# Scaling Up Differentially Private LASSO Regularized Logistic Regression via Faster Frank-Wolfe Iterations

arXiv: https://arxiv.org/abs/2310.19978 · HTML: https://mlsanity.com/paper/2310.19978/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 17 of 17)

- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Private Stochastic Convex Optimization: Optimal Rates in ℓ1 Geometry](https://mlsanity.com/paper/2103.01516/) (2021)
- [Diffprivlib: The IBM Differential Privacy Library](https://mlsanity.com/paper/1907.02444/) (2019)
- [Non-Euclidean Differentially Private Stochastic Convex Optimization: Optimal Rates in Linear Time](https://mlsanity.com/paper/2103.01278/) (2021)
- [High Dimensional Differentially Private Stochastic Optimization with Heavy-tailed Data](https://mlsanity.com/paper/2107.11136/) (2021)
- [LinkedIn's Audience Engagements API: A Privacy Preserving Data Analytics System at Scale](https://mlsanity.com/paper/2002.05839/) (2020)
- [A General Framework for Auditing Differentially Private Machine Learning](https://mlsanity.com/paper/2210.08643/) (2022)
- [Breaking the Linear Iteration Cost Barrier for Some Well-known Conditional Gradient Methods Using MaxIP Data-structures](https://mlsanity.com/paper/2111.15139/) (2021)
- [Frank-Wolfe and friends: a journey into projection-free first-order optimization methods](https://mlsanity.com/paper/2106.10261/) (2021)
- [Heavy Ball Momentum for Conditional Gradient](https://mlsanity.com/paper/2110.04243/) (2021)
- [The Challenge of Differentially Private Screening Rules](https://mlsanity.com/paper/2303.10303/) (2023)
- [Differential Privacy for Sparse Classification Learning](https://mlsanity.com/paper/1908.00780/) (2019)
- [A Knowledge Transfer Framework for Differentially Private Sparse Learning](https://mlsanity.com/paper/1909.06322/) (2019)
- [Differentially Private Empirical Risk Minimization with Sparsity-Inducing Norms](https://mlsanity.com/paper/1905.04873/) (2019)
- [A Back-to-Basics Empirical Study of Priority Queues](https://mlsanity.com/paper/1403.0252/) (2014)
- [Sparse Private LASSO Logistic Regression](https://mlsanity.com/paper/2304.12429/) (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)

## Built on by (most cited first, 8 of 8)

- [SoK: A Review of Differentially Private Linear Models For High-Dimensional Data](https://mlsanity.com/paper/2404.01141/) (2024)
- [High-Dimensional Distributed Sparse Classification with Scalable Communication-Efficient Global Updates](https://mlsanity.com/paper/2407.06346/) (2024)
- [Feature Selection from Differentially Private Correlations](https://mlsanity.com/paper/2408.10862/) (2024)
- [Differentially Private Iterative Screening Rules for Linear Regression](https://mlsanity.com/paper/2502.18578/) (2025)
- [Better Locally Private Sparse Estimation Given Multiple Samples Per User](https://mlsanity.com/paper/2408.04313/) (2024)
- [More Options for Prelabor Rupture of Membranes, A Bayesian Analysis](https://mlsanity.com/paper/2408.10876/) (2024)
- [Adversarial Machine Learning Attacks on Financial Reporting via Maximum Violated Multi-Objective Attack](https://mlsanity.com/paper/2507.05441/) (2025)
- [Bayesian Meta-Analyses Could Be More: A Case Study in Trial of Labor After a Cesarean-section Outcomes and Complications](https://mlsanity.com/paper/2601.10089/) (2026)

## Abstract (arXiv)

To the best of our knowledge, there are no methods today for training differentially private regression models on sparse input data. To remedy this, we adapt the Frank-Wolfe algorithm for L1 penalized linear regression to be aware of sparse inputs and to use them effectively. In doing so, we reduce the training time of the algorithm from O( T D S + T N S) to O(N S + T √D logD + T S2), where T is the number of iterations and a sparsity rate S of a dataset with N rows and D features. Our results demonstrate that this procedure can reduce runtime by a factor of up to 2,200×, depending on the value of the privacy parameter ε and the sparsity of the dataset.