Times Square Sampling: An Adaptive Algorithm for Free Energy Estimation

Estimating free energy differences, an important problem in computational drug discovery and in a wide range of other application areas, commonly involves a computationally intensive process of sampling a family of high-dimensional probability distributions and a procedure for computing estimates ba...

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Bibliographic Details
Published in:Journal of computational and graphical statistics 2024-07, Vol.33 (3), p.1073-1083
Main Authors: Predescu, Cristian, Snarski, Michael, Robinson-Mosher, Avi, Sritharan, Duluxan, Szalay, Tamas, Shaw, David E.
Format: Article
Language:English
Subjects:
Adaptive algorithms
Adaptive Monte Carlo
Adaptive sampling
Asymptotic methods
Free energy
Free energy calculations
Maximum likelihood estimation
Maximum likelihood estimators
Partition function ratios
Simulated tempering
Statistical analysis
Stochastic approximation
Variance
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Summary:Estimating free energy differences, an important problem in computational drug discovery and in a wide range of other application areas, commonly involves a computationally intensive process of sampling a family of high-dimensional probability distributions and a procedure for computing estimates based on those samples. The variance of the free energy estimate of interest typically depends strongly on how the total computational resources available for sampling are divided among the distributions, but determining an efficient allocation is difficult without sampling the distributions. Here we introduce the Times Square sampling algorithm, a novel on-the-fly estimation method that dynamically allocates resources in such a way as to significantly accelerate the estimation of free energies and other observables, while providing rigorous convergence guarantees for the estimators. We also show that it is possible, surprisingly, for on-the-fly free energy estimation to achieve lower asymptotic variance than the maximum-likelihood estimator MBAR, raising the prospect that on-the-fly estimation could reduce variance in a variety of other statistical applications. Supplementary materials for this article are available online.
ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2023.2291108