Related papers: Greedy Frank-Wolfe Algorithm for Exemplar Selectio…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

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…

Simultaneous feature selection and non-linear function estimation is challenging in modeling, especially in high-dimensional settings where the number of variables exceeds the available sample size. In this article, we investigate the…

In this paper, we propose a novel method for fast face recognition called L1/2 Regularized Sparse Representation using Hierarchical Feature Selection (HSR). By employing hierarchical feature selection, we can compress the scale and…

In this paper we propose a computationally efficient algorithm for on-line variable selection in multivariate regression problems involving high dimensional data streams. The algorithm recursively extracts all the latent factors of a…

Sparse representation has attracted much attention from researchers in fields of signal processing, image processing, computer vision and pattern recognition. Sparse representation also has a good reputation in both theoretical research and…

We consider the problem of minimizing a smooth and convex function over the $n$-dimensional spectrahedron -- the set of real symmetric $n\times n$ positive semidefinite matrices with unit trace, which underlies numerous applications in…

In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…

We propose a semi-stochastic Frank-Wolfe algorithm with away-steps for regularized empirical risk minimization and extend it to problems with block-coordinate structure. Our algorithms use adaptive step-size and we show that they converge…

The sparse regression problem, also known as best subset selection problem, can be cast as follows: Given a set $S$ of $n$ points in $\mathbb{R}^d$, a point $y\in \mathbb{R}^d$, and an integer $2 \leq k \leq d$, find an affine combination…

In the social sciences, it is often necessary to debias studies and surveys before valid conclusions can be drawn. Debiasing algorithms enable the computational removal of bias using sample weights. However, an issue arises when only a…

Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…

Many large-scale systems rely on high-quality deep representations (embeddings) to facilitate tasks like retrieval, search, and generative modeling. Matryoshka Representation Learning (MRL) recently emerged as a solution for adaptive…

Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often…

We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…

In this paper, we consider large-scale linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose a scalable \textbf{F}rank-\textbf{W}olfe based…

The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing…

We propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily…

Feature selection is important step in machine learning since it has shown to improve prediction accuracy while depressing the curse of dimensionality of high dimensional data. The neural networks have experienced tremendous success in…