Controller-Augmented Hidden Markov Models: A Computational Framework for Constrained Sequential Inference

• URL: http://arxiv.org/abs/2606.13850v1
• Date: Thu, 11 Jun 2026 19:29:09 GMT
• Title: Controller-Augmented Hidden Markov Models: A Computational Framework for Constrained Sequential Inference
• Abstract summary: We present Controller-Augmented Hidden Markov Models (CHMMs)<n>CHMMs is a framework that compiles each constraint into a finite-state controller tracking the minimal sufficient history.<n>We evaluate CHMMs against 6 alternative decoders on 3 real-world sequence-labeling tasks.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hidden Markov models are foundational for sequential inference, but their Markovian assumption fails under pathwise constraints such as precedence requirements, visitation cardinalities, or monotonic state progression, which induce long-range dependencies that invalidate standard dynamic programming algorithms. To deal with this, we present Controller-Augmented Hidden Markov Models (CHMMs), a framework that compiles each constraint into a finite-state controller tracking the minimal sufficient history, after which standard forward--backward and Viterbi recursions on the augmented chain compute exact constrained posteriors and maximum a posteriori paths in both discrete and continuous time, the latter through uniformization. We establish four theoretical guarantees: exactness of constrained inference, monotone ascent of constrained EM, inference complexity linear in the controller cardinality, and a total-variation bound under constraint misspecification. A catalog of controller encodings covering 11 constraint families across the ordering, visitation, path, and temporal categories operationalizes the framework. Empirically, we evaluate CHMMs against 6 alternative decoders on 3 real-world sequence-labeling tasks of substantively different character: gene-structure decoding in \emph{Drosophila melanogaster}, free-living activity recognition in CASAS smart-home environments, and protocol-defined human activity recognition from wearable sensors. The results reveal a clean local-versus-cumulative dichotomy in which controller augmentation is uniquely able to recover globally feasible trajectories on cumulative-constraint regimes, whilst simpler decoders are matched in validity on locally-dominated regimes. Together, theory and experiment characterize when exact controller augmentation is necessary and when simpler approaches suffice.

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