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An ensemble method is introduced that utilizes randomization and loss function gradients to compute a prediction. Multiple weakly-correlated estimators approximate the gradient at randomly sampled points on the error surface and are…

The gaussian spread regression model for the calibration of site specific ensemble temperature forecasts depends on the apparently restrictive assumption that the uncertainty around temperature forecasts is normally distributed. We…

A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variables. The high computational cost in running large ensemble…

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…

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…

Given a nonlinear model, a probabilistic forecast may be obtained by Monte Carlo simulations. At a given forecast horizon, Monte Carlo simulations yield sets of discrete forecasts, which can be converted to density forecasts. The resulting…

It has been documented that Spread-Error equality and a flat rank histogram are necessary but insufficient for demonstrating ensemble forecast reliability. Nevertheless, these metrics are heavily relied upon, both in the literature and at…

In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…

Precipitation forecasts are less accurate compared to other meteorological fields because several key processes affecting precipitation distribution and intensity occur below the resolved scale of global weather prediction models. This…

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…

Label noise in training data can significantly degrade a model's generalization performance for supervised learning tasks. Here we focus on the problem that noisy labels are primarily mislabeled samples, which tend to be concentrated near…

Several tasks in information retrieval (IR) rely on assumptions regarding the distribution of some property (such as term frequency) in the data being processed. This thesis argues that such distributional assumptions can lead to incorrect…

This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on…

Estimating the uncertainty in deep neural network predictions is crucial for many real-world applications. A common approach to model uncertainty is to choose a parametric distribution and fit the data to it using maximum likelihood…

In this paper, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and…

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…

Improvement of time series forecasting accuracy through combining multiple models is an important as well as a dynamic area of research. As a result, various forecasts combination methods have been developed in literature. However, most of…

Reliable uncertainty measures are required when using data based machine learning interatomic potentials (MLIPs) for atomistic simulations. In this work, we propose for sparse Gaussian Process Regression type MLIP a stochastic uncertainty…

Continual learning aims to enable machine learning models to continually learn from a shifting data distribution without forgetting what has already been learned. Such shifting distributions can be broken into disjoint subsets of related…

Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…