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In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In…
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
Mean field theory has provided theoretical insights into various algorithms by letting the problem size tend to infinity. We argue that the applications of mean-field theory go beyond theoretical insights as it can inspire the design of…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…
Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
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…
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
In this paper we consider a system of quadratic equations |<z_j, x>|^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be…
Let $g(X)$ be a polynomial over a finite field ${\mathbb F}_q$ with degree $o(q^{1/2})$, and let $\chi$ be the quadratic residue character. We give a polynomial time algorithm to recover $g(X)$ (up to perfect square factors) given the…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effective under strong regularity assumptions, but…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…