Active Subsampling for Measurement-Constrained M-Estimation of Individualized Thresholds with High-Dimensional Data

2026-06-17 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning, Health & Medical Research · Depth: Expert, extended

Summary

A novel K-step active subsampling algorithm is proposed for measurement-constrained M-estimation of individualized thresholds in high-dimensional data, addressing scenarios where labeled data acquisition is costly, such as in electronic health record studies. Published on November 20, 2024, the method iteratively samples informative observations and solves a regularized M-estimator. Theoretical analysis reveals a phase transition phenomenon based on the conditional density's smoothness parameter, β. For β > (1+√3)/2, a two-step algorithm (K=2) achieves a parametric convergence rate of O_p((s log d/N)^1/2), which is faster than the minimax optimal rate for i.i.d. samples. The algorithm's superior performance is demonstrated in simulations and applied to a diabetes dataset from 130 US hospitals, comprising 12,586 observations and d=60 variables, with label budgets of N=3000, 4000, and 5000.

Key takeaway

For AI Scientists and Machine Learning Engineers working with high-dimensional data and limited labeling budgets, adopting the K-step active subsampling algorithm, particularly its two-step variant, can dramatically improve individualized threshold estimation efficiency. You should prioritize sampling data points near the current estimated threshold to achieve faster convergence rates, especially when the conditional density is sufficiently smooth. This approach offers a significant advantage over passive sampling methods, reducing the labeled data required for accurate models.

Key insights

Active subsampling significantly accelerates individualized threshold estimation in high-dimensional, label-constrained settings.

Principles

• Iterative sampling of informative data points improves estimation accuracy.
• Convergence rates exhibit phase transitions based on data smoothness (β parameter).
• Optimal performance can be achieved with a minimal number of active sampling steps.

Method

The K-step active subsampling algorithm iteratively selects the most informative observations, then solves a regularized M-estimator using a smoothed surrogate loss and path-following optimization.

In practice

• Apply a two-step (K=2) active subsampling for sufficiently smooth data (β > 1.37).
• Use cross-validation to select optimal tuning parameters like λ and b.
• Allocate a larger proportion of the label budget to later steps for stability.

Topics

• Active Subsampling
• M-Estimation
• High-Dimensional Data
• Individualized Thresholds
• Label Budgeting
• Convergence Rate

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.