Reduced-Rank Hidden Markov Models

Details Reduced-Rank Hidden Markov Models Reduced-Rank Hidden Markov Models

2009-10-06

arxiv.org/abs/0910.0902v3

Computer Science

Learning

Updated robot experiment figure, added details on KDE, fixed a couple of errors

Scientific paper

We introduce the Reduced-Rank Hidden Markov Model (RR-HMM), a generalization of HMMs that can model smooth state evolution as in Linear Dynamical Systems (LDSs) as well as non-log-concave predictive distributions as in continuous-observation HMMs. RR-HMMs assume an m-dimensional latent state and n discrete observations, with a transition matrix of rank k <= m. This implies the dynamics evolve in a k-dimensional subspace, while the shape of the set of predictive distributions is determined by m. Latent state belief is represented with a k-dimensional state vector and inference is carried out entirely in R^k, making RR-HMMs as computationally efficient as k-state HMMs yet more expressive. To learn RR-HMMs, we relax the assumptions of a recently proposed spectral learning algorithm for HMMs (Hsu, Kakade and Zhang 2009) and apply it to learn k-dimensional observable representations of rank-k RR-HMMs. The algorithm is consistent and free of local optima, and we extend its performance guarantees to cover the RR-HMM case. We show how this algorithm can be used in conjunction with a kernel density estimator to efficiently model high-dimensional multivariate continuous data. We also relax the assumption that single observations are sufficient to disambiguate state, and extend the algorithm accordingly. Experiments on synthetic data and a toy video, as well as on a difficult robot vision modeling problem, yield accurate models that compare favorably with standard alternatives in simulation quality and prediction capability.

Affiliated with

Also associated with

No associations

Rating

Reduced-Rank Hidden Markov Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reduced-Rank Hidden Markov Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reduced-Rank Hidden Markov Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-357299