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Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…

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 ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…

Estimating extreme quantiles is an important task in many applications, including financial risk management and climatology. More important than estimating the quantile itself is to insure zero coverage error, which implies the quantile…

Impact assessment of natural hazards requires the consideration of both extreme and non-extreme events. Extensive research has been conducted on the joint modeling of bulk and tail in univariate settings; however, the corresponding body of…

In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…

Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…

Detecting anomalies in a temporal sequence of graphs can be applied is areas such as the detection of accidents in transport networks and cyber attacks in computer networks. Existing methods for detecting abnormal graphs can suffer from…

The hybrid approach to experimental design aims to control frequentist operating characteristics of Bayesian decision procedures. These operating characteristics are assessed by simulating sampling distributions of posterior summaries under…

Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…

In this paper we leverage on probability over Riemannian manifolds to rethink the interpretation of priors and posteriors in Bayesian inference. The main mindshift is to move away from the idea that "a prior distribution establishes a…

Bayesian inference offers benefits over maximum likelihood, but it also comes with computational costs. Computing the posterior is typically intractable, as is marginalizing that posterior to form the posterior predictive distribution. In…

We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…

One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…

Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning…

Predicting outcomes in external domains is challenging due to hidden confounders that potentially influence both predictors and outcomes. Well-established methods frequently rely on stringent assumptions, explicit knowledge about the…

Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…

This paper studies the threshold estimation of a TAR model when the underlying threshold parameter is a random variable. It is shown that the Bayesian estimator is consistent and its limit distribution is expressed in terms of a limit…

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…