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Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems
TLDR
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
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Robust Spectral Compressed Sensing via Structured Matrix Completion
  • Y. Chen, Yuejie Chi
  • Computer Science, Mathematics
  • IEEE Transactions on Information Theory
  • 30 April 2013
TLDR
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
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Exact and Stable Covariance Estimation From Quadratic Sampling via Convex Programming
TLDR
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
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Near-Optimal Joint Object Matching via Convex Relaxation
TLDR
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
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Sequential Search with Refinement: Model and Application with Click-Stream Data
TLDR
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
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Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
TLDR
We present nonconvex optimization algorithms for low-rank matrix factorization that combine optimization and statistical models with performance guarantees. Expand
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Compressive Two-Dimensional Harmonic Retrieval via Atomic Norm Minimization
  • Yuejie Chi, Y. Chen
  • Mathematics, Computer Science
  • IEEE Transactions on Signal Processing
  • 1 February 2015
TLDR
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
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Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment
TLDR
In this paper, a generalized Dijkstra algorithm is proposed to handle SPP with fuzzy parameters. Expand
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Recursive least squares constant modulus algorithm for blind adaptive array
TLDR
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
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Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution
TLDR
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
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