[Paper Review] A generalized risk approach to path inference based on hidden Markov models

Jüri Lember, Alexey Koloydenko|arXiv (Cornell University)|Jul 21, 2010

Bayesian Methods and Mixture Models40 references3 citations

TL;DR

This paper introduces a generalized risk-based framework for path inference in hidden Markov models (HMMs), proposing a new class of interpretable, tunable decoders that hybridize the traditional Viterbi (MAP) and posterior decoding (PD) estimators. Unlike prior algorithmic hybrids, these risk-based decoders are computationally efficient, work 'out-of-the-box' in practice, and are validated on real bioinformatics data with improved accuracy and robustness through dynamic programming algorithms using forward-backward procedures.

ABSTRACT

Motivated by the unceasing interest in hidden Markov models (HMMs), this paper re-examines hidden path inference in these models, using primarily a risk-based framework. While the most common maximum a posteriori (MAP), or Viterbi, path estimator and the minimum error, or Posterior Decoder (PD), have long been around, other path estimators, or decoders, have been either only hinted at or applied more recently and in dedicated applications generally unfamiliar to the statistical learning community. Over a decade ago, however, a family of algorithmically defined decoders aiming to hybridize the two standard ones was proposed (Brushe et al., 1998). The present paper gives a careful analysis of this hybridization approach, identifies several problems and issues with it and other previously proposed approaches, and proposes practical resolutions of those. Furthermore, simple modifications of the classical criteria for hidden path recognition are shown to lead to a new class of decoders. Dynamic programming algorithms to compute these decoders in the usual forward-backward manner are presented. A particularly interesting subclass of such estimators can be also viewed as hybrids of the MAP and PD estimators. Similar to previously proposed MAP-PD hybrids, the new class is parameterized by a small number of tunable parameters. Unlike their algorithmic predecessors, the new risk-based decoders are more clearly interpretable, and, most importantly, work "out of the box" in practice, which is demonstrated on some real bioinformatics tasks and data. Some further generalizations and applications are discussed in conclusion.

Motivation & Objective

• To address limitations in existing path estimators for HMMs, particularly the lack of interpretability and practical usability in the hybridization of MAP and PD decoders.
• To develop a principled, risk-based approach to path inference that generalizes classical criteria and enables systematic interpolation between MAP and PD estimators.
• To provide dynamic programming algorithms for computing the new decoders efficiently using forward-backward procedures, ensuring practical applicability.
• To demonstrate the effectiveness of the proposed decoders on real-world bioinformatics datasets, showing improved performance over standard methods.
• To generalize the framework to extensions of HMMs, such as semi-Markov and factorial HMMs, while maintaining computational feasibility.

Proposed method

• Proposes a generalized risk approach to path inference, defining a new class of decoders based on minimizing a risk function that balances prior and posterior information.
• Introduces a parameterized family of estimators that interpolate between the Viterbi (MAP) and posterior decoding (PD) paths, with tunable parameters for empirical optimization.
• Develops dynamic programming algorithms using forward and backward computations to efficiently compute the new decoders, analogous to the Viterbi and posterior decoding algorithms.
• Applies the framework to HMMs with discrete, finite state spaces and conditionally independent observations, leveraging the Markov property of the posterior distribution.
• Uses cross-validation and labeled data to tune the risk-based parameters, ensuring optimal performance on unseen data.
• Extends the approach to more complex models, such as variable-duration and factorial HMMs, by maintaining the same computational structure.

Experimental results

Research questions

• RQ1 How can a principled, risk-based framework be developed to unify and generalize existing path estimators in HMMs?
• RQ2 What are the limitations of prior algorithmic hybridizations of MAP and PD decoders, and how can they be resolved through a more interpretable, statistical framework?
• RQ3 Can a new class of decoders be constructed that systematically interpolates between Viterbi and posterior decoding while maintaining computational efficiency?
• RQ4 How do the proposed risk-based decoders perform in practice compared to standard estimators on real bioinformatics data?
• RQ5 To what extent can the framework be extended to more complex HMM variants, such as semi-Markov or factorial models?

Key findings

• The proposed risk-based decoders are interpretable, tunable, and work 'out-of-the-box' without requiring custom algorithmic adjustments, unlike earlier hybrid approaches.
• The new decoders are computed efficiently using dynamic programming with forward-backward procedures, ensuring scalability to long sequences.
• In bioinformatics experiments, the new decoders achieved improved accuracy over standard MAP and PD estimators, particularly in scenarios with ambiguous state transitions.
• The framework successfully handles inadmissible paths and ensures positivity of posterior probabilities through constrained optimization, avoiding spurious solutions.
• Parameter tuning via cross-validation leads to consistent performance gains, demonstrating robustness across different datasets.
• The approach generalizes naturally to extended HMMs, including semi-Markov and factorial models, with minimal modifications to the core algorithm.