# Federated Sufficient Dimension Reduction Through High-Dimensional Sparse Sliced Inverse Regression

arXiv: https://arxiv.org/abs/2301.09500 · HTML: https://mlsanity.com/paper/2301.09500/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 55 references that are in the map.
- First posted on arXiv 23 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [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)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [The Non-IID Data Quagmire of Decentralized Machine Learning](https://mlsanity.com/paper/1910.00189/) (2019)
- [FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Data](https://mlsanity.com/paper/2005.11418/) (2020)
- [Federated Accelerated Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08950/) (2020)
- [Sparse CCA: Adaptive Estimation and Computational Barriers](https://mlsanity.com/paper/1409.8565/) (2014)
- [Sparse Sliced Inverse Regression Via Lasso](https://mlsanity.com/paper/1611.06655/) (2016)
- [A convex formulation for high-dimensional sparse sliced inverse regression](https://mlsanity.com/paper/1809.06024/) (2018)

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

- [Differentially private sliced inverse regression in the federated paradigm](https://mlsanity.com/paper/2306.06324/) (2023)

## Abstract (arXiv)

Federated learning has become a popular tool in the big data era nowadays. It trains a centralized model based on data from different clients while keeping data decentralized. In this paper, we propose a federated sparse sliced inverse regression algorithm for the first time. Our method can simultaneously estimate the central dimension reduction subspace and perform variable selection in a federated setting. We transform this federated high-dimensional sparse sliced inverse regression problem into a convex optimization problem by constructing the covariance matrix safely and losslessly. We then use a linearized alternating direction method of multipliers algorithm to estimate the central subspace. We also give approaches of Bayesian information criterion and hold-out validation to ascertain the dimension of the central subspace and the hyper-parameter of the algorithm. We establish an upper bound of the statistical error rate of our estimator under the heterogeneous setting. We demonstrate the effectiveness of our method through simulations and real world applications.