Related papers: Learning minimal volume uncertainty ellipsoids
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…
Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In…
We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This model is motivated by applications in molecular microscopy and image processing, where each…
Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…
We solve the ground state of the deuteron using a variational neural network ansatz for the wave function in momentum space. This ansatz provides a flexible representation of both the $S$ and the $D$ states, with relative errors in the…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…
Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…
We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex…
In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn $x=(x_1,\ldots,x_n) \in \{0,1\}^n$ from a stream of random linear equations over $\mathrm{F}_2$ that are correct with…
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume the domain has a boundary with positive reach. We propose a data splitting approach to correct…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
Likelihood ratios are used for a variety of applications in particle physics data analysis, including parameter estimation, unfolding, and anomaly detection. When the data are high-dimensional, neural networks provide an effective tools for…
Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for…
Path planning has long been one of the major research areas in robotics, with PRM and RRT being two of the most effective classes of planners. Though generally very efficient, these sampling-based planners can become computationally…