1,026 research outputs found
Characterization of the convergence of stationary Fokker-Planck learning
The convergence properties of the stationary Fokker-Planck algorithm for the
estimation of the asymptotic density of stochastic search processes is studied.
Theoretical and empirical arguments for the characterization of convergence of
the estimation in the case of separable and nonseparable nonlinear optimization
problems are given. Some implications of the convergence of stationary
Fokker-Planck learning for the inference of parameters in artificial neural
network models are outlined
Dynamics of the Desai-Zwanzig model in multiwell and random energy landscapes
We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. {\bf 19}1-24 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multi-well potential energy landscape, coupled via a Curie-Weiss type (quadratic) interaction potential. The location and depth of the local minima of the potential are either deterministic or random. We characterize the structure and nature of bifurcations and phase transitions for this system, by means of extensive numerical simulations and of analytical calculations for an explicitly solvable model. Our numerical experiments are based on Monte Carlo simulations, the numerical solution of the time-dependent nonlinear Fokker-Planck (McKean-Vlasov equation), the minimization of the free energy functional and a continuation algorithm for the stationary solutions
Convergence of Langevin MCMC in KL-divergence
Langevin diffusion is a commonly used tool for sampling from a given
distribution. In this work, we establish that when the target density is
such that is smooth and strongly convex, discrete Langevin
diffusion produces a distribution with in
steps, where is the dimension of the sample
space. We also study the convergence rate when the strong-convexity assumption
is absent. By considering the Langevin diffusion as a gradient flow in the
space of probability distributions, we obtain an elegant analysis that applies
to the stronger property of convergence in KL-divergence and gives a
conceptually simpler proof of the best-known convergence results in weaker
metrics
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