13,152 research outputs found
Using bijective maps to improve free energy estimates
We derive a fluctuation theorem for generalized work distributions, related
to bijective mappings of the phase spaces of two physical systems, and use it
to derive a two-sided constraint maximum likelihood estimator of their free
energy difference which uses samples from the equilibrium configurations of
both systems. As an application, we evaluate the chemical potential of a dense
Lennard-Jones fluid and study the construction and performance of suitable
maps.Comment: 17 pages, 11 figure
Estimation of Markov Chain via Rank-Constrained Likelihood
This paper studies the estimation of low-rank Markov chains from empirical
trajectories. We propose a non-convex estimator based on rank-constrained
likelihood maximization. Statistical upper bounds are provided for the
Kullback-Leiber divergence and the risk between the estimator and the
true transition matrix. The estimator reveals a compressed state space of the
Markov chain. We also develop a novel DC (difference of convex function)
programming algorithm to tackle the rank-constrained non-smooth optimization
problem. Convergence results are established. Experiments show that the
proposed estimator achieves better empirical performance than other popular
approaches.Comment: Accepted at ICML 201
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