1,123 research outputs found
Ensemble of expanded ensembles: A generalized ensemble approach with enhanced flexibility and parallelizability
Over the past decade, alchemical free energy methods like Hamiltonian replica
exchange (HREX) and expanded ensemble (EXE) have gained popularity for the
computation of solvation free energies and binding free energies. These methods
connect the end states of interest via nonphysical pathways defined by states
with different modified Hamiltonians. However, there exist systems where
traversing all alchemical intermediate states is challenging, even if
alchemical biases (e.g., in EXE) or coordinate exchanges (e.g., in HREX) are
applied. This issue is exacerbated when the state space is multidimensional,
which can require extensive communications between hundreds of cores that
current parallelization schemes do not fully support.
To address this challenge, we present the method of ensemble of expanded
ensembles (EEXE), which integrates the principles of EXE and HREX.
Specifically, the EEXE method periodically exchanges coordinates of EXE
replicas sampling different ranges of states and allows combining weights
across replicas. With the solvation free energy calculation of anthracene, we
show that the EEXE method achieves accuracy akin to the EXE and HREX methods in
free energy calculations, while offering higher flexibility in parameter
specification. Additionally, its parallelizability opens the door to wider
applications, such as estimating free energy profiles of serial mutations.
Importantly, extensions to the EEXE approach can be done asynchronously,
allowing looser communications between larger numbers of loosely coupled
processors, such as when using cloud computing, than methods such as replica
exchange. They also allow adaptive changes to the parameters of ensembles in
response to data collected. All algorithms for the EEXE method are available in
the Python package ensemble_md, which offers an interface for EEXE simulation
management without modifying the source code in GROMACS
Bayesian Estimation of Regression Quantiles in the Presence of Autocorrelated Errors
This is a study of Bayesian quantile regression that broadly considered the estimation of regression quantiles in the presence of autocorrelated error. Regression models are based on several important statistical assumptions upon which their inferences rely. Autocorrelation of the error terms violates the ordinary least squares regression assumption that error terms are uncorrelated which invalidate Gauss Markov theorem. This study designed schemes for estimation and making inference of regression quantiles in the presence of autocorrelated errors using Bayesian approach. Bayesian method to quantile regression models regards unknown parameters as random variables and the parameter uncertainty was taken into account without relying on asymptotic approximations.The empirical analysis used the data set from Central Bank of Nigeria bulletin which comprised of Nigeria GDP growth, export rate, import rate, inflation rate and exchange rate from the period of 1985–2018. Bayesian inferences with autocorrelated error in the framework of quantile regression accounted better for the variability in the distribution of autocorrelation and gave robust and less biased estimates in dealing with non normality and non constant variance assumptions, the results of the research reported minimal Mean Square Errors in Bayesian approach than classical approach across the entire distribution.
Keywords: Bayesian Estimation; Regression Quantiles; Autocorrelated Errors; Regression Analysis
Improved Distributed Algorithms for Random Colorings
Markov Chain Monte Carlo (MCMC) algorithms are a widely-used algorithmic tool
for sampling from high-dimensional distributions, a notable example is the
equilibirum distribution of graphical models. The Glauber dynamics, also known
as the Gibbs sampler, is the simplest example of an MCMC algorithm; the
transitions of the chain update the configuration at a randomly chosen
coordinate at each step. Several works have studied distributed versions of the
Glauber dynamics and we extend these efforts to a more general family of Markov
chains. An important combinatorial problem in the study of MCMC algorithms is
random colorings. Given a graph of maximum degree and an integer
, the goal is to generate a random proper vertex -coloring of
.
Jerrum (1995) proved that the Glauber dynamics has mixing time
when . Fischer and Ghaffari (2018), and independently Feng, Hayes,
and Yin (2018), presented a parallel and distributed version of the Glauber
dynamics which converges in rounds for
for any . We improve this result to for
a fixed . This matches the state of the art for randomly sampling
colorings of general graphs in the sequential setting. Whereas previous works
focused on distributed variants of the Glauber dynamics, our work presents a
parallel and distributed version of the more general flip dynamics presented by
Vigoda (2000) (and refined by Chen, Delcourt, Moitra, Perarnau, and Postle
(2019)), which recolors local maximal two-colored components in each step.Comment: 25 pages, 2 figure
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