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Federated learning has become a popular tool in the big data era nowadays. Ittrains a centralized model based on data from different clients while keepingdata decentralized. In this paper, we propose a federated sparse sliced inverseregression algorithm for the first time. Our method can simultaneously estimatethe central dimension reduction subspace and perform variable selection in afederated setting. We transform this federated high-dimensional sparse slicedinverse regression problem into a convex optimization problem by constructingthe covariance matrix safely and losslessly. We then use a linearizedalternating direction method of multipliers algorithm to estimate the centralsubspace. We also give approaches of Bayesian information criterion andhold-out validation to ascertain the dimension of the central subspace and thehyper-parameter of the algorithm. We establish an upper bound of thestatistical error rate of our estimator under the heterogeneous setting. Wedemonstrate the effectiveness of our method through simulations and real worldapplications.

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