Related papers: Multilevel Monte Carlo Variational Inference

Markov Chain Monte Carlo (MCMC) sampling methods are widely used but often encounter either slow convergence or biased sampling when applied to multimodal high dimensional distributions. In this paper, we present a general framework of…

Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language…

Sequence generation models are commonly refined with reinforcement learning over user-defined metrics. However, high gradient variance hinders the practical use of this method. To stabilize this method, we adapt to contextual generation of…

We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…

We propose a novel training method based on nonlinear multilevel minimization techniques, commonly used for solving discretized large scale partial differential equations. Our multilevel training method constructs a multilevel hierarchy by…

Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods,…

This position paper summarizes a recently developed research program focused on inference in the context of data centric science and engineering applications, and forecasts its trajectory forward over the next decade. Often one endeavours…

Learning strategies for imperfect information games from samples of interaction is a challenging problem. A common method for this setting, Monte Carlo Counterfactual Regret Minimization (MCCFR), can have slow long-term convergence rates…

In this contribution, we propose a new computationally efficient method to combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC). This approach can be used with generic MCMC kernels, but is especially well suited to…

Modern computational advances have enabled easy parallel implementations of Markov chain Monte Carlo (MCMC). However, almost all work in estimating the variance of Monte Carlo averages, including the efficient batch means (BM) estimator,…

This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized…

We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in…

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…

In this paper, the minimization of computational cost on evaluating multi-dimensional integrals is explored. More specifically, a method based on an adaptive scheme for error variance selection in Monte Carlo integration (MCI) is presented.…

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high…

We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…

Constructing unbiased estimators from Markov chain Monte Carlo (MCMC) outputs is a difficult problem that has recently received a lot of attention in the statistics and machine learning communities. However, the current unbiased MCMC…

We present a trainable framework for efficiently generating gauge configurations, and discuss ongoing work in this direction. In particular, we consider the problem of sampling configurations from a 4D $SU(3)$ lattice gauge theory, and…

We present a novel multilevel Monte Carlo approach for estimating quantities of interest for stochastic partial differential equations (SPDEs). Drawing inspiration from [Giles and Szpruch: Antithetic multilevel Monte Carlo estimation for…