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Multiple systems estimation using a Poisson loglinear model is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. Information criteria are often used for selecting between the large…

This paper studies the Schatten-$q$ error of low-rank matrix estimation by singular value decomposition under perturbation. We specifically establish a perturbation bound on the low-rank matrix estimation via a perturbation projection error…

This paper provides a new tractable lower bound for the sparse recovery threshold of sensing matrices. This lower bound is used as a proxy to quantify the quality of sensing matrices in two different applications. First, it serves as…

Modern deep learning reconstruction algorithms generate impressively realistic scans from sparse inputs, but can often produce significant inaccuracies. This makes it difficult to provide statistically guaranteed claims about the true state…

A new error bound for the linear complementarity problem when the matrix involved is a B-matrix is presented, which improves the corresponding result in [C.Q. Li et al., A new error bound for linear complementarity problems for B-matrices.…

Bootstrapping has been a primary tool for ensemble and uncertainty quantification in machine learning and statistics. However, due to its nature of multiple training and resampling, bootstrapping deep neural networks is computationally…

This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…

Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…

In this work we report on a new bootstrap method for quantum mechanical problems that closely mirrors the setup from conformal field theory (CFT). We use the equations of motion to develop an analogue of the conformal block expansion for…

Tensor completion is a core machine learning algorithm used in recommender systems and other domains with missing data. While the matrix case is well-understood, theoretical results for tensor problems are limited, particularly when the…

We apply the bootstrap technique to find the moments of certain multi-trace and multi-matrix random matrix models suggested by noncommutative geometry. Using bootstrapping we are able to find the relationships between the coupling constant…

Spectral inference provides fast algorithms and provable optimality for latent topic analysis. But for real data these algorithms require additional ad-hoc heuristics, and even then often produce unusable results. We explain this poor…

Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to…

Spectral functions of large matrices contains important structural information about the underlying data, and is thus becoming increasingly important. Many times, large matrices representing real-world data are \emph{sparse} or \emph{doubly…

Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…

This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…

The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…

Astroparticle experiments such as IceCube or MAGIC require a deconvolution of their measured data with respect to the response function of the detector to provide the distributions of interest, e.g. energy spectra. In this paper,…

The singular subspaces perturbation theory is of fundamental importance in probability and statistics. It has various applications across different fields. We consider two arbitrary matrices where one is a leave-one-column-out submatrix of…

Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…