Saint Martin
EnsemblinggeophysicalmodelswithBayesianNeural Networks
Ensembles of geophysical models improve prediction accuracy and express uncertainties. We develop a novel data-driven ensembling strategy for combining geophysical models using Bayesian Neural Networks, which infers spatiotemporally varying model weights and bias, while accounting for heteroscedastic uncertainties in the observations. This produces more accurate and uncertaintyaware predictions without sacrificing interpretability.
Structure-Blind Signal Recovery
Dmitry Ostrovsky, Zaid Harchaoui, Anatoli Juditsky, Arkadi S. Nemirovski
We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of the minimax risk. However, when the set is unspecified, designing an estimator that is blind to the hidden structure of the signal remains a challenging problem. We propose a new family of estimators to recover signals observed in Gaussian noise. Instead of specifying the set where the signal lives, we assume the existence of a well-performing linear estimator. Proposed estimators enjoy exact oracle inequalities and can be efficiently computed through convex optimization.
Generative Modelling of Structurally Constrained Graphs
Graph diffusion models have emerged as state-of-the-art techniques in graph generation; yet, integrating domain knowledge into these models remains challenging. Domain knowledge is particularly important in real-world scenarios, where invalid generated graphs hinder deployment in practical applications.
Ensembling geophysical models with Bayesian Neural Networks
Ensembles of geophysical models improve prediction accuracy and express uncertainties. We develop a novel data-driven ensembling strategy for combining geophysical models using Bayesian Neural Networks, which infers spatiotem-porally varying model weights and bias, while accounting for heteroscedastic uncertainties in the observations. This produces more accurate and uncertainty-aware predictions without sacrificing interpretability.