Tractable Inference and Observation Likelihood Evaluation in Latent Structure Influence Models

Karimi, Sajjad; Shamsollahi, Mohammad Bagher

doi:10.1109/tsp.2020.3025522

Cited by 4 publications

(6 citation statements)

References 29 publications

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“…2 ) [28]. Simulated and real datasets' results confirmed that the proposed inference has less error and superior performance than SVI and CFVI.…”

Section: Introductionmentioning

confidence: 67%

“…This approximate algorithm is fast and acceptable for many practical applications, while exact inference can be demanding and time-consuming. Hellinger distances are small enough, indicating that the proposed approximate inference is sufficiently close to the exact inference when considering various channels, hidden states, and other parameters [28]. Further, the proposed inference algorithm has superior performance than existing approximate inference algorithms.…”

Section: Maximization and Re-estimation Algorithmmentioning

confidence: 83%

“…2 ) instead of O(T N 2C ) for an LSIM with C channels of N states apiece observing T data points [28]. This approximate algorithm is fast and acceptable for many practical applications, while exact inference can be demanding and time-consuming.…”

Section: Maximization and Re-estimation Algorithmmentioning

confidence: 99%

“…In this section, we define symbols and variables with the same notations as [6], [28]. Some new definitions are also considered for future probabilistic manipulation.…”

Section: Proposed Learning Frameworkmentioning

confidence: 99%

“…The forward, backward, and one-slice parameters are the most critical parameters in the inference that have an essential role in re-estimation transformation. The marginal forward, oneslice, and backward parameters are respectively defined as follows [28]…”

Section: Maximization and Re-estimation Algorithmmentioning

confidence: 99%

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Tractable Maximum Likelihood Estimation for Latent Structure Influence Models With Applications to EEG & ECoG Processing

Karimi

Shamsollahi

2023

IEEE Trans. Pattern Anal. Mach. Intell.

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Brain signals are nonlinear and nonstationary time series, which provide information about spatiotemporal patterns of electrical activity in the brain. CHMMs are suitable tools for modeling multi-channel time-series dependent on both time and space, but state-space parameters grow exponentially with the number of channels. To cope with this limitation, we consider the influence model as the interaction of hidden Markov chains called Latent Structure Influence Models (LSIMs). LSIMs are capable of detecting nonlinearity and nonstationarity, making them well suited for multi-channel brain signals. We apply LSIMs to capture the spatial and temporal dynamics in multichannel EEG/ECoG signals. The current manuscript extends the scope of the re-estimation algorithm from HMMs to LSIMs. We prove that the re-estimation algorithm of LSIMs will converge to stationary points corresponding to Kullback-Leibler divergence. We prove convergence by developing a new auxiliary function using the influence model and a mixture of strictly log-concave or elliptically symmetric densities. The theories that support this proof are derived from previous studies by Baum, Liporace, Dempster, and Juang. We then develop a closed-form expression for re-estimation formulas using tractable marginal forwardbackward parameters defined in our previous study. Simulated datasets and EEG/ECoG recordings confirm the practical convergence of the derived re-estimation formulas. We also study the use of LSIMs for modeling and classification on simulated and EEG/ECoG datasets. Based on AIC and BIC, LSIMs perform better than HMMs in modeling embedded Lorenz systems and ECoG recordings. LSIMs are more reliable and better classifiers than HMMs and SVMs in 2class simulated CHMMs. EEG biometric verification results indicate that the LSIM-based method improves the area under curve (AUC) values by about 6.8% and decreases the standard deviation of AUC values from 5.4% to 3.3% compared to the existing HMM-based method for all conditions on the BED dataset.

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“…2 ) [28]. Simulated and real datasets' results confirmed that the proposed inference has less error and superior performance than SVI and CFVI.…”

Section: Introductionmentioning

confidence: 67%

Section: Maximization and Re-estimation Algorithmmentioning

confidence: 83%

Section: Maximization and Re-estimation Algorithmmentioning

confidence: 99%

“…In this section, we define symbols and variables with the same notations as [6], [28]. Some new definitions are also considered for future probabilistic manipulation.…”

Section: Proposed Learning Frameworkmentioning

confidence: 99%

Section: Maximization and Re-estimation Algorithmmentioning

confidence: 99%

See 3 more Smart Citations