ghosh, J. & Zhou, M.. (2018). Nonparametric Bayesian sparse graph linear dynamical systems. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1952-1960 Available from https://proceedings.mlr.press/v84/kalantari18a.html.

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