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We propose a new model for forming beliefs and learning about unknown probabilities (such as the probability of picking a red marble from a bag with an unknown distribution of coloured marbles). The most widespread model for such situations…
Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of ensemble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional…
A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov…
We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…
While Internet of Things (IoT) devices and sensors create continuous streams of information, Big Data infrastructures are deemed to handle the influx of data in real-time. One type of such a continuous stream of information is time series…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
We show how to treat systematic uncertainties using Bayesian deep networks for regression. First, we analyze how these networks separately trace statistical and systematic uncertainties on the momenta of boosted top quarks forming fat jets.…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
A learning procedure takes as input a dataset and performs inference for the parameters $\theta$ of a model that is assumed to have given rise to the dataset. Here we consider learning procedures whose output is a probability distribution,…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…
Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…
Despite an artificial intelligence-assisted modeling of disordered crystals is a widely used and well-tried method of new materials design, the issues of its robustness, reliability, and stability are still not resolved and even not…
Deep learning has achieved strong performance in Time Series Forecasting (TSF). However, we identify a critical representation paradox, termed Latent Chaos: models with accurate predictions often learn latent representations that are…
Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…
In long-term time series forecasting (LTSF) tasks, an increasing number of models have acknowledged that discrete time series originate from continuous dynamic systems and have attempted to model their dynamical structures. Recognizing the…
Ensemble forecasts of weather and climate are subject to systematic biases in the ensemble mean and variance, leading to inaccurate estimates of the forecast mean and variance. To address these biases, ensemble forecasts are post-processed…
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the…
Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…
Experimental data is often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are…