Comparative Analysis of Viterbi Training and Maximum Likelihood Estimation for HMMs

12/16/2013
by   Armen E. Allahverdyan, et al.
0

We present an asymptotic analysis of Viterbi Training (VT) and contrast it with a more conventional Maximum Likelihood (ML) approach to parameter estimation in Hidden Markov Models. While ML estimator works by (locally) maximizing the likelihood of the observed data, VT seeks to maximize the probability of the most likely hidden state sequence. We develop an analytical framework based on a generating function formalism and illustrate it on an exactly solvable model of HMM with one unambiguous symbol. For this particular model the ML objective function is continuously degenerate. VT objective, in contrast, is shown to have only finite degeneracy. Furthermore, VT converges faster and results in sparser (simpler) models, thus realizing an automatic Occam's razor for HMM learning. For more general scenario VT can be worse compared to ML but still capable of correctly recovering most of the parameters.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/11/2018

Maximum likelihood estimation in hidden Markov models with inhomogeneous noise

We consider parameter estimation in hidden finite state space Markov mod...
research
10/27/2020

Fast Stochastic Quadrature for Approximate Maximum-Likelihood Estimation

Recent stochastic quadrature techniques for undirected graphical models...
research
06/08/2021

General-order observation-driven models: ergodicity and consistency of the maximum likelihood estimator

The class of observation-driven models (ODMs) includes many models of no...
research
06/30/2017

Neural Sequence Model Training via α-divergence Minimization

We propose a new neural sequence model training method in which the obje...
research
11/07/2018

Iterative Marginal Maximum Likelihood DOD and DOA Estimation for MIMO Radar in the Presence of SIRP Clutter

The spherically invariant random process (SIRP) clutter model is commonl...
research
12/19/2017

Approximate Profile Maximum Likelihood

We propose an efficient algorithm for approximate computation of the pro...
research
05/07/2022

A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using Template Model Builder

A very common way to estimate the parameters of a hidden Markov model (H...

Please sign up or login with your details

Forgot password? Click here to reset