1 research outputs found
Improving Viterbi is Hard: Better Runtimes Imply Faster Clique Algorithms
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 given a sequence of observations from a HMM with 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. We show that the Viterbi algorithm runtime is optimal up to
subpolynomial factors even when the number of distinct observations is small.
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 -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
speedup for the Viterbi algorithm when there are few distinct transition
probabilities in the HMM