# On the Subbagging Estimation for Massive Data

arXiv: https://arxiv.org/abs/2103.00631 · HTML: https://mlsanity.com/paper/2103.00631/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 28 Feb 2021.

## Builds on (most cited first, 2 of 2)

- [Optimal Subsampling for Large Sample Logistic Regression](https://mlsanity.com/paper/1702.01166/) (2017)
- [Optimal Distributed Subsampling for Maximum Quasi-Likelihood Estimators with Massive Data](https://mlsanity.com/paper/2005.10435/) (2020)

## Built on by (most cited first, 1 of 1)

- [Scalable Subsampling Inference for Deep Neural Networks](https://mlsanity.com/paper/2405.08276/) (2024)

## Abstract (arXiv)

This article introduces subbagging (subsample aggregating) estimation approaches for big data analysis with memory constraints of computers. Specifically, for the whole dataset with size N, mN subsamples are randomly drawn, and each subsample with a subsample size kNll N to meet the memory constraint is sampled uniformly without replacement. Aggregating the estimators of mN subsamples can lead to subbagging estimation. To analyze the theoretical properties of the subbagging estimator, we adapt the incomplete U-statistics theory with an infinite order kernel to allow overlapping drawn subsamples in the sampling procedure. Utilizing this novel theoretical framework, we demonstrate that via a proper hyperparameter selection of kN and mN, the subbagging estimator can achieve √N-consistency and asymptotic normality under the condition (kNmN)/N→ α ∈ (0,∞]. Compared to the full sample estimator, we theoretically show that the √N-consistent subbagging estimator has an inflation rate of 1/α in its asymptotic variance. Simulation experiments are presented to demonstrate the finite sample performances. An American airline dataset is analyzed to illustrate that the subbagging estimate is numerically close to the full sample estimate, and can be computationally fast under the memory constraint.