Communication-efficient Distributed Sparse Linear Discriminant Analysis

We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime. Our method distributes the data of size N into m machines, and estimates a local sparse LDA estimator on each machine using the data subset of size N/m. After the distributed estimation, our method aggregates the debiased local estimators from m machines, and sparsifies the aggregated estimator. We show that the aggregated estimator attains the same statistical rate as the centralized estimation method, as long as the number of machines m is chosen appropriately. Moreover, we prove that our method can attain the model selection consistency under a milder condition than the centralized method. Experiments on both synthetic and real datasets corroborate our theory.