$p$-Generalized Probit Regression and Scalable Maximum Likelihood Estimation via Sketching and Coresets

• URL: http://arxiv.org/abs/2203.13568v1
• Date: Fri, 25 Mar 2022 10:54:41 GMT
• Title: $p$-Generalized Probit Regression and Scalable Maximum Likelihood Estimation via Sketching and Coresets
• Authors: Alexander Munteanu, Simon Omlor, Christian Peters
• Abstract summary: We study the $p$-generalized probit regression model, which is a generalized linear model for binary responses. We show how the maximum likelihood estimator for $p$-generalized probit regression can be approximated efficiently up to a factor of $(1+varepsilon)$ on large data.
• Score: 74.37849422071206
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the $p$-generalized probit regression model, which is a generalized linear model for binary responses. It extends the standard probit model by replacing its link function, the standard normal cdf, by a $p$-generalized normal distribution for $p\in[1, \infty)$. The $p$-generalized normal distributions \citep{Sub23} are of special interest in statistical modeling because they fit much more flexibly to data. Their tail behavior can be controlled by choice of the parameter $p$, which influences the model's sensitivity to outliers. Special cases include the Laplace, the Gaussian, and the uniform distributions. We further show how the maximum likelihood estimator for $p$-generalized probit regression can be approximated efficiently up to a factor of $(1+\varepsilon)$ on large data by combining sketching techniques with importance subsampling to obtain a small data summary called coreset.

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