Scale-invariant Optimal Sampling for Rare-events Data with Sparse Models

2026-08-23

AI Summary

本文针对稀有事件数据中的缩放问题，提出了一种尺度不变的最优抽样方法，通过自适应lasso和最大样本条件似然估计来减少预测误差。

Abstract

Subsampling is effective in tackling computational challenges for massive data with rare events. Overly aggressive subsampling may adversely affect estimation efficiency, and optimal subsampling is essential to mitigate the information loss. However, existing optimal subsampling probabilities depend on data scales, and some scaling transformations may result in inefficient subsamples. This problem is more significant when there are inactive features, because their influence on the subsampling probabilities can be arbitrarily magnified by inappropriate scaling transformations. We tackle this challenge and introduce a scale-invariant optimal subsampling function in the context of sparse models, where inactive features are commonly assumed. Instead of focusing on estimating model parameters, we define an optimal subsampling function to minimize the prediction error, using adaptive lasso to outline the estimation procedure and study its theoretical guarantee. We first introduce the adaptive lasso estimator for rare-events data and establish its oracle properties, thereby validating the use of subsampling. Then we derive a scale-invariant optimal subsampling function that minimizes the prediction error of the inverse probability weighted (IPW) adaptive lasso. Finally, we present an estimator based on the maximum sampled conditional likelihood (MSCL) to further improve the estimation efficiency. We conduct numerical experiments using both simulated and real-world data sets to demonstrate the performance of the proposed methods.

Problem

• scale-invariant
• optimal subsampling
• rare events
• sparse models
• inactive features

Innovation

• scale-invariant optimal subsampling
• adaptive lasso
• rare events data
• inverse probability weighted (IPW)
• maximum sampled conditional likelihood (MSCL)