Related papers: Uniform Sampling for Matrix Approximation

We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

Data scientists often draw on multiple relational data sources for analysis. A standard assumption in learning and approximate query answering is that the data is a uniform and independent sample of the underlying distribution. To avoid the…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…

Imbalanced data is a frequently encountered problem in machine learning. Despite a vast amount of literature on sampling techniques for imbalanced data, there is a limited number of studies that address the issue of the optimal sampling…

Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…

In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…

Matrix completion is a classical problem that has received recurring interest across a wide range of fields. In this paper, we revisit this problem in an ultra-sparse sampling regime, where each entry of an unknown, $n\times d$ matrix $M$…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Datasets with sheer volume have been generated from fields including computer vision, medical imageology, and astronomy whose large-scale and high-dimensional properties hamper the implementation of classical statistical models. To tackle…

Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…

The statistical leverage scores of a matrix $A$ are the squared row-norms of the matrix containing its (top) left singular vectors and the coherence is the largest leverage score. These quantities are of interest in recently-popular…

Class imbalance in real-world data poses a common bottleneck for machine learning tasks, since achieving good generalization on under-represented examples is often challenging. Mitigation strategies, such as under or oversampling the data…

Sampling techniques are used in many fields, including design of experiments, image processing, and graphics. The techniques in each field are designed to meet the constraints specific to that field such as uniform coverage of the range of…

Subsampling is a popular approach to alleviating the computational burden for analyzing massive datasets. Recent efforts have been devoted to various statistical models without explicit regularization. In this paper, we develop an efficient…

We give a row sampling algorithm for the quantile loss function with sample complexity nearly linear in the dimensionality of the data, improving upon the previous best algorithm whose sampling complexity has at least cubic dependence on…