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

arXiv: https://arxiv.org/abs/2203.13568 · HTML: https://mlsanity.com/paper/2203.13568/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 58 references that are in the map.
- First posted on arXiv 25 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)
- [On Coresets for Logistic Regression](https://mlsanity.com/paper/1805.08571/) (2018)
- [Coresets and Sketches](https://mlsanity.com/paper/1601.00617/) (2016)
- [New Frameworks for Offline and Streaming Coreset Constructions](https://mlsanity.com/paper/1612.00889/) (2016)
- [Coresets for Near-Convex Functions](https://mlsanity.com/paper/2006.05482/) (2020)
- [Coresets for Classification -- Simplified and Strengthened](https://mlsanity.com/paper/2106.04254/) (2021)
- [Oblivious sketching for logistic regression](https://mlsanity.com/paper/2107.06615/) (2021)
- [Online Row Sampling](https://mlsanity.com/paper/1604.05448/) (2016)
- [Streaming Coresets for Symmetric Tensor Factorization](https://mlsanity.com/paper/2006.01225/) (2020)
- [Tight Lower Bound for Linear Sketches of Moments](https://mlsanity.com/paper/1306.6295/) (2013)

## Built on by (most cited first, 11 of 11)

- [Online Lewis Weight Sampling](https://mlsanity.com/paper/2207.08268/) (2022)
- [Almost Linear Constant-Factor Sketching for ℓ1 and Logistic Regression](https://mlsanity.com/paper/2304.00051/) (2023)
- [Optimal Sketching Bounds for Sparse Linear Regression](https://mlsanity.com/paper/2304.02261/) (2023)
- [Scalable Learning of Item Response Theory Models](https://mlsanity.com/paper/2403.00680/) (2024)
- [Optimal bounds for ℓp sensitivity sampling via ℓ2 augmentation](https://mlsanity.com/paper/2406.00328/) (2024)
- [Turnstile ℓp leverage score sampling with applications](https://mlsanity.com/paper/2406.00339/) (2024)
- [Ridge Leverage Score Sampling for ℓp Subspace Approximation](https://mlsanity.com/paper/2407.03262/) (2024)
- [Improved Learning via k-DTW: A Novel Dissimilarity Measure for Curves](https://mlsanity.com/paper/2505.23431/) (2025)
- [Data subsampling for Poisson regression with pth-root-link](https://mlsanity.com/paper/2410.22872/) (2024)
- [Sharper Bounds for ℓp Sensitivity Sampling](https://mlsanity.com/paper/2306.00732/) (2023)
- [Scalable Learning of Multivariate Distributions via Coresets](https://mlsanity.com/paper/2603.19792/) (2026)

## Abstract (arXiv)

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∈[1, ∞). The p-generalized normal distributions citepSub23 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.