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In this paper, we consider the "foreach" sparse recovery problem with failure probability $p$. The goal of which is to design a distribution over $m \times N$ matrices $\Phi$ and a decoding algorithm $\algo$ such that for every…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Star-shaped bodies are an important nonconvex generalization of convex bodies (e.g., linear programming with violations). Here we present an efficient algorithm for sampling a given star-shaped body. The complexity of the algorithm grows…

High-energy large-scale particle colliders generate data at extraordinary rates. Developing real-time high-throughput data compression algorithms to reduce data volume and meet the bandwidth requirement for storage has become increasingly…

This paper presents a novel approach at the intersection of machine learning and number theory, focusing on the classification of prime and non-prime numbers. At the core of our research is the development of a highly sparse encoding…

Demanding sparsity in estimated models has become a routine practice in statistics. In many situations, we wish to require that the sparsity patterns attained honor certain problem-specific constraints. Hierarchical sparse modeling (HSM)…

We describe two techniques that significantly improve the running time of several standard machine-learning algorithms when data is sparse. The first technique is an algorithm that effeciently extracts one-way and two-way counts--either…

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…

In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension $n\times p$ and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal…

The Sparse GEneral Matrix-Matrix multiplication (SpGEMM) $C = A \times B$ is a fundamental routine extensively used in domains like machine learning or graph analytics. Despite its relevance, the efficient execution of SpGEMM on vector…

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…

In this work, we consider learning sparse models in large scale settings, where the number of samples and the feature dimension can grow as large as millions or billions. Two immediate issues occur under such challenging scenario: (i)…

We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…

A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…

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…

We introduce Sparse-HFS, a scalable algorithm that can compute solutions to SSL problems using only O(n polylog(n)) space and O(m polylog(n)) time.

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors $p$ is large, possibly much larger than $n$, but only $s$ regressors are significant. The method is a…

Deep convolutional networks are well-known for their high computational and memory demands. Given limited resources, how does one design a network that balances its size, training time, and prediction accuracy? A surprisingly effective…