Learning Mixtures and Trace Reconstruction

Arya Mazumdar

We present a generic complex-analytic method of learning mixtures of distributions and apply it to learn Gaussian mixtures with shared variance, binomial mixtures with shared success probability, and Poisson mixtures, among others. The method was first introduced to reconstruct a sequence from their random subsequences, which is called the trace reconstruction problem. We show some new results in trace reconstruction and mention some further extensions of the complex analytic method in learning mixtures.