Online Generalized Additive Model

TL;DR

This paper introduces an online smoothing backfitting method for generalized additive models that efficiently updates estimates using sufficient statistics, enabling scalable analysis of multidimensional data with theoretical guarantees.

Contribution

It proposes a novel online algorithm for generalized additive models using local polynomial smoothers with theoretical analysis of asymptotic properties.

Findings

The method achieves asymptotic normality of estimates.

It provides a trade-off between accuracy and computational cost.

Validated with simulations and real data examples.

Abstract

Additive models and generalized additive models are effective semiparametric tools for multidimensional data. In this article we propose an online smoothing backfitting method for generalized additive models with local polynomial smoothers. The main idea is to use a second order expansion to approximate the nonlinear integral equations to maximize the local quasilikelihood and store the coefficients as the sufficient statistics which can be updated in an online manner by a dynamic candidate bandwidth method. The updating procedure only depends on the stored sufficient statistics and the current data block. We derive the asymptotic normality as well as the relative efficiency lower bounds of the online estimates, which provides insight into the relationship between estimation accuracy and computational cost driven by the length of candidate bandwidth sequence. Simulations and real data examples are provided to validate our findings.