Related papers: Thinning a Wishart Random Matrix
Investigation of the underlying physics or biology from empirical data requires a quantifiable notion of similarity - when do two observed data sets indicate nearly identical generating processes, and when they do not. The discriminating…
In this paper, we address the problem of how a network of agents can collaboratively fit a linear model when each agent only ever has an arbitrary summand of the regression data. This problem generalizes previously studied…
Many stochastic optimization problems include chance constraints that enforce constraint satisfaction with a specific probability; however, solving an optimization problem with chance constraints assumes that the solver has access to the…
We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
We provide a general framework to improve trade-offs between the number of full batch and sample queries used to solve structured optimization problems. Our results apply to a broad class of randomized optimization algorithms that…
We study the sample complexity of estimating the covariance matrix $T$ of a distribution $\mathcal{D}$ over $d$-dimensional vectors, under the assumption that $T$ is Toeplitz. This assumption arises in many signal processing problems, where…
Data sharpening has been shown to reduce bias in nonparametric regression and density estimation. Its performance on nonlinear first order autoregressive models is studied theoretically and numerically in this paper. Although the asymptotic…
We study the gaps between consecutive singular values of random rectangular matrices. Specifically, if $M$ is an $n \times p$ random matrix with independent and identically distributed entries and $\Sigma$ is a $n \times n$ deterministic…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the empirically much more important real case still poses…
Graph sampling is a technique to pick a subset of vertices and/ or edges from original graph. It has a wide spectrum of applications, e.g. survey hidden population in sociology [54], visualize social graph [29], scale down Internet AS graph…
We provide the probability distribution function of matrix elements each of which is the inner product of two vectors. The vectors we are considering here are independently distributed but not necessarily Gaussian variables. When the number…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth…
Sampling methods that choose a subset of the data proportional to its diversity in the feature space are popular for data summarization. However, recent studies have noted the occurrence of bias (under- or over-representation of a certain…
Recently, an extensive amount of research has been focused on compressing and accelerating Deep Neural Networks (DNN). So far, high compression rate algorithms require part of the training dataset for a low precision calibration, or a…
We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples. Truncated samples…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…