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We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient…

This work introduces a novel and efficient Bayesian federated learning algorithm, namely, the Federated Averaging stochastic Hamiltonian Monte Carlo (FA-HMC), for parameter estimation and uncertainty quantification. We establish rigorous…

Recently a machine learning approach to Monte-Carlo simulations called Neural Markov Chain Monte-Carlo (NMCMC) is gaining traction. In its most popular form it uses neural networks to construct normalizing flows which are then trained to…

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…

Lack of standardization and various intrinsic parameters for magnetic resonance (MR) image acquisition results in heterogeneous images across different sites and devices, which adversely affects the generalization of deep neural networks.…

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a…

We propose using Normalizing Flows as a trainable kernel within the molecular dynamics update of Hamiltonian Monte Carlo (HMC). By learning (invertible) transformations that simplify our dynamics, we can outperform traditional methods at…

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic…

Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an…

Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new…

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm…

The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical…

Continuous normalizing flows (CNFs) learn the probability path between a reference distribution and a target distribution by modeling the vector field generating said path using neural networks. Recently, Lipman et al. (2022) introduced a…

This paper presents a structure-preserving Bayesian approach for learning nonseparable Hamiltonian systems using stochastic dynamic models allowing for statistically-dependent, vector-valued additive and multiplicative measurement noise.…

Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis. Typical problems in Bayesian workflows…

We propose a novel method ($floZ$), based on normalizing flows, to estimate the Bayesian evidence (and its numerical uncertainty) from a pre-existing set of samples drawn from the unnormalized posterior distribution. We validate it on…

Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…

Many modern applications of Bayesian inference, such as in cosmology, are based on complicated forward models with high-dimensional parameter spaces. This considerably limits the sampling of posterior distributions conditioned on observed…

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…