Related papers: Learning on dynamic statistical manifolds

Uncertainty-quantification methods are applied to estimate the confidence of deep-neural-networks classifiers over their predictions. However, most widely used methods are known to be overconfident. We address this problem by developing an…

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…

Though deep neural networks have achieved impressive success on various vision tasks, obvious performance degradation still exists when models are tested in out-of-distribution scenarios. In addressing this limitation, we ponder that the…

A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or…

Deep learning offers promising new ways to accurately model aleatoric uncertainty in robotic state estimation systems, particularly when the uncertainty distributions do not conform to traditional assumptions of being fixed and Gaussian. In…

Machine Learning (ML) models are extensively used in various applications due to their significant advantages over traditional learning methods. However, the developed ML models often underperform when deployed in the real world due to the…

In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…

In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

Modern challenges of robustness, fairness, and decision-making in machine learning have led to the formulation of multi-distribution learning (MDL) frameworks in which a predictor is optimized across multiple distributions. We study the…

Among the many ways of quantifying uncertainty in a regression setting, specifying the full quantile function is attractive, as quantiles are amenable to interpretation and evaluation. A model that predicts the true conditional quantiles…

Predictive uncertainty in hydrological modelling is quantified by using post-processing or Bayesian-based methods. The former methods are not straightforward and the latter ones are not distribution-free (i.e. assumptions on the probability…

Uncertainty quantification is an important part of many performance critical applications. This paper provides a simple alternative to existing approaches such as ensemble learning and bayesian neural networks. By directly modeling the loss…

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…

We develop a systematic information-theoretic framework for quantification and mitigation of error in probabilistic Lagrangian (i.e., path-based) predictions which are obtained from dynamical systems generated by uncertain (Eulerian) vector…

Due to their flexibility and predictive performance, machine-learning based regression methods have become an important tool for predictive modeling and forecasting. However, most methods focus on estimating the conditional mean or specific…

Imbalanced data distributions are prevalent in real-world scenarios, posing significant challenges in both imbalanced classification and imbalanced regression tasks. They often cause deep learning models to overfit in areas of high sample…

Regularizing continual learning techniques is important for anticipating algorithmic behavior under new realizations of data. We introduce a new approach to continual learning by imposing the properties of a parabolic partial differential…

We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…

We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d.~observations. Our approach…