用于非凸稀疏惩罚分位数回归的去中心化平滑ADMM
Decentralized Smoothing ADMM for Quantile Regression with Non-Convex Sparse Penalties
AI总结：
针对物联网分布式分位数回归，本文提出DSAD，在平滑ADMM中结合MCP、SCAD与全变差范数，实现节点一致、可靠收敛和更高估计精度。
摘要：
在快速发展的物联网（IoT）生态系统中，有效的数据分析技术对于处理传感器产生的分布式数据至关重要。为解决现有方法（如次梯度方法）的局限，即无法有效区分活跃系数与非活跃系数，本文提出用于惩罚分位数回归的去中心化平滑交替方向乘子法（DSAD）。该方法利用minimax concave penalty（MCP，极小极大凹惩罚）和平滑剪切绝对偏差（SCAD）等非凸稀疏惩罚，改进对重要预测变量的识别与保留。DSAD在平滑ADMM框架中引入全变差范数，在分布式节点之间达成一致，并确保不同数据源上的模型性能一致。该方法克服了去中心化场景中与非凸惩罚相关的传统收敛挑战。我们给出理论证明和大量仿真结果以验证DSAD的有效性，结果表明，与已有方法相比，其在实现可靠收敛和提升估计精度方面具有优越性。
英文摘要：
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.
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