Algebraic and Analytic Approaches for Parameter Learning in Mixture Models

• URL: http://arxiv.org/abs/2001.06776v1
• Date: Sun, 19 Jan 2020 05:10:56 GMT
• Title: Algebraic and Analytic Approaches for Parameter Learning in Mixture Models
• Authors: Akshay Krishnamurthy, Arya Mazumdar, Andrew McGregor, Soumyabrata Pal
• Abstract summary: We present two different approaches for parameter learning in several mixture models in one dimension. For some of these distributions, our results represent the first guarantees for parameter estimation.
• Score: 66.96778152993858
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $k<N$ Poisson distributions, each with integral rate parameters bounded by $N$. Our second approach uses algebraic and combinatorial tools and applies to binomial mixtures with shared trial parameter $N$ and differing success parameters, as well as to mixtures of geometric distributions. Again, as an example, for binomial mixtures with $k$ components and success parameters discretized to resolution $\epsilon$, $O(k^2(N/\epsilon)^{8/\sqrt{\epsilon}})$ samples suffice to exactly recover the parameters. For some of these distributions, our results represent the first guarantees for parameter estimation.

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