# Differentially private sliced inverse regression in the federated paradigm

arXiv: https://arxiv.org/abs/2306.06324 · HTML: https://mlsanity.com/paper/2306.06324/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 61 references that are in the map.
- First posted on arXiv 10 Jun 2023.

## Builds on (most cited first, 20 of 20)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [Fingerprinting Codes and the Price of Approximate Differential Privacy](https://mlsanity.com/paper/1311.3158/) (2013)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [Privacy-preserving parametric inference: a case for robust statistics](https://mlsanity.com/paper/1911.10167/) (2019)
- [Differentially Private False Discovery Rate Control](https://mlsanity.com/paper/1807.04209/) (2018)
- [Heterogeneity-aware and communication-efficient distributed statistical inference](https://mlsanity.com/paper/1912.09623/) (2019)
- [Subspace Recovery from Heterogeneous Data with Non-isotropic Noise](https://mlsanity.com/paper/2210.13497/) (2022)
- [Wishart Mechanism for Differentially Private Principal Components Analysis](https://mlsanity.com/paper/1511.05680/) (2015)
- [Sparse Sliced Inverse Regression Via Lasso](https://mlsanity.com/paper/1611.06655/) (2016)
- [Differential Privacy for Government Agencies -- Are We There Yet?](https://mlsanity.com/paper/2102.08847/) (2021)
- [Differentially Private High Dimensional Sparse Covariance Matrix Estimation](https://mlsanity.com/paper/1901.06413/) (2019)
- [A convex formulation for high-dimensional sparse sliced inverse regression](https://mlsanity.com/paper/1809.06024/) (2018)
- [Federated Sufficient Dimension Reduction Through High-Dimensional Sparse Sliced Inverse Regression](https://mlsanity.com/paper/2301.09500/) (2023)

## Built on by (most cited first, 1 of 1)

- [Differentially Private Sliced Inverse Regression: Minimax Optimality and Algorithm](https://mlsanity.com/paper/2401.08150/) (2024)

## Abstract (arXiv)

Sliced inverse regression (SIR), which includes linear discriminant analysis (LDA) as a special case, is a popular and powerful dimension reduction tool. In this article, we extend SIR to address the challenges of decentralized data, prioritizing privacy and communication efficiency. Our approach, named as federated sliced inverse regression (FSIR), facilitates collaborative estimation of the sufficient dimension reduction subspace among multiple clients, solely sharing local estimates to protect sensitive datasets from exposure. To guard against potential adversary attacks, FSIR further employs diverse perturbation strategies, including a novel vectorized Gaussian mechanism that guarantees differential privacy at a low cost of statistical accuracy. Additionally, FSIR naturally incorporates a collaborative variable screening step, enabling effective handling of high-dimensional client data. Theoretical properties of FSIR are established for both low-dimensional and high-dimensional settings, supported by extensive numerical experiments and real data analysis.