Improving Viterbi is Hard: Better Runtimes Imply Faster Clique Algorithms

Arturs Backurs, Christos Tzamos
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:311-321, 2017.

Abstract

The classic algorithm of Viterbi computes the most likely path in a Hidden Markov Model (HMM) that results in a given sequence of observations. It runs in time $O(Tn^2)$ given a sequence of T observations from a HMM with n states. Despite significant interest in the problem and prolonged effort by different communities, no known algorithm achieves more than a polylogarithmic speedup. In this paper, we explain this difficulty by providing matching conditional lower bounds. Our lower bounds are based on assumptions that the best known algorithms for the All-Pairs Shortest Paths problem (APSP) and for the Max-Weight k-Clique problem in edge-weighted graphs are essentially tight. Finally, using a recent algorithm by Green Larsen and Williams for online Boolean matrix-vector multiplication, we get a $2^{\Omega(\sqrt{\log n})}$ speedup for the Viterbi algorithm when there are few distinct transition probabilities in the HMM.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-backurs17a, title = {Improving {V}iterbi is Hard: Better Runtimes Imply Faster Clique Algorithms}, author = {Arturs Backurs and Christos Tzamos}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {311--321}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/backurs17a/backurs17a.pdf}, url = {https://proceedings.mlr.press/v70/backurs17a.html}, abstract = {The classic algorithm of Viterbi computes the most likely path in a Hidden Markov Model (HMM) that results in a given sequence of observations. It runs in time $O(Tn^2)$ given a sequence of T observations from a HMM with n states. Despite significant interest in the problem and prolonged effort by different communities, no known algorithm achieves more than a polylogarithmic speedup. In this paper, we explain this difficulty by providing matching conditional lower bounds. Our lower bounds are based on assumptions that the best known algorithms for the All-Pairs Shortest Paths problem (APSP) and for the Max-Weight k-Clique problem in edge-weighted graphs are essentially tight. Finally, using a recent algorithm by Green Larsen and Williams for online Boolean matrix-vector multiplication, we get a $2^{\Omega(\sqrt{\log n})}$ speedup for the Viterbi algorithm when there are few distinct transition probabilities in the HMM.} }
Endnote
%0 Conference Paper %T Improving Viterbi is Hard: Better Runtimes Imply Faster Clique Algorithms %A Arturs Backurs %A Christos Tzamos %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-backurs17a %I PMLR %P 311--321 %U https://proceedings.mlr.press/v70/backurs17a.html %V 70 %X The classic algorithm of Viterbi computes the most likely path in a Hidden Markov Model (HMM) that results in a given sequence of observations. It runs in time $O(Tn^2)$ given a sequence of T observations from a HMM with n states. Despite significant interest in the problem and prolonged effort by different communities, no known algorithm achieves more than a polylogarithmic speedup. In this paper, we explain this difficulty by providing matching conditional lower bounds. Our lower bounds are based on assumptions that the best known algorithms for the All-Pairs Shortest Paths problem (APSP) and for the Max-Weight k-Clique problem in edge-weighted graphs are essentially tight. Finally, using a recent algorithm by Green Larsen and Williams for online Boolean matrix-vector multiplication, we get a $2^{\Omega(\sqrt{\log n})}$ speedup for the Viterbi algorithm when there are few distinct transition probabilities in the HMM.
APA
Backurs, A. & Tzamos, C.. (2017). Improving Viterbi is Hard: Better Runtimes Imply Faster Clique Algorithms. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:311-321 Available from https://proceedings.mlr.press/v70/backurs17a.html.

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