arXiv research

Faster reconstruction of compressed signals using conditional GAN and NPGD.

New method speeds up PGD for CV robustness evaluation.

Three new efficient algorithms project vectors onto weighted l1 ball.

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the low-rank matrix, and to run projected gradient descent on the nonconvex factoriz…

In this paper, we consider the problem of learning high-dimensional tensor regression problems with low-rank structure. One of the core challenges associated with learning high-dimensional models is computation since the underlying optimization problems are often non-convex. While convex relaxations could lead to polyn…

PGD-trained models have a preferential direction in their gradients, which improves robustness.

SPGD improves adversarial training efficiency and accuracy.

In this paper we study the performance of the Projected Gradient Descent(PGD) algorithm for $\ell_{p}$-constrained least squares problems that arise in the framework of Compressed Sensing. Relying on the Restricted Isometry Property, we provide convergence guarantees for this algorithm for the entire range of $0\leq p\…

Accelerated optimization methods improve robustness and privacy in estimation.

A parameter-free PGD algorithm for convex optimization.

Study analyzes error in neural network solving PDEs, providing convergence and error bounds.

We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introduces non-convexity in the objective. We focus on constraint sets that include both positive semi-defi…

Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic exercise. Furthermore, the estimate that these methods produce might not belong to th…

APGD algorithm reconstructs point set from partial distance measurements.

Efficient algorithms speed up adversarial training for linear models.

IGNN captures long-range graph dependencies using fixed-point equations.

Recent advances show that deep neural networks are not robust to deliberately crafted adversarial examples which many are generated by adding human imperceptible perturbation to clear input. Consider $l_2$ norms attacks, Project Gradient Descent (PGD) and the Carlini and Wagner (C\&W) attacks are the two main methods, …

Paper proposes efficient algorithms for designing SLOPE penalty sequences.

Gradient descent at edge of stability stabilizes implicitly, following projected gradient descent.

Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their close connection to generalized linear models, it is also natural to incorporat…

The paper examines how to protect LASSO-based feature selection from adversarial attacks.

Paper examines convergence rate of PGD for BP objective in inverse problems.

This paper proposes robust matrix variate regression models with rank constraints and vector regularization.

A new algorithm estimates sparse gradients on graphs with improved risk bounds.

New algorithm eliminates sign function in PGD attacks, improving performance.

Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these issues in the context of high-dimensional sparse linear regression, and propose novel…

PGD algorithms solve nonlinear inverse problems with generative priors using noisy measurements.

Algorithm minimizes loss and constraint violations in online convex optimization with smooth penalties.

New method reduces total cost constraints in CBwK to sqrt(T) with fairness application.

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densitie…

The paper addresses speckle noise in coherent imaging systems.

We study --both in theory and practice-- the use of momentum motions in classic iterative hard thresholding (IHT) methods. By simply modifying plain IHT, we investigate its convergence behavior on convex optimization criteria with non-convex constraints, under standard assumptions. In diverse scenaria, we observe that …

We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective …

Study benchmarks methods for learning non-Cartesian k-space trajectories and reconstruction.

In this paper we consider Multiple-Input-Multiple-Output (MIMO) detection using deep neural networks. We introduce two different deep architectures: a standard fully connected multi-layer network, and a Detection Network (DetNet) which is specifically designed for the task. The structure of DetNet is obtained by unfold…

BMM algorithm improves convergence for nonconvex optimization problems.

In this paper, we consider the problem of assessing the adversarial robustness of deep neural network models under both Markov chain Monte Carlo (MCMC) and Bayesian Dark Knowledge (BDK) inference approximations. We characterize the robustness of each method to two types of adversarial attacks: the fast gradient sign me…

Iterative hard thresholding (IHT) is a projected gradient descent algorithm, known to achieve state of the art performance for a wide range of structured estimation problems, such as sparse inference. In this work, we consider IHT as a solution to the problem of learning sparse discrete distributions. We study the hard…

The $\ell_1$-norm fails to produce sparse solutions in Laplacian constrained graphical models, leading to a complete graph.

We propose a rank-$k$ variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation ($1$-SVD) in Frank-Wolfe with a top-$k$ singular-vector computation ($k$-SVD), which can be done by repeatedly applying $1$-SVD $k$ times. …

State-of-the-art adversarial attacks on neural networks use expensive iterative methods and numerous random restarts from different initial points. Iterative FGSM-based methods without restarts trade off performance for computational efficiency because they do not adequately explore the image space and are highly sensi…

New algorithm improves learning efficiency in multi-task contextual bandits.

In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor discriminative capability, while learning-based methods seldom provide concrete the…

New algorithms for private GLM estimation with minimax lower bounds.

Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this paper, we present a generalized Fisher score to jointly select features. It aims …

This paper solves quadratic systems with sparse or generative priors.

InfoOT improves data alignment by maximizing mutual information.

We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs projected gradient descent based on a novel semi-stochastic gradient specifically desi…