تقرير
On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2
| العنوان: | On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2 |
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| المؤلفون: | Didier, Gustavo, Glatt-Holtz, Nathan E., Holbrook, Andrew J., Magee, Andrew F., Suchard, Marc A. |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Statistics - Computation, Mathematics - Probability |
| الوصف: | 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 SARS-CoV-2 across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology. Comment: To appear in the Proceedings of the National Academy of Sciences |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2306.15841 |
| رقم الأكسشن: | edsarx.2306.15841 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |