相关论文: Can Microcanonical Langevin Dynamics Leverage Mini…

In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant…

Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…

Variable selection in linear regression has been a central topic in statistical research for decades. Bayesian variable selection methods, which account for uncertainty in both the regression coefficients and the noise variance, have…

This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…

In this paper, we estimate the variance of two coupled paths derived with the Multilevel Monte Carlo method combined with the Euler Maruyama discretization scheme for the simulation of McKean-Vlasov stochastic differential equations with…

Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…

Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…

Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic…

In high dimensions, most machine learning method perform fragile even there are a little outliers. To address this, we hope to introduce a new method with the base learner, such as Bayesian regression or stochastic gradient descent to solve…

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC)…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

We present a novel technique for learning the mass matrices in samplers obtained from discretized dynamics that preserve some energy function. Existing adaptive samplers use Riemannian preconditioning techniques, where the mass matrices are…

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…

Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In…

Langevin algorithms are popular Markov chain Monte Carlo (MCMC) methods for large-scale sampling problems that often arise in data science. We propose Monte Carlo algorithms based on the discretizations of $P$-th order Langevin dynamics for…

A novel discretization is presented for forward-backward stochastic differential equations (FBSDE) with differentiable coefficients, simultaneously solving the BSDE and its Malliavin sensitivity problem. The control process is estimated by…

We revisit the problem of sampling from a target distribution that has a smooth strongly log-concave density everywhere in $\mathbb R^p$. In this context, if no additional density information is available, the randomized midpoint…

Macromolecular complexation leading to coupling of two or more cellular membranes is a crucial step in a number of biological functions of the cell. While other mechanisms may also play a role, adhesion always involves the fluctuations of…