  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.
