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We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

Algorithms for extracting hydrologic features and properties from digital elevation models (DEMs) are challenged by large datasets, which often cannot fit within a computer's RAM. Depression filling is an important preconditioning step to…

There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…

Data denoising is a persistent challenge across scientific and engineering domains. Real-world data is frequently corrupted by complex, non-linear noise, rendering traditional rule-based denoising methods inadequate. To overcome these…

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

Recommender system has intrinsic problems such as sparsity and fairness. Although it has been widely adopted for the past decades, research on fairness of recommendation algorithms has been largely neglected until recently. One important…

We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…

Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…

We revisit the task of releasing marginal queries under differential privacy with additive (correlated) Gaussian noise. We first give a construction for answering arbitrary workloads of weighted marginal queries, over arbitrary domains. Our…

Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem…

Developers perform online sensemaking on a daily basis, such as researching and choosing libraries and APIs. Prior research has introduced tools that help developers capture information from various sources and organize it into structures…

Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can transform the high-dimensional rank regularized problem to a low-dimensional factorized…

We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…

Pattern set mining, which is the task of finding a good set of patterns instead of all patterns, is a fundamental problem in data mining. Many different definitions of what constitutes a good set have been proposed in recent years. In this…

In this paper we relate a number of parsing algorithms which have been developed in very different areas of parsing theory, and which include deterministic algorithms, tabular algorithms, and a parallel algorithm. We show that these…