Faster and Sample Near-Optimal Algorithms for Proper Learning Mixtures of Gaussians
published: July 15, 2014, recorded: June 2014, views: 137
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given O(1/ε2) samples from an unknown mixture, our algorithm outputs a mixture that is ε-close in total variation distance, in time O(1/ε5). Our sample complexity is optimal up to logarithmic factors, and significantly improves upon both Kalai et al., whose algorithm has a prohibitive dependence on 1/ε, and Feldman et al., whose algorithm requires bounds on the mixture parameters and depends pseudo-polynomially in these parameters.
One of our main contributions is an improved and generalized algorithm for selecting a good candidate distribution from among competing hypotheses. Namely, given a collection of N hypotheses containing at least one candidate that is ε-close to an unknown distribution, our algorithm outputs a candidate which is O(ε)-close to the distribution. The algorithm requires O(logN/ε2) samples from the unknown distribution and O(NlogN/ε2) time, which improves previous such results (such as the Scheffé estimator) from a quadratic dependence of the running time on N to quasilinear. Given the wide use of such results for the purpose of hypothesis selection, our improved algorithm implies immediate improvements to any such use.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !