Tobias Ryden
Mathematical Statistics, Lund University


Subspace estimation methods for hidden Markov models: algorithms and
consistency

Abstract

Hidden Markov models (HMMs) are probabilistic functions
of finite Markov chains, or, put in other words, state space
models with finite state space. In this paper we examine subspace
estimation methods for HMMs whose output lies a finite
set as well. In particular we study the geometrical structure
arising from the non-minimality of the linear state space
representation of HMMs, and prove consistency, up to a
similarity transformation, of a subspace algorithm arising
from a certain factorization of the singular value decomposition
of the estimated linear prediction matrix.