Symmetric Tensor Completion from Multilinear Entries and Learning Product Mixtures over the Hypercube

Autor:	Schramm, Tselil, Weitz, Benjamin
Rok vydání:	2015
Předmět:	Computer Science - Data Structures and Algorithms Computer Science - Learning Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We give an algorithm for completing an order-$m$ symmetric low-rank tensor from its multilinear entries in time roughly proportional to the number of tensor entries. We apply our tensor completion algorithm to the problem of learning mixtures of product distributions over the hypercube, obtaining new algorithmic results. If the centers of the product distribution are linearly independent, then we recover distributions with as many as $\Omega(n)$ centers in polynomial time and sample complexity. In the general case, we recover distributions with as many as $\tilde\Omega(n)$ centers in quasi-polynomial time, answering an open problem of Feldman et al. (SIAM J. Comp.) for the special case of distributions with incoherent bias vectors. Our main algorithmic tool is the iterated application of a low-rank matrix completion algorithm for matrices with adversarially missing entries. Comment: Removed adversarial matrix completion algorithm after discovering that our matrix completion results can be derived from prior work
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1506.03137 Zobrazit plný text záznamu View this record from Arxiv