Related papers: Amortising over hyperparameters in Generalised Bay…

We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…

The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be…

Bayesian inference typically relies on a large number of model evaluations to estimate posterior distributions. Established methods like Markov Chain Monte Carlo (MCMC) and Amortized Bayesian Inference (ABI) can become computationally…

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…

Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to…

Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances…

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 present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…

In this paper, we leverage stochastic projection and lossy compression to establish new conditional mutual information (CMI) bounds on the generalization error of statistical learning algorithms. It is shown that these bounds are generally…

We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…

A significant barrier to the widespread adoption of Bayesian inference is the specification of prior distributions and likelihoods, which often requires specialized statistical expertise. This paper investigates the feasibility of using a…

Statistical inference in physics is often based on samples from a generator (sometimes referred to as a ``forward model") that emulate experimental data and depend on parameters of the underlying theory. Modern machine learning has…

Generalized Bayesian inference (GBI) is an alternative inference framework motivated by robustness to modeling errors, where a specific loss function is used to link the model parameters with observed data, instead of the log-likelihood…

Making inferences about physical properties of the Universe requires knowledge of the data likelihood. A Gaussian distribution is commonly assumed for the uncertainties with a covariance matrix estimated from a set of simulations. The noise…

Generalised Bayesian Inference (GBI) attempts to address model misspecification in a standard Bayesian setup by tempering the likelihood. The likelihood is raised to a fractional power, called the learning rate, which reduces its importance…

A conventional Bayesian approach to prediction uses the posterior distribution to integrate out parameters in a density for unobserved data conditional on the observed data and parameters. When the true posterior is intractable, it is…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

We introduce Flat Hilbert Bayesian Inference (FHBI), an algorithm designed to enhance generalization in Bayesian inference. Our approach involves an iterative two-step procedure with an adversarial functional perturbation step and a…

Parametric Bayesian modeling offers a powerful and flexible toolbox for machine learning. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we introduce a new class of…