Learning Mixtures of Gaussians

PAC Learning Mixtures of Axis-Aligned Gaussians with No Separation Assumption

We propose and analyze a new vantage point for the learning of mixtures of Gaussians: namely, the PAC-style model of learning probability distributions introduced by Kearns et al. [13]. Here the task is to construct a hypothesis mixture of Gaussians that is statistically indistinguishable from the actual mixture generating the data; specifically, the KL divergence should be at most ǫ. In this s...

PAC Learning Mixtures of Gaussians with No Separation Assumption

We propose and analyze a new vantage point for the learning of mixtures of Gaussians: namely, the PAC-style model of learning probability distributions introduced by Kearns et al. [12]. Here the task is to construct a hypothesis mixture of Gaussians that is statistically indistinguishable from the actual mixture generating the data; specifically, the KL divergence should be at most 2. In this s...

PAC Learning Axis-Aligned Mixtures of Gaussians with No Separation Assumption

We propose and analyze a new vantage point for the learn-ing of mixtures of Gaussians: namely, the PAC-style model of learningprobability distributions introduced by Kearns et al. [12]. Here the taskis to construct a hypothesis mixture of Gaussians that is statistically in-distinguishable from the actual mixture generating the data; specifically,the KL divergence should be a...

LEARNING MIXTURES OF GAUSSIANS Part I: Theory

A Probabilistic Analysis of EM for Mixtures of Separated, Spherical Gaussians

We show that, given data from a mixture of k well-separated spherical Gaussians in Rd , a simple two-round variant of EM will, with high probability, learn the parameters of the Gaussians to nearoptimal precision, if the dimension is high (d lnk). We relate this to previous theoretical and empirical work on the EM algorithm.