Recent years have seen a flurry of activities in designing provably efficient nonconvex
optimization procedures for solving statistical estimation problems. For various problems like …

This paper considers the problem of solving systems of quadratic equations, namely,
recovering an object of interest x^ ♮ ∈ R^ nx♮∈ R n from m quadratic equations/samples …

This paper is concerned with finding a solution x to a quadratic system of equations yi=|< ai,
x>|^ 2, i= 1, 2,..., m. We prove that it is possible to solve unstructured quadratic systems in n …

We consider the fundamental problem of solving quadratic systems of equations in, and is
unknown. We propose a novel method, which starts with an initial guess computed by …

Understanding the parameter estimation of softmax gating Gaussian mixture of experts has
remained a long-standing open problem in the literature. It is mainly due to three …

Statistical inference and information processing of high-dimensional data often require an
efficient and accurate estimation of their second-order statistics. With rapidly changing data …

Inference problems with conjectured statistical-computational gaps are ubiquitous
throughout modern statistics, computer science, statistical physics and discrete probability …

List-decodable Linear Regression Page 1 List-decodeable Linear Regression Sushrut
Karmalkar University of Texas at Austin sushrutk@cs.utexas.edu Adam R. Klivans University of …

In the list-decodable learning setup, an overwhelming majority (say a 1–β-fraction) of the
input data consists of outliers and the goal of an algorithm is to output a small list of …

Abstract Mixtures of Linear Regressions (MLR) is an important mixture model with many
applications. In this model, each observation is generated from one of the several unknown …