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The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant…

A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension by means of output kernels, and then, solving a regression problem in…

Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…

Conjugate pairs of distributions over infinite dimensional spaces are prominent in statistical learning theory, particularly due to the widespread adoption of Bayesian nonparametric methodologies for a host of models and applications. Much…

Learning the undirected graph structure of a Markov network from data is a problem that has received a lot of attention during the last few decades. As a result of the general applicability of the model class, a myriad of methods have been…

There is a rich literature on Bayesian methods for density estimation, which characterize the unknown density as a mixture of kernels. Such methods have advantages in terms of providing uncertainty quantification in estimation, while being…

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…

In recent years, large-scale Bayesian learning draws a great deal of attention. However, in big-data era, the amount of data we face is growing much faster than our ability to deal with it. Fortunately, it is observed that large-scale…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

In recent years, shrinkage priors have received much attention in high-dimensional data analysis from a Bayesian perspective. Compared with widely used spike-and-slab priors, shrinkage priors have better computational efficiency. But the…

Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…

Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping…

Bayesian neural networks and deep ensembles represent two modern paradigms of uncertainty quantification in deep learning. Yet these approaches struggle to scale mainly due to memory inefficiency issues, since they require parameter storage…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

Count data is prevalent in various fields like ecology, medical research, and genomics. In high-dimensional settings, where the number of features exceeds the sample size, feature selection becomes essential. While frequentist methods like…

A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…

Prediction rule ensembles (PREs) are a relatively new statistical learning method, which aim to strike a balance between predictive accuracy and interpretability. Starting from a decision tree ensemble, like a boosted tree ensemble or a…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

Clustering aims to divide a set of points into groups. The current paradigm assumes that the grouping is well-defined (unique) given the probability model from which the data is drawn. Yet, recent experiments have uncovered several…

This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…