publication . Preprint . Conference object . 2010

Settling the Polynomial Learnability of Mixtures of Gaussians

Ankur Moitra; Gregory Valiant;
Open Access English
  • Published: 23 Apr 2010
Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We give an algorithm for this problem that has a running time, and data requirement polynomial in the dimension and the inverse of the desired accuracy, with provably minimal assumptions on the Gaussians. As simple consequences of our learning algorithm, we can perform near-optimal clustering of the sample points and density estimation for mixtures of k Gaussians, efficiently. The building blocks of our algorithm are based on the work Kalai et al. [STOC 2010] that gives an efficient algorithm for learning mixtures of two Gaussians by consi...
free text keywords: Computer Science - Learning, Computer Science - Data Structures and Algorithms, 68Q32, Algorithm, Polynomial, Mathematical optimization, Mixture model, Univariate, Backtracking, Computational complexity theory, Time complexity, Gaussian process, symbols.namesake, symbols, Mathematics, Discrete mathematics, Density estimation
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