Moment-Based Variational Inference for Markov Jump Processes

Christian Wildner, Heinz Koeppl
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6766-6775, 2019.

Abstract

We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence from the approximate to the posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to latent parameter inference and demonstrate the method on several examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-wildner19a, title = {Moment-Based Variational Inference for {M}arkov Jump Processes}, author = {Wildner, Christian and Koeppl, Heinz}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {6766--6775}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/wildner19a/wildner19a.pdf}, url = {https://proceedings.mlr.press/v97/wildner19a.html}, abstract = {We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence from the approximate to the posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to latent parameter inference and demonstrate the method on several examples.} }
Endnote
%0 Conference Paper %T Moment-Based Variational Inference for Markov Jump Processes %A Christian Wildner %A Heinz Koeppl %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-wildner19a %I PMLR %P 6766--6775 %U https://proceedings.mlr.press/v97/wildner19a.html %V 97 %X We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence from the approximate to the posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to latent parameter inference and demonstrate the method on several examples.
APA
Wildner, C. & Koeppl, H.. (2019). Moment-Based Variational Inference for Markov Jump Processes. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:6766-6775 Available from https://proceedings.mlr.press/v97/wildner19a.html.

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