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Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems.…

Developing efficient solutions for inference problems in intelligent sensor networks is crucial for the next generation of location, tracking, and mapping services. This paper develops a scalable distributed probabilistic inference…

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

Motivated by the analysis of the distribution of university grades, which is usually asymmetric, we discuss two informative priors for the shape parameter of the skew-normal distribution, showing that they lead to closed-form…

Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an…

Inspired by the combination of feedforward and iterative computations in the virtual cortex, and taking advantage of the ability of denoising autoencoders to estimate the score of a joint distribution, we propose a novel approach to…

Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…

Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…

We propose a novel Bayesian model selection technique on linear mixed-effects models to compare multiple treatments with a control. A fully Bayesian approach is implemented to estimate the marginal inclusion probabilities that provide a…

Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…

Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

This paper develops a Bayesian framework for robust causal inference from longitudinal observational data. Many contemporary methods rely on structural assumptions, such as factor models, to adjust for unobserved confounding, but they can…

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…

We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…

We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…

Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive…

We develop methods for efficient amortized approximate Bayesian inference over posterior distributions of probabilistic clustering models, such as Dirichlet process mixture models. The approach is based on mapping distributed,…