Siddiqi et al 2009 Reduced-Rank Hidden Markov Models
Citation
Online version
Summary
This paper introduces Reduced-Rank Hidden Markov Models (RR-HMMs). RR-HMMs are similar to standard HMMs, except the rank of the transition matrix is less than the number of hidden states. Thus the dynamics evolve in a subspace of the hidden state probability space.
Method
Sample singles, doubles, and triples from the from the observed output of the RR-HMM. Then let:
The learning algorithm uses a singular value decomposition (SVD) of the correlation matrix between past and future observations. The algorithm is borrowed from Hsu et al 2009, with no change for the reduced-rank case. Learning is O(
is the initial state distribution, is the final state distribution, and is the transition matrix when x is observed. Note that denotes the Moore-Penrose pseudo-inverse of the matrix .
Inference can be performed using the model parameters:
Experimental Result
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