Related papers: Adaptive Thermostats for Noisy Gradient Systems
We present a deterministic algorithm called contact density dynamics that generates any prescribed target distribution in the physical phase space. Akin to the famous model of Nos\'e-Hoover, our algorithm is based on a non-Hamiltonian…
We introduce a numerical method for Brownian dynamics with position dependent diffusion tensor which is second order accurate for sampling the invariant measure while requiring only one force evaluation per timestep. Analysis of the…
Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated equations with random input data. A parametric system emerged…
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…
This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…
Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level…
Stochastic learning dynamics based on Langevin or Levy stochastic differential equations (SDEs) in deep neural networks control the variance of noise by varying the size of the mini-batch or directly those of injecting noise. Since the…
We propose a general and scalable approximate sampling strategy for probabilistic models with discrete variables. Our approach uses gradients of the likelihood function with respect to its discrete inputs to propose updates in a…
Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multi-modal probability distributions. Most popular methods, such as Markov chain Monte Carlo sampling, perform…
We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to…
D. B. Br\"{u}ckner et al. [Phys. Rev. Lett. 125, 058103 (2020)] have described a novel method for inferring the dynamics of systems governed by an underdamped Langevin equation in the presence of measurement noise. While this is a…
In this paper, we propose a novel warm restart technique using a new logarithmic step size for the stochastic gradient descent (SGD) approach. For smooth and non-convex functions, we establish an $O(\frac{1}{\sqrt{T}})$ convergence rate for…
This paper discusses the adaptive sampling problem in a nonholonomic mobile robotic sensor network for efficiently monitoring a spatial field. It is proposed to employ Gaussian process to model a spatial phenomenon and predict it at…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent…
We consider the problem of density estimation in the context of multiscale Langevin diffusion processes, where a single-scale homogenized surrogate model can be derived. In particular, our aim is to learn the density of the invariant…
We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…