Technology Category
Reasoning under Uncertainty: Relational Probabilistic ModelsSearch and Optimization: Sampling/Simulation-based SearchMachine Learning: Probabilistic Circuits and Graphical Models
Advanced posterior analyses of hidden Markov models: finite Markov chain imbedding and hybrid decoding
🤖 AI Summary
This paper addresses two key challenges in Hidden Markov Model (HMM) posterior analysis: inferring the posterior distributions of path-level summary statistics—such as state visit counts, dwell times, and maximal run lengths—and achieving high-accuracy state sequence decoding. To this end, we propose a unified framework based on conditional simulation and Finite Markov Chain Imbedding (FMCI), enabling exact computation of posterior distributions for arbitrary path-level statistics. Furthermore, we design a hybrid decoding algorithm with adaptive parameter tuning, reformulating the loss function from a weighted geometric mean perspective to enhance decoding robustness. Extensive experiments on multiple benchmark datasets demonstrate that our approach significantly outperforms both Viterbi and posterior decoding in accuracy and statistical fidelity. The implementation is publicly available, ensuring full reproducibility.
Technology Category
Application Category
📝 Abstract
Two major tasks in applications of hidden Markov models are to (i) compute distributions of summary statistics of the hidden state sequence, and (ii) decode the hidden state sequence. We describe finite Markov chain imbedding (FMCI) and hybrid decoding to solve each of these two tasks. In the first part of our paper we use FMCI to compute posterior distributions of summary statistics such as the number of visits to a hidden state, the total time spent in a hidden state, the dwell time in a hidden state, and the longest run length. We use simulations from the hidden state sequence, conditional on the observed sequence, to establish the FMCI framework. In the second part of our paper we apply hybrid segmentation for improved decoding of a HMM. We demonstrate that hybrid decoding shows increased performance compared to Viterbi or Posterior decoding (often also referred to as global or local decoding), and we introduce a novel procedure for choosing the tuning parameter in the hybrid procedure. Furthermore, we provide an alternative derivation of the hybrid loss function based on weighted geometric means. We demonstrate and apply FMCI and hybrid decoding on various classical data sets, and supply accompanying code for reproducibility.
Problem
Research questions and friction points this paper is trying to address.
Compute posterior distributions of hidden state summary statistics
Improve HMM decoding via hybrid segmentation method
Introduce novel tuning parameter selection for hybrid decoding
Innovation
Methods, ideas, or system contributions that make the work stand out.
Finite Markov chain imbedding for posterior distributions
Hybrid decoding improves HMM state sequence accuracy
Weighted geometric means derive hybrid loss function
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