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

Mathematics > Statistics Theory [Submitted on 21 Nov 2024 (v1), last revised 16 Jun 2026 (this version, v2)] Title:Active Subsampling for Measurement-Constrained M-Estimation of Individualized Thresholds with High-Dimensional Data View PDFAbstract:Measurement-constrained problems frequently arise in modern applications such as electronic health record studies. In such problems, despite the availability of large datasets, collecting labeled data can be highly costly or time-consuming, allowing only a small portion of the data to be labeled within a given budget. This raises a critical question: which data points are most beneficial to label given the budget constraint? We study this question in the context of estimating an optimal individualized threshold under a measurement-constrained M-estimation framework. In particular, our goal is to estimate a high-dimensional parameter $\theta$ in a linear threshold $\theta^TZ$ for a continuous variable $X$ such that the discrepancy between whether $X$ exceeds the threshold $\theta^TZ$ and a binary outcome $Y$ is minimized. In the measurement-constrained setting, we propose a novel $K$-step active subsampling algorithm to estimate $\theta$, which iteratively samples the most informative observations in the dataset and solves a regularized M-estimator. Our theoretical analysis reveals a sharp phase transition phenomenon with respect to $\beta$, the smoothness of the conditional density of $X$ given $Y$ and $Z$. Please see the paper for the full abstract. Submission history From: Jingyi Duan [view email][v1] Thu, 21 Nov 2024 00:21:17 UTC (3,349 KB) [v2] Tue, 16 Jun 2026 07:05:17 UTC (1,754 KB) Current browse context: math.ST References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.