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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…

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the…

In this paper, we investigate the adversarial robustness of nonparametric regression, a fundamental problem in machine learning, under the setting where an adversary can arbitrarily corrupt a subset of the input data. While the robustness…

In this letter, we address the problem of estimating Gaussian noise level from the trained dictionaries in update stage. We first provide rigorous statistical analysis on the eigenvalue distributions of a sample covariance matrix. Then we…

We investigate an existing distributed algorithm for learning sparse signals or data over networks. The algorithm is iterative and exchanges intermediate estimates of a sparse signal over a network. This learning strategy using exchange of…

Reinforcement Learning (RL) agents require the specification of a reward signal for learning behaviours. However, introduction of corrupt or stochastic rewards can yield high variance in learning. Such corruption may be a direct result of…

Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in…

We consider sparse variants of the classical Learning Parities with random Noise (LPN) problem. Our main contribution is a new algorithmic framework that provides learning algorithms against low-noise for both Learning Sparse Parities…

Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…

The concept class of low-degree polynomial threshold functions (PTFs) plays a fundamental role in machine learning. In this paper, we study PAC learning of $K$-sparse degree-$d$ PTFs on $\mathbb{R}^n$, where any such concept depends only on…

This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…

We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present…

In this paper, we study a simple and generic framework to tackle the problem of learning model parameters when a fraction of the training samples are corrupted. We first make a simple observation: in a variety of such settings, the…

Accurate channel estimation is critical for realizing the performance gains of massive multiple-input multiple-output (MIMO) systems. Traditional approaches to channel estimation typically assume ideal receiver hardware and linear signal…

We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of…

This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…