Accelerating Viterbi Algorithm Pei-Ching Li

Outline Introduction of Viterbi Algorithm – Example Architecture – Parallel on CUDA MIDI – hmmtrain Future Works

Introduction of Viterbi Algorithm a dynamic programming algorithm for finding the most likely sequence of hidden states called the Viterbi path. Hidden Markov Model

Example O = Walk->Walk->Shop->Clean

Example O = Walk->Walk->Shop->Clean

Example O = Walk->Walk->Shop->Clean

Example O = Walk->Walk->Shop->Clean

Example O = Walk->Walk->Shop->Clean S = Sunny->Sunny->Rainy->Rainy

Parallel Part CSE551 Final Project: Parallel Viterbi on a GPU – Authors: Seong Jae Lee, Miro Enev – Provenance: Autumm 2009, University of Washington

Architecture Input – transition probability – emission probability Algorithm – hmmgenerate – hmmviterbi – accuracy of hmmviterbi

Matlab 2011 [SEQ, STATES] = HMMGENERATE(LEN,TRANSITIONS,EMISSIONS) STATES = HMMVITERBI(SEQ,TRANSITIONS,EMISSIONS) Use MATLAB Coder to generate C/C++ code

Parallel on CUDA Focus on hmmviterbi() to accelerate – Calculate the values – Choose the maximum reduction

Parallel on CUDA (2 nd version)

Parallel on CUDA

MIDI Score : Length : 1 second Hmmtrain : – unknown states – initial guesses for TRANS and EMIS – hmmtrain (seq, TRANS_GUESS, EMIS_GUESS)

TRANS_GUESS : 12x12 – C → D, D → E, E → F, F → G0.8 – Othersrandom EMIS_GUESS : played or not – 0.9 vs. 0.1 – Not accepted

hmmtrain (seq, TRANS_GUESS, EMIS_GUESS) seq – Source – Output of band-pass filter Hmmtrain will use algo. – BaumWelch : hmmdecode Calculates the posterior state probabilities of a sequence of emissions – Viterbi : hmmviterbi

hmmtrain The results of models have big difference than the guess! Can’t use the results to get the great states when running Viterbi algorithm.

Future Works Finish the 3 rd version. Modify the guess models to get the better result!

THANK YOU

Appendix 1 : O(nm 2 ) n stands for the number of observations m is the number of possible states of an observation

Appendix 2 : Reference CSE551 Final Project: Parallel Viterbi on a GPU – Authors: Seong Jae Lee, Miro Enev – Provenance: Autumm 2009, University of Washington

Appendix 2 : CSE551 Final Project : Parallel Viterbi on a GPU

Appendix 3 : Auto-generated Probability Models Random + constraint – tmp = (float)rand() / (float)RAND_MAX; – prob = (tmp <= constraint) ? 0 : tmp; Guarantee probability of each row equals 1. Verify the sequence conformed to the models. – hmmestimate(seq, states)

Appendix 3 : Auto-generated Probability Models Viterbi algorithm – when back tracing the likely states, avoid to save the 0 state (rand() % N) + 1