# Differentially Private Sliced Inverse Regression: Minimax Optimality and Algorithm

arXiv: https://arxiv.org/abs/2401.08150 · HTML: https://mlsanity.com/paper/2401.08150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Builds on (most cited first, 11 of 11)

- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning](https://mlsanity.com/paper/2303.07152/) (2023)
- [Differentially Private False Discovery Rate Control](https://mlsanity.com/paper/1807.04209/) (2018)
- [A Distribution Free Conditional Independence Test with Applications to Causal Discovery](https://mlsanity.com/paper/2105.07555/) (2021)
- [Model-free Feature Screening and FDR Control with Knockoff Features](https://mlsanity.com/paper/1908.06597/) (2019)
- [Sparse Sliced Inverse Regression Via Lasso](https://mlsanity.com/paper/1611.06655/) (2016)
- [Sparse GCA and Thresholded Gradient Descent](https://mlsanity.com/paper/2107.00371/) (2021)
- [Asymptotic Distribution-Free Independence Test for High Dimension Data](https://mlsanity.com/paper/2110.07652/) (2021)
- [Differentially Private Estimation and Inference in High-Dimensional Regression with FDR Control](https://mlsanity.com/paper/2310.16260/) (2023)
- [Adaptive False Discovery Rate Control with Privacy Guarantee](https://mlsanity.com/paper/2305.19482/) (2023)
- [Differentially private sliced inverse regression in the federated paradigm](https://mlsanity.com/paper/2306.06324/) (2023)

## Abstract (arXiv)

Privacy preservation has become a critical concern in high-dimensional data analysis due to the growing prevalence of data-driven applications. Since its proposal, sliced inverse regression has emerged as a widely utilized statistical technique to reduce the dimensionality of covariates while maintaining sufficient statistical information. In this paper, we propose optimally differentially private algorithms specifically designed to address privacy concerns in the context of sufficient dimension reduction. We establish lower bounds for differentially private sliced inverse regression in low and high dimensional settings. Moreover, we develop differentially private algorithms that achieve the minimax lower bounds up to logarithmic factors. Through a combination of simulations and real data analysis, we illustrate the efficacy of these differentially private algorithms in safeguarding privacy while preserving vital information within the reduced dimension space. As a natural extension, we can readily offer analogous lower and upper bounds for differentially private sparse principal component analysis, a topic that may also be of potential interest to the statistics and machine learning community.