This content will become publicly available on January 16, 2025
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. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology.
more » « less- NSF-PAR ID:
- 10490728
- Publisher / Repository:
- On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 121
- Issue:
- 3
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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