Communication-efficient Distributed Sparse Linear Discriminant Analysis
Abstract
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.
BibTeX
@InProceedings{pmlr-v54-tian17a,
title = {{Communication-efficient Distributed Sparse Linear Discriminant Analysis}},
author = {Tian, Lu and Gu, Quanquan},
booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
pages = {1178--1187},
year = {2017},
editor = {Singh, Aarti and Zhu, Jerry},
volume = {54},
series = {Proceedings of Machine Learning Research},
month = {20--22 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v54/tian17a/tian17a.pdf},
url = {https://proceedings.mlr.press/v54/tian17a.html},
abstract = {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.}
}