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The problem of large scale multiple testing arises in many contexts, including testing for pairwise interaction among large numbers of neurons. With advances in technologies, it has become common to record from hundreds of neurons…
Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their scalability…
The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…
We introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov Chain Monte Carlo sampling procedure to iteratively train network layers, avoiding…
Although generative models hold promise for discovering molecules with optimized desired properties, they often fail to suggest synthesizable molecules that improve upon the known molecules seen in training. We find that a key limitation is…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
Modern language models rely on the transformer architecture and attention mechanism to perform language understanding and text generation. In this work, we study learning a 1-layer self-attention model from a set of prompts and associated…
The Markov chain Monte Carlo (MCMC) method is the computational workhorse for Bayesian inverse problems. However, MCMC struggles in high-dimensional parameter spaces, since its iterates must sequentially explore the high-dimensional space.…
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…
We present a novel Bayesian inference tool that uses a neural network to parameterise efficient Markov Chain Monte-Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of…
Cyclical MCMC is a novel MCMC framework recently proposed by Zhang et al. (2019) to address the challenge posed by high-dimensional multimodal posterior distributions like those arising in deep learning. The algorithm works by generating a…
In this paper, we address the challenge of Markov Chain Monte Carlo (MCMC) algorithms within the approximate Bayesian Computation (ABC) framework, which often get trapped in local optima due to their inherent local exploration mechanism. We…
Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…
We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given…
We consider stochastic optimization problems where data is drawn from a Markov chain. Existing methods for this setting crucially rely on knowing the mixing time of the chain, which in real-world applications is usually unknown. We propose…
Energy-based modeling is a promising approach to unsupervised learning, which yields many downstream applications from a single model. The main difficulty in learning energy-based models with the "contrastive approaches" is the generation…
We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…
Markov chain Monte Carlo (MCMC) methods are ubiquitous tools for simulation-based inference in many fields but designing and identifying good MCMC samplers is still an open question. This paper introduces a novel MCMC algorithm, namely,…
Extrapolation in reinforcement learning is the ability to generalize at test time given states that could never have occurred at training time. Here we consider four factors that lead to improved extrapolation in a simple Gridworld…
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…