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Ensemble forecast based on physics-informed models is one of the most widely used forecast algorithms for complex turbulent systems. A major difficulty in such a method is the model error that is ubiquitous in practice. Data-driven machine…
Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in…
When multiple forecasts are available for a probability distribution, forecast combining enables a pragmatic synthesis of the information to extract the wisdom of the crowd. The linear opinion pool has been widely used, whereby the…
Many Numerical Weather Prediction (NWP) models and their associated Model Output Statistics (MOS) are available. Combining all of these predictions in an optimal way is however not straightforward. This can be achieved thanks to Expert…
Recent advancements in deep learning have led to the development of Foundation Models (FMs) for weather forecasting, yet their ability to predict extreme weather events remains limited. Existing approaches either focus on general weather…
Forecast combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from single (target) series…
In statistical decision theory, a model is said to be Pareto optimal (or admissible) if no other model carries less risk for at least one state of nature while presenting no more risk for others. How can you rationally aggregate/combine a…
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable `mixing' conditions on random…
Conformal prediction is a popular method to construct prediction intervals with marginal coverage guarantees from black-box machine learning models. In applications with potentially high-impact events, such as flooding or financial crises,…
Given the continuous increase in dataset sizes and the complexity of forecasting models, the trade-off between forecast accuracy and computational cost is emerging as an extremely relevant topic, especially in the context of ensemble…
In matched observational studies where treatment assignment is not randomized, sensitivity analysis helps investigators determine how sensitive their estimated treatment effect is to some unmeasured con- founder. The standard approach…
Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…
We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be…
In this paper, we bridge the gap between hyperparameter optimization and ensemble learning by performing Bayesian optimization of an ensemble with regards to its hyperparameters. Our method consists in building a fixed-size ensemble,…
In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior…
The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…
In the estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the…
Aggregating multiple learners through an ensemble of models aim to make better predictions by capturing the underlying distribution of the data more accurately. Different ensembling methods, such as bagging, boosting, and stacking/blending,…