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Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
It has been shown both experimentally and theoretically that sparse signal recovery can be significantly improved given that part of the signal's support is known \emph{a priori}. In practice, however, such prior knowledge is usually…
Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…
Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection,…
We present fast classification techniques for sparse generalized linear and additive models. These techniques can handle thousands of features and thousands of observations in minutes, even in the presence of many highly correlated…
In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to…
Is it possible to find the sparsest vector (direction) in a generic subspace $\mathcal{S} \subseteq \mathbb{R}^p$ with $\mathrm{dim}(\mathcal{S})= n < p$? This problem can be considered a homogeneous variant of the sparse recovery problem,…
We consider the online sparse linear regression problem, which is the problem of sequentially making predictions observing only a limited number of features in each round, to minimize regret with respect to the best sparse linear regressor,…
The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for…
Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…
We consider estimation in a high-dimensional linear model with strongly correlated variables. We propose to cluster the variables first and do subsequent sparse estimation such as the Lasso for cluster-representatives or the group Lasso…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for…
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…
Random non-linear Fourier features have recently shown remarkable performance in a wide-range of regression and classification applications. Motivated by this success, this article focuses on a sparse non-linear Fourier feature (NFF) model.…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…