# Divide-and-Conquer Information-Based Optimal Subdata Selection Algorithm

## TL;DR

This paper introduces a divide-and-conquer version of the IBOSS algorithm for selecting informative subdata from large datasets that cannot fit into memory, maintaining efficiency and statistical properties.

## Contribution

It develops a divide-and-conquer IBOSS method for large data, providing theoretical guarantees and practical evaluation for memory-limited environments.

## Key findings

- Estimator retains efficiency with a small number of partitions
- The method is computationally feasible for very large datasets
- Numerical experiments confirm theoretical properties

## Abstract

The information-based optimal subdata selection (IBOSS) is a computationally efficient method to select informative data points from large data sets through processing full data by columns. However, when the volume of a data set is too large to be processed in the available memory of a machine, it is infeasible to implement the IBOSS procedure. This paper develops a divide-and-conquer IBOSS approach to solving this problem, in which the full data set is divided into smaller partitions to be loaded into the memory and then subsets of data are selected from each partitions using the IBOSS algorithm. We derive both finite sample properties and asymptotic properties of the resulting estimator. Asymptotic results show that if the full data set is partitioned randomly and the number of partitions is not very large, then the resultant estimator has the same estimation efficiency as the original IBOSS estimator. We also carry out numerical experiments to evaluate the empirical performance of the proposed method.