# Sparse Private LASSO Logistic Regression

arXiv: https://arxiv.org/abs/2304.12429 · HTML: https://mlsanity.com/paper/2304.12429/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 24 Apr 2023.

## Builds on (most cited first, 8 of 8)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [Differential Privacy on Finite Computers](https://mlsanity.com/paper/1709.05396/) (2017)
- [Differential Privacy for Sparse Classification Learning](https://mlsanity.com/paper/1908.00780/) (2019)
- [Differentially-Private Logistic Regression for Detecting Multiple-SNP Association in GWAS Databases](https://mlsanity.com/paper/1407.8067/) (2014)

## Built on by (most cited first, 3 of 3)

- [Scaling Up Differentially Private LASSO Regularized Logistic Regression via Faster Frank-Wolfe Iterations](https://mlsanity.com/paper/2310.19978/) (2023)
- [Probing the Transition to Dataset-Level Privacy in ML Models Using an Output-Specific and Data-Resolved Privacy Profile](https://mlsanity.com/paper/2306.15790/) (2023)
- [Better Locally Private Sparse Estimation Given Multiple Samples Per User](https://mlsanity.com/paper/2408.04313/) (2024)

## Abstract (arXiv)

LASSO regularized logistic regression is particularly useful for its built-in feature selection, allowing coefficients to be removed from deployment and producing sparse solutions. Differentially private versions of LASSO logistic regression have been developed, but generally produce dense solutions, reducing the intrinsic utility of the LASSO penalty. In this paper, we present a differentially private method for sparse logistic regression that maintains hard zeros. Our key insight is to first train a non-private LASSO logistic regression model to determine an appropriate privatized number of non-zero coefficients to use in final model selection. To demonstrate our method's performance, we run experiments on synthetic and real-world datasets.