Learning reaction coordinates via cross-entropy minimization: Application to alanine dipeptide

Integrating diffusion maps with umbrella sampling: application to alanine dipeptide.

Nonlinear dimensionality reduction techniques can be applied to molecular simulation trajectories to systematically extract a small number of variables with which to parametrize the important dynamical motions of the system. For molecular systems exhibiting free energy barriers exceeding a few k(B)T, inadequate sampling of the barrier regions between stable or metastable basins can lead to a po...

Properties of cross-entropy minimization

Pattern discovery via entropy minimization

We propose a framework for learning hiddenvariable models by optimizing entropies, in which entropy minimization, posterior maximization, and free energy minimization are all equivalent. Solutions for the maximum a posteriori (MAP) estimator yield powerful learning algorithms that combine all the charms of expectation-maximization and deterministic annealing. Contained as special cases are the ...

Calculation of conformational transitions and barriers in solvated systems: Application to the alanine dipeptide in water

Optimal free energy paths ~OFEPs! for conformational transitions are parallel to the mean force at every nonstationary point of the free energy landscape. In contrast to adiabatic paths, which are parallel to the force, OFEPs include the effect of entropy and are relevant even for systems with diffusive degrees of freedom. In this study the OFEPs are computed for the alanine dipeptide in soluti...

Structure and parameter learning via entropy minimization, with applications to mixture and hidden Markov models

We develop a computationally efficient framework for finding compact and highly accurate hidden-variable models via entropy minimization. The main results are: 1) An entropic prior that favors small, unambiguous, maximally structured models. 2) A priorbalancing manipulation of Bayes’ rule that allows one to gradually introduce or remove constraints in the course of iterative reestimation. #1 an...