Disentangling Gaussians
Prof. Ankur Moitra (MIT)
Sunday, 8 February 2015, 3:30 PM
Harvard, Science Center E
In a remarkable study in 1894, Karl Pearson introduced the problem of learning the parameters of a mixture of Gaussians given random samples from it. This has been a central problem in statistics (and later machine learning) ever since, but the standard estimators fall well short of what we would like because there are no efficient algorithms to compute them! Here I will describe recent, efficient algorithms with provable guarantees that work even when the components overlap. These algorithms are based on reasoning about certain systems of polynomial equations through the heat equation. I will also describe the broader context into which this works fits, and some of the other exciting problems at the intersection of theoretical computer science, machine learning and statistics.