Related papers: Learning minimal volume uncertainty ellipsoids
While substantial advances are observed in probabilistic forecasting for power system operation and electricity market applications, most approaches are still developed in a univariate framework. This prevents from informing about the…
We study the problem of finding confidence ellipsoids for an arbitrary distribution in high dimensions. Given samples from a distribution $D$ and a confidence parameter $\alpha$, the goal is to find the smallest volume ellipsoid $E$ which…
This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…
In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…
This paper addresses the estimation of uncertain distributed diffusion coefficients in elliptic systems based on noisy measurements of the model output. We formulate the parameter identification problem as an infinite dimensional…
We present a machine learning approach to the solution of chance constrained optimizations in the context of voltage regulation problems in power system operation. The novelty of our approach resides in approximating the feasible region of…
We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish universal lower bounds for this estimation problem, for…
We study the problem of finding the Lowner-John ellipsoid, i.e., an ellipsoid with minimum volume that contains a given convex set. We reformulate the problem as a generalized copositive program, and use that reformulation to derive…
Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…
Despite the celebrated success of stochastic control approaches for uncertain systems, such approaches are limited in the ability to handle non-Gaussian uncertainties. This work presents an adaptive robust control for linear uncertain…
We present and analyze an algorithm for estimating the size, under a Gaussian or uniform measure, of a localized neighborhood in neural network parameter space with behavior similar to an ``anchor'' point. We refer to this as the "local…
A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation…
Construction of tight confidence regions and intervals is central to statistical inference and decision making. This paper develops new theory showing minimum average volume confidence regions for categorical data. More precisely, consider…
We propose a novel polyhedral uncertainty set for robust optimization, termed the smooth uncertainty set, which captures dependencies of uncertain parameters by constraining their pairwise differences. The bounds on these differences may be…
In a linear regression model of fixed dimension $p \leq n$, we construct confidence regions for the unknown parameter vector based on the Lasso estimator that uniformly and exactly hold the prescribed in finite samples as well as in an…
We consider robust shortest path problems, where the aim is to find a path that optimizes the worst-case performance over an uncertainty set containing all relevant scenarios for arc costs. The usual approach for such problems is to assume…
A trapping region is a compact set that is forward invariant with respect to the dynamics. Existence of a trapping region certifies boundedness of trajectories, and the size of the set provides an estimate of the ultimate bound. Prior work…
We suggest a general approach to quantification of different forms of aleatoric uncertainty in regression tasks performed by artificial neural networks. It is based on the simultaneous training of two neural networks with a joint loss…
We outline new approaches to incorporate ideas from deep learning into wave-based least-squares imaging. The aim, and main contribution of this work, is the combination of handcrafted constraints with deep convolutional neural networks, as…
We study volumes of sections of convex origin-symmetric bodies in $\mathbb{R}% ^{n}$ induced by orthonormal systems on probability spaces. The approach is based on volume estimates of \ John-L\"{o}wner ellipsoids and expectations of norms…