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Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…

Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature…

Accurate uncertainty quantification in graph neural networks (GNNs) is essential, especially in high-stakes domains where GNNs are frequently employed. Conformal prediction (CP) offers a promising framework for quantifying uncertainty by…

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…

Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…

Spread regression is an extension of linear regression that allows for the inclusion of a predictor that contains information about the variance. It can be used to take the information from a weather forecast ensemble and produce a…

Earth System Models (ESMs) are the state of the art for projecting the effects of climate change. However, longstanding uncertainties in their ability to simulate regional and local precipitation extremes and related processes inhibit…

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

The heavy-tailed behavior of the generalized extreme-value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires, etc. However, estimating the distribution's parameters using…

Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…

Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…

Seasonal forecasting is a crucial task when it comes to detecting the extreme heat and colds that occur due to climate change. Confidence in the predictions should be reliable since a small increase in the temperatures in a year has a big…

Event attribution in the context of climate change seeks to understand the role of anthropogenic greenhouse gas emissions on extreme weather events, either specific events or classes of events. A common approach to event attribution uses…

Weather forecasting is mostly based on the outputs of deterministic numerical weather forecasting models. Multiple runs of these models with different initial conditions result in forecast ensembles which is are used for estimating the…

What does it mean to say that, for example, the probability for rain tomorrow is between 20% and 30%? The theory for the evaluation of precise probabilistic forecasts is well-developed and is grounded in the key concepts of proper scoring…

What is the best description that we can construct of a thermodynamic system that is not in equilibrium, given only one, or a few, extra parameters over and above those needed for a description of the same system at equilibrium? Here, we…

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…

Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To…