Online Smooth Backfitting for Generalized Additive Models

Abstract

We propose an online smoothing backfitting method for generalized additive models coupled with local linear estimation. The idea can be extended to general nonlinear optimization problems. The strategy is to use an appropriate-order expansion to approximate the nonlinear equations and store the coefficients as sufficient statistics which can be updated in an online manner by the dynamic candidate bandwidth method. We investigate the statistical and algorithmic convergences of the proposed method. By defining the relative statistical efficiency and computational cost, we further establish a framework to characterize the tradeoff between estimation performance and computation performance. Simulations and real data examples are provided to illustrate the proposed method and algorithm. Supplementary materials for this article are available online.

KEYWORD:

• Algorithmic convergence
• Online learning
• Statistical efficiency
• Streaming data

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Ying Yang’s research is partially supported by China Postdoctoral Science Foundation 2022TQ0360, 2022M723334 and the Guozhi Xu Posdoctoral Research Foundation. Fang Yao’s research is partially supported by the National Key R&D Program of China (No. 2020YFE0204200, 2022YFA1003801), the National Natural Science Foundation of China (No. 12292981, 11931001, 11871080), the LMAM and the LMEQF. Peng Zhao’s research is partially supported by the National Natural Science Foundation of China (No. 11871252), Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering and the Priority Academic Program Development of Jiangsu Higher Education Institutions.