Difference between revisions of "Siddiqi et al 2009 Reduced-Rank Hidden Markov Models"
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== Summary == | == Summary == | ||
− | This paper introduces Reduced-Rank Hidden Markov Models (RR-HMMs). RR- | + | This [[Category::paper]] introduces Reduced-Rank Hidden Markov Models (RR-HMMs). A RR-HMM is similar to standard [[UsesMethod::HMM]], except the rank of the transition matrix is less than the number of hidden states. The dynamics evolve in a subspace of the hidden state probability space. |
== Method == | == Method == | ||
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== Experimental Result == | == Experimental Result == | ||
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[[File:Siddiqi et al 2009 Results.png]] | [[File:Siddiqi et al 2009 Results.png]] | ||
Revision as of 03:08, 11 October 2011
Citation
Online version
Summary
This paper introduces Reduced-Rank Hidden Markov Models (RR-HMMs). A RR-HMM is similar to standard HMM, except the rank of the transition matrix is less than the number of hidden states. The dynamics evolve in a subspace of the hidden state probability space.
Method
Let be the observed output of the RR-HMM and 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.
is the initial state distribution, is the final state distribution, and is the transition matrix when x is observed. is the rank of the reduced state space. 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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