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Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…
Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…
Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one encounters already for a few qubits, the…
The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte Carlo methods. We study here an advanced version of familiar Markov Chain Monte…
Sampling from binary quadratic distributions (BQDs) is a fundamental but challenging problem in discrete optimization and probabilistic inference. Previous work established theoretical guarantees for stochastic localization (SL) in…
Recent research has led to the development of MCMC algorithms with likelihood-informed proposals when targeting posterior distributions supported on discrete state spaces. Our work is placed within this field and puts forward a new MCMC…
Markov Chain Monte Carlo (MCMC) methods are algorithms for sampling probability distributions, commonly applied to the Boltzmann distribution in physical and chemical models such as protein folding and the Ising model. These methods enable…
Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are…
We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…
We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an approach inspired by optimal transport allows us to bound…
The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
In this expository paper we abstract and describe a simple MCMC scheme for sampling from intractable target densities. The approach has been introduced in Gon\c{c}alves et al. (2017a) in the specific context of jump-diffusions, and is based…
Constrained decoding enables Language Models (LMs) to produce samples that provably satisfy hard constraints. However, existing constrained-decoding approaches often distort the underlying model distribution, a limitation that is especially…
Inferring directed acyclic graphs (DAGs) from data via Markov chain Monte Carlo (MCMC) is computationally challenging in moderate-to-high dimensional settings because their discrete sampling space grows super-exponentially with the number…
In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…
Motivated by the problem of exploring discrete but very complex state spaces in Bayesian models, we propose a novel Markov Chain Monte Carlo search algorithm: the taxicab sampler. We describe the construction of this sampler and discuss how…