Stochastic gradient-based Monte Carlo methods such as stochastic gradient Langevin dynamics are useful tools for posterior inference on large scale datasets in many machine learning applications. These methods scale to large datasets by using noisy gradients calculated using a mini-batch or subset of the dataset. However, the high variance inherent in these noisy gradients degrades performance ...

We study the treatment of the constraints in stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking account of the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochast...

A new type of Langevin equation exhibiting a nontrivial phase transition associated with the presence of multiplicative noise is discussed. The equation is derived as a mesoscopic representation of the microscopic annealed Ising model ~AIM! proposed by Thorpe and Beeman, and reproduces perfectly its basic phenomenology. The AIM exhibits a nontrivial behavior as the temperature is increased, in ...

Effective field theory of interacting BFKL pomerons is investigated and Langevin equation for the theory, which arises after the introduction of additional auxiliary field, is obtained. The Langevin equations are considered for the case of interacting BFKL pomerons with both splitting and merging vertexes and for the interaction which includes additional " toy " four pomeron interaction vertex....

A broad class of implicit or partially implicit time discretizations for the Langevin diffusion are considered and used as proposals for the Metropolis-Hastings algorithm. Ergodic properties of our proposed schemes are studied. We show that introducing implicitness in the discretization leads to a process that often inherits the convergence rate of the continuous time process. These contrast wi...

We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in discrete time, and consider how to remove or reduce the bias. We point out the difficulty is that the heat flow is exactly solvable, but neither its forward nor bac...

The advantages of performing Langevin Dynamics in extended systems are discussed. A simple Langevin Dynamics scheme for producing the canonical ensemble is reviewed, and is then extended to the Hoover ensemble. We show that the resulting equations of motion generate the isobaricisothermal ensemble. The Parrinello-Rahman ensemble is then discussed and we show that despite the presence of intrins...