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Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as…

Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group){Throughout the paper, we use segmentation, clustering, and grouping, and their verb forms, interchangeably.} high-dimensional…

We study the sparse entropy-regularized reinforcement learning (ERL) problem in which the entropy term is a special form of the Tsallis entropy. The optimal policy of this formulation is sparse, i.e.,~at each state, it has non-zero…

In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…

We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…

Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

In current MIMO mobile communication systems, phase noise can significantly impair performance. To allow for compensation of these impairments, accurate phase noise modeling is necessary. Numerical modeling of the phase noise process at a…

A technique for characterizing and correcting the linearity of radiometric instruments is known by the names the "flux-addition method" and the "combinatorial technique". In this paper, we develop a rigorous uncertainty quantification…

We propose and investigate a new method of quantum process tomography (QPT) which we call projected least squares (PLS). In short, PLS consists of first computing the least-squares estimator of the Choi matrix of an unknown channel, and…

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an…

Partial least square regression (PLSR) is a widely-used statistical model to reveal the linear relationships of latent factors that comes from the independent variables and dependent variables. However, traditional methods to solve PLSR…

We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…

With deep neural networks providing state-of-the-art machine learning models for numerous machine learning tasks, quantifying the robustness of these models has become an important area of research. However, most of the research literature…

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as…

The problem of probabilistic verification of a neural network investigates the probability of satisfying the safe constraints in the output space when the input is given by a probability distribution. It is significant to answer this…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

To deal with high-dimensional unlabeled datasets in many areas, principal component analysis (PCA) has become a rising technique for unsupervised feature selection (UFS). However, most existing PCA-based methods only consider the structure…

The least squares (LS) estimate is the archetypical solution of linear regression problems. The asymptotic Gaussianity of the scaled LS error is often used to construct approximate confidence ellipsoids around the LS estimate, however, for…

The adversarial worst-case load shedding (AWLS) problem is pivotal for identifying critical contingencies under line outages. It is naturally cast as a bilevel program: the upper level simulates an attacker determining worst-case line…