DDAC-SpAM: A Distributed Algorithm for Fitting High-dimensional Sparse Additive Models with Feature Division and Decorrelation

TL;DR

The paper introduces DDAC-SpAM, a distributed algorithm that divides features and decorrelates data to efficiently fit high-dimensional sparse additive models, with proven theoretical guarantees and empirical validation.

Contribution

It proposes a novel feature division and decorrelation approach for distributed sparse additive modeling, enabling accurate sparsity recovery without strict correlation constraints.

Findings

The algorithm achieves consistent sparsity pattern recovery.

It provides statistical inference for additive components.

Demonstrates effectiveness on synthetic and real datasets.

Abstract

Distributed statistical learning has become a popular technique for large-scale data analysis. Most existing work in this area focuses on dividing the observations, but we propose a new algorithm, DDAC-SpAM, which divides the features under a high-dimensional sparse additive model. Our approach involves three steps: divide, decorrelate, and conquer. The decorrelation operation enables each local estimator to recover the sparsity pattern for each additive component without imposing strict constraints on the correlation structure among variables. The effectiveness and efficiency of the proposed algorithm are demonstrated through theoretical analysis and empirical results on both synthetic and real data. The theoretical results include both the consistent sparsity pattern recovery as well as statistical inference for each additive functional component. Our approach provides a practical solution for fitting sparse additive models, with promising applications in a wide range of domains.