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We propose an adaptively weighted stochastic gradient Langevin dynamics algorithm (SGLD), so-called contour stochastic gradient Langevin dynamics (CSGLD), for Bayesian learning in big data statistics. The proposed algorithm is essentially a…
Numerical stochastic perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice field theory. The standard algorithms based on the Langevin equation, however, suffer from several limitations which in…
In this manuscript using the asymptotic method of multiscale nonlinear theory we construct a nonlinear theory of the appearance of large-scale structures in the stratified conductive medium with the presence of small-scale oscillations of…
Using complex Langevin method we probe the possibility of dynamical supersymmetry breaking in supersymmetric quantum mechanics models with complex actions. The models we consider are invariant under the combined operation of parity and time…
We present a systematic analysis of stochastic processes conditioned on an empirical measure $Q_T$ defined in a time interval $[0,T]$ for large $T$. We build our analysis starting from a discrete time Markov chain. Results for a continuous…
The decay of unstable states when several metastable states are available for occupation is investigated using path-integral techniques. Specifically, a method is described which allows the probabilities with which the metastable states are…
The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the…
For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…
The convergence behavior of Stochastic Gradient Descent (SGD) crucially depends on the stepsize configuration. When using a constant stepsize, the SGD iterates form a Markov chain, enjoying fast convergence during the initial transient…
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the…
Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in…
This paper is devoted to the development of a theoretical and computational framework to efficiently sample the statistically significant thermally activated reaction pathways, in multi-dimensional systems obeying Langevin dynamics. We show…
We study a stochastic lattice gas of particles undergoing asymmetric diffusion in two dimensions. Transitions between a low-density uniform phase and high-density non-uniform phases characterized by localized or extended structure are…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
Given a particle system obeying overdamped Langevin dynamics, we demonstrate that it is always possible to construct a thermodynamically consistent macroscopic model which obeys a gradient flow with respect to its non-equilibrium free…
Stochastic evolutions of classical field theories have recently become popular in the study of problems such as determination of the rates of topological transitions and the statistical mechanics of nonlinear coherent structures. To obtain…
Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…