Related papers: Federated Bayesian Computation via Piecewise Deter…

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC)…

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent…

Decision trees have found widespread application within the machine learning community due to their flexibility and interpretability. This paper is directed towards learning decision trees from data using a Bayesian approach, which is…

In this paper, we propose a novel class of Piecewise Deterministic Markov Processes (PDMPs) that are designed to sample from probability distributions $\pi$ supported on a convex set $\mathcal{M}$. This class of PDMPs adapts the concept of…

Reliable Bayesian predictive inference has long been an open problem under unidentified transformation models, since the Markov Chain Monte Carlo (MCMC) chains of posterior predictive distribution (PPD) values are generally poorly mixed. We…

Markov chain Monte Carlo (MCMC) algorithms have long been the main workhorses of Bayesian inference. Among them, Hamiltonian Monte Carlo (HMC) has recently become very popular due to its efficiency resulting from effective use of the…

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models,…

We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

Bayesian causal discovery aims to infer the posterior distribution over causal models from observed data, quantifying epistemic uncertainty and benefiting downstream tasks. However, computational challenges arise due to joint inference over…

Striking a balance between protecting data privacy and enabling collaborative computation is a critical challenge for distributed machine learning. While privacy-preserving techniques for federated learning have been extensively developed,…

Federated Learning (FL) involves training a model over a dataset distributed among clients, with the constraint that each client's dataset is localized and possibly heterogeneous. In FL, small and noisy datasets are common, highlighting the…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…

Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of…

By formulating the inverse problem of partial differential equations (PDEs) as a statistical inference problem, the Bayesian approach provides a general framework for quantifying uncertainties. In the inverse problem of PDEs, parameters are…

Markov chain Monte Carlo (MCMC) is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is post-processed and…

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…

Autoencoders gained popularity in the deep learning revolution given their ability to compress data and provide dimensionality reduction. Although prominent deep learning methods have been used to enhance autoencoders, the need to provide…