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# Algebraic and Analytic Approaches for Parameter Learning in Mixture Models

*Proceedings of the 31st International Conference on Algorithmic Learning Theory*, PMLR 117:468-489, 2020.

#### Abstract

We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared success probability, and Poisson mixtures, among others. An example result is that $\exp(O(N^{1/3}))$ samples suffice to exactly learn a mixture of $k

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