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This paper introduces scalable filtering methods for factorial hidden Markov models (fHMM) that leverage tensor algebra to directly analyze time-series data without converting to a larger hidden Markov model (HMM) representation. By addressing the computational challenges associated with the forward filtering algorithm in fHMMs, the authors demonstrate significant performance improvements that allow for the analysis of larger systems and datasets. The proposed approach not only enhances efficiency but also expands the applicability of fHMMs in real-world scenarios where multiple independent factors influence observations.
Tensor algebra enables efficient analysis of factorial hidden Markov models, overcoming the computational bottlenecks of traditional methods.
A common method for the representation and analysis of time-series data is the hidden Markov model (HMM), where each observation is associated with a hidden state that evolves over time. However, many real-world systems are influenced by multiple independent factors, which are more naturally represented by factorial hidden Markov models (fHMM), where several hidden Markov chains jointly generate the observed data. Although an fHMM provides a richer and more realistic representation of many real-world systems, it can be reformulated as an equivalent HMM, but with a significantly larger state-space, leading to a severe increase in computational cost. In particular, the forward filtering algorithm, which is central to evaluation, decoding, and estimation tasks, becomes prohibitively expensive even for small systems. This work focuses on developing scalable methods for time-series analysis using tensor algebra to exploit the multidimensional structure of fHMM directly, without constructing intermediate HMM representations. Our novel filtering approach significantly improves computational performance and enables the efficient analysis of large systems and datasets, extending the scope of fHMM and providing a practical framework for data intensive applications.
