On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2.

ABSTRACT: The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's infinitesimal generator (rate) matrix. Motivated by the derivative's extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a "blessing of dimensionality" result that is universal for a large class of rate matrices with random entries. Finall

SUBMITTER: Didier G 

PROVIDER: S-EPMC10801879 | biostudies-literature | 2024 Jan

REPOSITORIES: biostudies-literature