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 exponential complexity. We propose a new recursive formulation to compute marginal forward and backward parameters by $mathcal {O}(T{(NC)}^{2})$ instead of $mathcal {O}(TN^{text{2},C})$ for $C$ channels of $N$ states apiece observing $T$ 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. Classi...
Source: IEEE Transactions on Signal Processing - Category: Biomedical Engineering Source Type: research