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The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…

Discovering latent representations of the observed world has become increasingly more relevant in data analysis. Much of the effort concentrates on building latent variables which can be used in prediction problems, such as classification…

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…

We address the problem of predicting spatio-temporal processes with temporal patterns that vary across spatial regions, when data is obtained as a stream. That is, when the training dataset is augmented sequentially. Specifically, we…

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…

Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…

Structure learning algorithms that learn the graph of a Bayesian network from observational data often do so by assuming the data correctly reflect the true distribution of the variables. However, this assumption does not hold in the…

State-space systems encompass a broad class of algorithms used for modeling and forecasting time series. For such systems to be effective, two objectives must be met: (i) accurate point forecasts of the time series must be produced, and…

Most forecasting methods use recent past observations (lags) to model the future values of univariate time series. Selecting an adequate number of lags is important for training accurate forecasting models. Several approaches and heuristics…

Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…

Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective…

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last…

Neural networks predictions are unreliable when the input sample is out of the training distribution or corrupted by noise. Being able to detect such failures automatically is fundamental to integrate deep learning algorithms into robotics.…

Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify…

This paper, which is Part 1 of a two-part paper series, considers a simulation-based inference with learned summary statistics, in which such a learned summary statistic serves as an empirical-likelihood with ameliorative effects in the…

Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…

Since state-of-the-art uncertainty estimation methods are often computationally demanding, we investigate whether incorporating prior information can improve uncertainty estimates in conventional deep neural networks. Our focus is on…

Graph contrastive learning has shown great promise when labeled data is scarce, but large unlabeled datasets are available. However, it often does not take uncertainty estimation into account. We show that a variational Bayesian neural…

Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…

An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…