Efficient Computation of Updated Lower Expectations for Imprecise Continuous-Time Hidden Markov Chains

Thomas Krak, Jasper De Bock, Arno Siebes
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:193-204, 2017.

Abstract

We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden state of the chain. The prefix ‘imprecise’ refers to the fact that we do not consider a classical continuous-time Markov chain, but replace it with a robust extension that allows us to represent various types of model uncertainty, using the theory of imprecise probabilities. The inference problem amounts to computing lower expectations of functions on the state-space of the chain, given observations of the output variables. We develop and investigate this problem with very few assumptions on the output variables in particular, they can be chosen to be either discrete or continuous random variables. Our main result is a polynomial runtime algorithm to compute the lower expectation of functions on the state-space at any given time-point, given a collection of observations of the output variables.

Cite this Paper

BibTeX
@InProceedings{pmlr-v62-krak17a, title = {Efficient Computation of Updated Lower Expectations for Imprecise Continuous-Time Hidden {M}arkov Chains}, author = {Krak, Thomas and De Bock, Jasper and Siebes, Arno}, booktitle = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {193--204}, year = {2017}, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien}, volume = {62}, series = {Proceedings of Machine Learning Research}, month = {10--14 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v62/krak17a/krak17a.pdf}, url = {https://proceedings.mlr.press/v62/krak17a.html}, abstract = {We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden state of the chain. The prefix ‘imprecise’ refers to the fact that we do not consider a classical continuous-time Markov chain, but replace it with a robust extension that allows us to represent various types of model uncertainty, using the theory of imprecise probabilities. The inference problem amounts to computing lower expectations of functions on the state-space of the chain, given observations of the output variables. We develop and investigate this problem with very few assumptions on the output variables in particular, they can be chosen to be either discrete or continuous random variables. Our main result is a polynomial runtime algorithm to compute the lower expectation of functions on the state-space at any given time-point, given a collection of observations of the output variables.} }
Endnote
%0 Conference Paper %T Efficient Computation of Updated Lower Expectations for Imprecise Continuous-Time Hidden Markov Chains %A Thomas Krak %A Jasper De Bock %A Arno Siebes %B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2017 %E Alessandro Antonucci %E Giorgio Corani %E Inés Couso %E Sébastien Destercke %F pmlr-v62-krak17a %I PMLR %P 193--204 %U https://proceedings.mlr.press/v62/krak17a.html %V 62 %X We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden state of the chain. The prefix ‘imprecise’ refers to the fact that we do not consider a classical continuous-time Markov chain, but replace it with a robust extension that allows us to represent various types of model uncertainty, using the theory of imprecise probabilities. The inference problem amounts to computing lower expectations of functions on the state-space of the chain, given observations of the output variables. We develop and investigate this problem with very few assumptions on the output variables in particular, they can be chosen to be either discrete or continuous random variables. Our main result is a polynomial runtime algorithm to compute the lower expectation of functions on the state-space at any given time-point, given a collection of observations of the output variables.
APA
Krak, T., De Bock, J. & Siebes, A.. (2017). Efficient Computation of Updated Lower Expectations for Imprecise Continuous-Time Hidden Markov Chains. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 62:193-204 Available from https://proceedings.mlr.press/v62/krak17a.html.

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