The Highest Expected Reward Decoding for HMMs with Application to Recombination Detection

Hidden Markov models are traditionally decoded by the Viterbi algorithm which finds the highest probability state path in the model. In recent years, several limitations of the Viterbi decoding have been demonstrated, and new algorithms have been developed to address them \citep{Kall2005,Brejova2007,Gross2007,Brown2010}. In this paper, we propose a new efficient highest expected reward decoding algorithm (HERD) that allows for uncertainty in boundaries of individual sequence features. We demonstrate usefulness of our approach on jumping HMMs for recombination detection in viral genomes.

💡 Research Summary

The paper addresses a fundamental limitation of the classic Viterbi algorithm for decoding Hidden Markov Models (HMMs). Viterbi seeks the single most probable state path, which works well when the underlying sequence features have precisely defined boundaries. In many biological contexts, however, especially in viral genomics where recombination events create mosaic genomes, the exact start and end of a feature are uncertain. Small shifts in a boundary can dramatically reduce the overall path probability, causing Viterbi to miss biologically relevant events.

To overcome this, the authors introduce the Highest Expected Reward Decoding (HERD) algorithm. Instead of maximizing joint probability, HERD maximizes the expected sum of a user‑defined reward function that assigns positive scores to states that correspond to biologically meaningful segments. The reward function can be shaped to tolerate boundary jitter: a “window” around a putative recombination breakpoint receives high reward, while points farther away receive lower but non‑zero reward. Consequently, HERD prefers paths that capture the overall reward even if the exact boundary is slightly misplaced, providing a more robust interpretation of ambiguous data.

Mathematically, HERD augments the standard log‑probability dynamic programming recurrence with an additive reward term r_j(t) for being in state j at time t:
δ_t(j) = max_i