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. If time permits, I will also describe some applications in recovering sparse signals from a mixture of responses.
The talk is primarily based on:
- Trace Reconstruction: Generalized and Parameterized
- Algebraic and Analytic Approaches for Parameter Learning in Mixture Models.
Thanks to Arya for allowing us to record the talk!