Tractable Inference and Observation Likelihood Evaluation in Latent Structure Influence Models

Latent Structure Influence Models (LSIMs) are a particular kind of Coupled Hidden Markov Models (CHMMs). Against CHMMs, LSIMs overcome the exponential growth of state-space parameters by considering the influence model for coupled Markov chains. Nevertheless, the exact inference in LSIMs requires ex...

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Veröffentlicht in:IEEE transactions on signal processing Jg. 68; S. 5736 - 5745
Hauptverfasser: Karimi, Sajjad, Shamsollahi, Mohammad Bagher
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Approximate inference
Approximation algorithms
Boyen-Koller algorithm
Brain modeling
Channels
Classification
Computational modeling
Consumer goods
convex combination
coupled hidden Markov model
Data points
Evaluation
forward and backward parameters
Heuristic algorithms
Hidden Markov models
Inference algorithms
influence model
Latent class analysis
latent structure influence model
Machine learning
Markov chains
Mathematical models
Parameters
Signal processing algorithms
squared euclidean distance
Statistical inference
ISSN:1053-587X, 1941-0476
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Zusammenfassung:Latent Structure Influence Models (LSIMs) are a particular kind of Coupled Hidden Markov Models (CHMMs). Against CHMMs, LSIMs overcome the exponential growth of state-space parameters by considering the influence model for coupled Markov chains. Nevertheless, the exact inference in LSIMs requires exponential complexity. We propose a new recursive formulation to compute marginal forward and backward parameters by <inline-formula><tex-math notation="LaTeX">\mathcal {O}(T{(NC)}^{2})</tex-math></inline-formula> instead of <inline-formula><tex-math notation="LaTeX">\mathcal {O}(TN^{\text{2}\,C})</tex-math></inline-formula> for <inline-formula><tex-math notation="LaTeX">C</tex-math></inline-formula> channels of <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula> states apiece observing <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula> data points. This formulation is derived systematically and carefully to increase the inference accuracy. Furthermore, a solution is presented for the evaluation problem of LSIMs based on the proposed marginal forward parameter. This solution is essential in statistical multi-channel time-series classification. The results show that the proposed algorithm is generally more accurate and reliable than other existing algorithms. Novelties in deriving the marginal backward parameter plays an important role in this superiority. The Hellinger distance is computed between the proposed and exact forward and one-slice parameters for various simulation scenarios. Distances are small enough, indicating that the proposed inference algorithm is sufficiently close to exact inference for various channels, hidden state numbers, and other parameters. Statistical multi-channel time-series classification is also considered for both proposed and exact algorithms. Classification results are almost similar, indicating that the proposed approximate inference is proper and acceptable in the classification task. Finally, the iEEG dataset's parameter learning indicates that the proposed inference algorithm leads to a higher log-likelihood than the existing algorithms.
Bibliographie:ObjectType-Article-1
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2020.3025522