Online Markov Decoding: Lower Bounds and Near-Optimal Approximation Algorithms

TL;DR

This paper introduces near-optimal online decoding algorithms for ergodic Markov chains that perform close to offline algorithms with low latency, supported by theoretical bounds and empirical improvements on genome data.

Contribution

It presents the first efficient online algorithms with provable near-optimal performance for general ergodic Markov models, extending to non-stationary settings and establishing fundamental lower bounds.

Findings

Algorithms outperform existing online methods by over 30% on genome data.

Performance is close to the optimal offline algorithm even with latency of one.

Lower bounds show no online method can significantly surpass these algorithms.

Abstract

We resolve the fundamental problem of online decoding with general $n^{th}$ order ergodic Markov chain models. Specifically, we provide deterministic and randomized algorithms whose performance is close to that of the optimal offline algorithm even when latency is small. Our algorithms admit efficient implementation via dynamic programs, and readily extend to (adversarial) non-stationary or time-varying settings. We also establish lower bounds for online methods under latency constraints in both deterministic and randomized settings, and show that no online algorithm can perform significantly better than our algorithms. Empirically, just with latency one, our algorithm outperforms the online step algorithm by over 30\% in terms of decoding agreement with the optimal algorithm on genome sequence data.