We consider the fundamental problem of solving quadratic systems of equations in $n$ variables, where $y_i = |\langle \boldsymbol{a}_i, \boldSymbol{x} \rangle|^2$, $i = 1, \ldots, m$ is unknown.Expand

This paper explores the problem of spectral compressed sensing, which aims to recover a spectrally sparse signal from a small random subset of its time domain samples.Expand

We explore a quadratic (or rank-one) measurement model which imposes minimal memory requirements and low computational complexity during the sampling process, and is shown to be optimal in preserving various low-dimensional covariance structures.Expand

Joint matching over a collection of objects aims at aggregating information from a large collection of similar instances (e.g. images, graphs, shapes) to improve maps between pairs of them.Expand

We propose an identification and estimation strategy of a sequential search model that relies on exclusion restrictions to separate consumer preference and search cost.Expand

We present nonconvex optimization algorithms for low-rank matrix factorization that combine optimization and statistical models with performance guarantees.Expand

This paper is concerned with estimation of two-dimensional frequencies from partial time samples, which arises in many applications such as radar, inverse scattering, and super-resolution imaging.Expand

An approximation to the CM cost function is proposed, which allows the use of the recursive least squares (RLS) optimization technique for blind adaptive beamforming.Expand

This paper uncovers a striking phenomenon in nonconvex optimization: even in the absence of explicit regularization, gradient descent enforces proper regularization implicitly under various statistical models.Expand