# Independence-Encouraging Subsampling for Nonparametric Additive Models

## TL;DR

This paper introduces independence-encouraging subsampling (IES), a novel method for selecting representative subsamples from large datasets to efficiently fit nonparametric additive models while maintaining statistical properties.

## Contribution

The paper proposes IES, a subsampling technique inspired by orthogonal arrays, to improve the efficiency of additive model fitting on large datasets without sacrificing theoretical guarantees.

## Key findings

- IES subsample converges to an orthogonal array
- Backfitting over IES subsample converges to a unique solution
- Numerical experiments validate the effectiveness of IES

## Abstract

The additive model is a popular nonparametric regression method due to its ability to retain modeling flexibility while avoiding the curse of dimensionality. The backfitting algorithm is an intuitive and widely used numerical approach for fitting additive models. However, its application to large datasets may incur a high computational cost and is thus infeasible in practice. To address this problem, we propose a novel approach called independence-encouraging subsampling (IES) to select a subsample from big data for training additive models. Inspired by the minimax optimality of an orthogonal array (OA) due to its pairwise independent predictors and uniform coverage for the range of each predictor, the IES approach selects a subsample that approximates an OA to achieve the minimax optimality. Our asymptotic analyses demonstrate that an IES subsample converges to an OA and that the backfitting algorithm over the subsample converges to a unique solution even if the predictors are highly dependent in the original big data. The proposed IES method is also shown to be numerically appealing via simulations and a real data application.