The study of Gaussian mixture distributions goes back to the late 19th century, when Pearson introduced the method of moments to analyze the statistics of a crab population. They have since become one of the most popular tools of modeling and data analysis, extensively used in speech recognition, computer vision and other fields. Yet their properties are still not well understood.
In my talk I will discuss some theoretical aspects of the problem of learning Gaussian mixtures. In particular, I will discuss our recent result with Mikhail Belkin, which, in a certain sense, completes work on an active recent topic in theoretical computer science by establishing quite general conditions for polynomial learnability of mixture distributions.