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• W2964031187 abstract "In this paper, we present a novel algorithm for the maximum a posteriori decoding (MAPD) of time-homogeneous Hidden Markov Models (HMM), improving the worst-case running time of the classical Viterbi algorithm by a logarithmic factor. In our approach, we interpret the Viterbi algorithm as a repeated computation of matrix-vector (max, +)-multiplications. On time-homogeneous HMMs, this computation is online: a matrix, known in advance, has to be multiplied with several vectors revealed one at a time. Our main contribution is an algorithm solving this version of matrix-vector (max, +)-multiplication in subquadratic time, by performing a polynomial preprocessing of the matrix. Employing this fast multiplication algorithm, we solve the MAPD problem in O(mn2/log n) time for any time-homogeneous HMM of size n and observation sequence of length m, with an extra polynomial preprocessing cost negligible for m > n. To the best of our knowledge, this is the first algorithm for the MAPD problem requiring subquadratic time per observation, under the assumption – usually verified in practice – that the transition probability matrix does not change with time." @default.
• W2964031187 created "2019-07-30" @default.
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• W2964031187 creator A5061874157 @default.
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• W2964031187 date "2016-02-12" @default.
• W2964031187 modified "2023-09-24" @default.
• W2964031187 title "Decoding Hidden Markov Models faster than viterbi via online matrix-vector (max, +)-multiplication" @default.
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