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For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…

We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears…

We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where $\epsilon\in…

We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…

The use of generalized LASSO is a common technique for recovery of structured high-dimensional signals. Each generalized LASSO program has a governing parameter whose optimal value depends on properties of the data. At this optimal value,…

Much of the existing literature in sparse recovery is concerned with the following question: given a sparsity pattern and a corresponding regularizer, derive conditions on the dictionary under which exact recovery is possible. In this…

Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…

Convex sparsity-inducing regularizations are ubiquitous in high-dimensional machine learning, but solving the resulting optimization problems can be slow. To accelerate solvers, state-of-the-art approaches consist in reducing the size of…

The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…

Fused Lasso was proposed to characterize the sparsity of the coefficients and the sparsity of their successive differences for the linear regression. Due to its wide applications, there are many existing algorithms to solve fused Lasso.…

We present novel analysis and algorithms for solving sparse phase retrieval and sparse principal component analysis (PCA) with convex lifted matrix formulations. The key innovation is a new mixed atomic matrix norm that, when used as…

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…

Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce…

Many works in convex optimization provide rates for achieving a small primal gap. However, this quantity is typically unavailable in practice. In this work, we show that solving a regularized surrogate with algorithms based on simple…

Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter…

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this…

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…

In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…

Although an ever-growing number of applications employ deep learning based systems for prediction, decision-making, or state estimation, almost no certification processes have been established that would allow such systems to be deployed in…