Results 31 to 40 of about 1,163,681 (226)
Sum-of-Squares Lower Bounds for Non-Gaussian Component Analysis [PDF]
IEEE Annual Symposium on Foundations of Computer ScienceNon-Gaussian Component Analysis (NGCA) is the statistical task of finding a non-Gaussian direction in a high-dimensional dataset. Specifically, given i.i.d.
Ilias Diakonikolas +3 more
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Mathematics, 2023 The partial correlation coefficient (Pcor) is a vital statistical tool employed across various scientific domains to decipher intricate relationships and reveal inherent mechanisms.
Jingying Yang, Guishu Bai, Mei Yan
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Private Graphon Estimation via Sum-of-Squares [PDF]
Symposium on the Theory of ComputingWe develop the first pure node-differentially-private algorithms for learning stochastic block models and for graphon estimation with polynomial running time for any constant number of blocks.
Hongjie Chen +5 more
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Square Root Convexity of Fisher Information along Heat Flow in Dimension Two
Entropy, 2023 Recently, Ledoux, Nair, and Wang proved that the Fisher information along the heat flow is log-convex in dimension one, that is d2dt2log(I(Xt))≥0 for n=1, where Xt is a random variable with density function satisfying the heat equation. In this paper, we
Junliang Liu, Xiaoshan Gao
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The sum-of-squares hierarchy on the sphere and applications in quantum information theory [PDF]
Mathematical programming, 2019 We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of sum-of-squares relaxations. Exploiting the polynomial kernel technique, we obtain a quadratic improvement of the known convergence rate by Reznick and ...
K. Fang, Hamza Fawzi
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Sum-of-Squares Lower Bounds for Sherrington-Kirkpatrick via Planted Affine Planes [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2020 The Sum-of-Squares (SoS) hierarchy is a semi-definite programming meta-algorithm that captures state-of-the-art polynomial time guarantees for many optimization problems such as Max-$k$-CSPs and Tensor PCA.
Mrinalkanti Ghosh +4 more
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Rational Optimization using Sum-of-Squares Techniques [PDF]
, 2007 Motivated by many control applications, this paper deals with the global solutions of unconstrained optimization problems. First, a simple SOS method is presented to find the infimum of a polynomial, which can be handled efficiently using the relevant ...
Aghdam, Amir G. +2 more
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Pell’s equation, sum-of-squares and equilibrium measures on a compact set
Comptes Rendus. Mathématique, 2023 We first interpret Pell’s equation satisfied by Chebyshev polynomials for each degree $t$, as a certain Positivstellensatz, which then yields for each integer $t$, what we call a generalized Pell’s equation, satisfied by reciprocals of Christoffel ...
Lasserre, Jean B.
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Linearized analysis versus optimization-based nonlinear analysis for nonlinear systems [PDF]
, 2009 For autonomous nonlinear systems stability and input-output properties in small enough (infinitesimally small) neighborhoods of (linearly) asymptotically stable equilibrium points can be inferred from the properties of the linearized dynamics.
Packard, Andrew, Topcu, Ufuk
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A Fast Factorisation of Semi-Primes Using Sum of Squares
Mathematical and Computational Applications, 2019 For several centuries, prime factorisation of large numbers has drawn much attention due its practical applications and the associated challenges.
Anthony Overmars +1 more
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