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The concept of sparsity has been extensively applied for regularization in image reconstruction. Typically, sparsifying transforms are either pre-trained on ground-truth images or adaptively trained during the reconstruction. Thereby,…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

Supervised Dictionary Learning has gained much interest in the recent decade and has shown significant performance improvements in image classification. However, in general, supervised learning needs a large number of labelled samples per…

Sparse learning is ubiquitous in many machine learning tasks. It aims to regularize the goodness-of-fit objective by adding a penalty term to encode structural constraints on the model parameters. In this paper, we develop a flexible sparse…

Selective rationalization aims to produce decisions along with rationales (e.g., text highlights or word alignments between two sentences). Commonly, rationales are modeled as stochastic binary masks, requiring sampling-based gradient…

Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…

Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm…

The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared…

Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…

Deep learning has been wildly successful in practice and most state-of-the-art machine learning methods are based on neural networks. Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of…

We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$-norm. However, several important learning applications cannot benefit from this approach as…

We propose a computationally efficient and high-performance classification algorithm by incorporating class structural information in analysis dictionary learning. To achieve more consistent classification, we associate a class…

This paper presents meta-sparsity, a framework for learning model sparsity, basically learning the parameter that controls the degree of sparsity, that allows deep neural networks (DNNs) to inherently generate optimal sparse shared…

In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data…