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We propose a framework for the statistical evaluation of variational auto-encoders (VAEs) and test two instances of this framework in the context of modelling images of handwritten digits and a corpus of English text. Our take on evaluation…

Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…

Variational auto-encoders (VAEs) are a popular and powerful deep generative model. Previous works on VAEs have assumed a factorized likelihood model, whereby the output uncertainty of each pixel is assumed to be independent. This…

In this paper we extend existing Bayesian methods for variable selection in Gaussian process regression, to select both the regression terms and the active covariates in the spatial correlation structure. We then use the estimated posterior…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

Simultaneous inference for high-dimensional non-Gaussian time series is always considered to be a challenging problem. Such tasks require not only robust estimation of the coefficients in the random process, but also deriving limiting…

The focus of this work is on spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models, soft-thresholded Gaussian processes and develop the efficient posterior computation algorithms.…

We address the problem of learning graphical models which correspond to high dimensional autoregressive stationary stochastic processes. A graphical model describes the conditional dependence relations among the components of a stochastic…

We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…

Uncertainty estimation in deep neural networks is essential for designing reliable and robust AI systems. Applications such as video surveillance for identifying suspicious activities are designed with deep neural networks (DNNs), but DNNs…

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

The vector autoregressive (VAR) model has been widely used for modeling temporal dependence in a multivariate time series. For large (and even moderate) dimensions, the number of AR coefficients can be prohibitively large, resulting in…

Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multivariate data sets in a format amenable for human…

In financial risk management, Value at Risk (VaR) is widely used to estimate potential portfolio losses. VaR's limitation is its inability to account for the magnitude of losses beyond a certain threshold. Expected Shortfall (ES) addresses…

We discuss the issue of estimating large-scale vector autoregressive (VAR) models with stochastic volatility in real-time situations where data are sampled at different frequencies. In the case of a large VAR with stochastic volatility, the…

Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each…