New tensor algorithm slashes computational cost of factorial HMMs

Factorial hidden Markov models (fHMMs) are powerful tools for time-series analysis, representing multiple independent hidden state chains that jointly generate observed data. However, converting an fHMM into an equivalent standard HMM results in an exponentially larger state space, making the central forward filtering algorithm prohibitively expensive even for small systems. This computational bottleneck has limited fHMM applications to small-scale problems.

Barrios and Sgouralis introduce tensorized algorithms that operate directly on the multidimensional structure of fHMMs, bypassing the intermediate HMM construction entirely. Their approach leverages tensor algebra to perform filtering, decoding, and estimation tasks with significantly improved scalability. The method extends the practical scope of fHMMs to large datasets and complex systems, opening new possibilities in fields like finance, genomics, and sensor networks where multiple independent factors influence observed time-series.