Related papers: Constrained Sampling with Primal-Dual Langevin Mon…
In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…
Sampling-based methods have become a cornerstone of contemporary approaches to Model Predictive Control (MPC), as they make no restrictions on the differentiability of the dynamics or cost function and are straightforward to parallelize.…
This paper is motivated by addressing open questions in distributionally robust chance-constrained programs (DRCCP) using the popular Wasserstein ambiguity sets. Specifically, the computational techniques for those programs typically place…
We study the problem of sampling from a probability distribution on $\mathbb R^p$ defined via a convex and smooth potential function. We consider a continuous-time diffusion-type process, termed Penalized Langevin dynamics (PLD), the drift…
We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the…
Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the…
We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algorithms based on monotone polygonal (tamed) Euler schemes, to…
We introduce Preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates efficient sampling of probability distributions with non-trivial geometry. PMC utilises a Normalising Flow (NF) in order to…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was recently constructed, based on techniques such as variational optimization and left trivialization. We appropriately add tractable noise to the…
We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…
Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
For engineering applications of artificial intelligence, Bayesian learning holds significant advantages over standard frequentist learning, including the capacity to quantify uncertainty. Langevin Monte Carlo (LMC) is an efficient…
In this paper we discuss distributional robustness in the context of stochastic model predictive control (SMPC) for linear time-invariant systems. We derive a simple approximation of the MPC problem under an additive zero-mean i.i.d. noise…
In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution.…