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In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

Variable selection plays an important role in high dimensional statistical modeling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality $p$, estimation accuracy…

This paper presents a novel stochastic barrier function (SBF) framework for safety analysis of stochastic systems based on piecewise (PW) functions. We first outline a general formulation of PW-SBFs. Then, we focus on PW-Constant (PWC) SBFs…

In this study, we propose a method Distributionally Robust Safe Screening (DRSS), for identifying unnecessary samples and features within a DR covariate shift setting. This method effectively combines DR learning, a paradigm aimed at…

Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…

The lasso model has been widely used for model selection in data mining, machine learning, and high-dimensional statistical analysis. However, with the ultrahigh-dimensional, large-scale data sets now collected in many real-world…

Non-negative and bounded-variable linear regression problems arise in a variety of applications in machine learning and signal processing. In this paper, we propose a technique to accelerate existing solvers for these problems by…

Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing…

Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…

This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework…

This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…

Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint…

Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space…

We give two provably accurate feature-selection techniques for the linear SVM. The algorithms run in deterministic and randomized time respectively. Our algorithms can be used in an unsupervised or supervised setting. The supervised…

Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the…

In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…