8 papers
Robustness of Hidden-Variable Theories and Matrix Scaling
Giulio Malavolta, Harold Nieuwboer, Akshay Ramachandran +1
Motivated by quantum foundations and complexity theory, Aaronson formalized a hidden-variable theory inspired by a proposal by Schrödinger. To any quantum state and unitary, this S…
Optimal Bounds for Tyler's M-Estimator for Elliptical Distributions
Lap Chi Lau, Akshay Ramachandran
A fundamental problem in statistics is estimating the shape matrix of an Elliptical distribution. This generalizes the familiar problem of Gaussian covariance estimation, for which…
Computational Aspects of the Trace Norm Contraction Coefficient
Idris Delsol, Omar Fawzi, Jan Kochanowski +1
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal su…
Strongly Polynomial Frame Scaling to High Precision
Daniel Dadush, Akshay Ramachandran
The frame scaling problem is: given vectors , marginals , and precision , find lef…
Hidden convexity, optimization, and algorithms on rotation matrices
Akshay Ramachandran, Kevin Shu, Alex L. Wang
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices . Such problems are nonconvex due t…
Near optimal sample complexity for matrix and tensor normal models via geodesic convexity
Cole Franks, Rafael Oliveira, Akshay Ramachandran +1
The matrix normal model, i.e., the family of Gaussian matrix-variate distributions whose covariance matrices are the Kronecker product of two lower dimensional factors, is frequent…
Spectral analysis of matrix scaling and operator scaling
Tsz Chiu Kwok, Lap Chi Lau, Akshay Ramachandran
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear co…
The Paulsen Problem, Continuous Operator Scaling, and Smoothed Analysis
Tsz Chiu Kwok, Lap Chi Lau, Yin Tat Lee +1
The Paulsen problem is a basic open problem in operator theory: Given vectors that are -nearly satisfying the Parseval's condition and the equ…