Decentralized Smoothing ADMM for Quantile Regression with Non-Convex Sparse Penalties

TL;DR

This paper proposes a decentralized smoothing ADMM method for penalized quantile regression that effectively handles non-convex sparse penalties, improving predictor selection and convergence in distributed IoT data analysis.

Contribution

It introduces DSAD, a novel decentralized algorithm incorporating non-convex penalties and smoothing techniques, addressing convergence issues in distributed quantile regression.

Findings

Demonstrates superior convergence properties over existing methods.

Improves predictor selection accuracy with non-convex penalties.

Validates effectiveness through extensive simulations.

Abstract

In the rapidly evolving internet-of-things (IoT) ecosystem, effective data analysis techniques are crucial for handling distributed data generated by sensors. Addressing the limitations of existing methods, such as the sub-gradient approach, which fails to distinguish between active and non-active coefficients effectively, this paper introduces the decentralized smoothing alternating direction method of multipliers (DSAD) for penalized quantile regression. Our method leverages non-convex sparse penalties like the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD), improving the identification and retention of significant predictors. DSAD incorporates a total variation norm within a smoothing ADMM framework, achieving consensus among distributed nodes and ensuring uniform model performance across disparate data sources. This approach overcomes traditional convergence challenges associated with non-convex penalties in decentralized settings. We present theoretical proofs and extensive simulation results to validate the effectiveness of the DSAD, demonstrating its superiority in achieving reliable convergence and enhancing estimation accuracy compared with prior methods.