Algebraic and Analytic Approaches for Parameter Learning in Mixture Models
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 Cite this Paper BibTeX @InProceedings{pmlr-v117-krishnamurthy20a, title = {Algebraic and Analytic Approaches for Parameter Learning in Mixture Models}, author = {Krishnamurthy, Akshay and Mazumdar, Arya and McGregor, Andrew and Pal, Soumyabrata}, booktitle = {Proceedings of the 31st International Conference on Algorithmic Learning Theory}, pages = {468--489}, year = {2020}, editor = {Kontorovich, Aryeh and Neu, Gergely}, volume = {117}, series = {Proceedings of Machine Learning Research}, month = {08 Feb--11 Feb}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v117/krishnamurthy20a/krishnamurthy20a.pdf}, url = {https://proceedings.mlr.press/v117/krishnamurthy20a.html}, 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 Copy to Clipboard Download Endnote %0 Conference Paper %T Algebraic and Analytic Approaches for Parameter Learning in Mixture Models %A Akshay Krishnamurthy %A Arya Mazumdar %A Andrew McGregor %A Soumyabrata Pal %B Proceedings of the 31st International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2020 %E Aryeh Kontorovich %E Gergely Neu %F pmlr-v117-krishnamurthy20a %I PMLR %P 468--489 %U https://proceedings.mlr.press/v117/krishnamurthy20a.html %V 117 %X We present two differe