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Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

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…

Weather forecasting has seen a shift in methods from numerical simulations to data-driven systems. While initial research in the area focused on deterministic forecasting, recent works have used diffusion models to produce skillful ensemble…

To facilitate effective decision-making, precipitation datasets should include uncertainty estimates. Quantile regression with machine learning has been proposed for issuing such estimates. Distributional regression offers distinct…

We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…

The problem of combining individual forecasters to produce a forecaster with improved performance is considered. The connections between probability elicitation and classification are used to pose the combining forecaster problem as that of…

Mesoscale forecasts are now routinely performed as elements of operational forecasts and their outputs do appear convincing. However, despite their realistic appearance at times the comparison to observations is less favorable. At the grid…

Ensembling is a powerful technique for improving the accuracy of machine learning models, with methods like stacking achieving strong results in tabular tasks. In time series forecasting, however, ensemble methods remain underutilized, with…

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…

In this paper, a first sample-based formulation of the recently considered population observers, or ensemble observers, which estimate the state distribution of dynamic populations from measurements of the output distribution is…

We study how the training data distribution affects confidence and performance in image classification models. We introduce Embedding Density, a model-agnostic framework that estimates prediction confidence by measuring the distance of test…

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

The quality of probabilistic forecasts is crucial for decision-making under uncertainty. While proper scoring rules incentivize truthful reporting of precise forecasts, they fall short when forecasters face epistemic uncertainty about their…

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…

Ensemble data assimilation is a problem in determining the most likely phase space trajectory of a model of an observed dynamical sys- tem as it receives inputs from measurements passing information to the model. Using methods developed in…

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by…