Related papers: Grouping Priors and the Bayesian Elastic Net

Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

We consider Bayesian variable selection in sparse high-dimensional regression, where the number of covariates $p$ may be large relative to the samples size $n$, but at most a moderate number $q$ of covariates are active. Specifically, we…

In recent years, neural networks have revolutionized various domains, yet challenges such as hyperparameter tuning and overfitting remain significant hurdles. Bayesian neural networks offer a framework to address these challenges by…

We study prior distributions for Poisson parameter estimation under $L^1$ loss. Specifically, we construct a new family of prior distributions whose optimal Bayesian estimators (the conditional medians) can be any prescribed increasing…

Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

Meta-reinforcement learning trains a single reinforcement learning agent on a distribution of tasks to quickly generalize to new tasks outside of the training set at test time. From a Bayesian perspective, one can interpret this as…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Bayesian optimisation is a well-known sample-efficient method for the optimisation of expensive black-box functions. However when dealing with big search spaces the algorithm goes through several low function value regions before reaching…

Consider the task of estimating a random vector $X$ from noisy observations $Y = X + Z$, where $Z$ is a standard normal vector, under the $L^p$ fidelity criterion. This work establishes that, for $1 \leq p \leq 2$, the optimal Bayesian…

We obtain rates of contraction of posterior distributions in inverse problems defined by scales of smoothness classes. We derive abstract results for general priors, with contraction rates determined by Galerkin approximation. The rate…

Noninformative priors constructed for estimation purposes are usually not appropriate for model selection and testing. The methodology of integral priors was developed to get prior distributions for Bayesian model selection when comparing…

Optimising black-box functions is important in many disciplines, such as tuning machine learning models, robotics, finance and mining exploration. Bayesian optimisation is a state-of-the-art technique for the global optimisation of…

Approximate Bayesian inference typically revolves around computing the posterior parameter distribution. In practice, however, the main object of interest is often a model's predictions rather than its parameters. In this work, we propose…

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

Priors are important for achieving proper posteriors with physically meaningful covariance structures for Gaussian random fields (GRFs) since the likelihood typically only provides limited information about the covariance structure under…

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

It is a relatively well-known fact that in problems of Bayesian model selection improper priors should, in general, be avoided. In this paper we derive a proper and parsimonious uniform prior for regression coefficients. We then use this…