Statistical Performance Guarantee for Subgroup Identification with Generic Machine Learning

Michael Lingzhi Li; Kosuke Imai

Home/Archive/arXiv

arXiv · 2310.07973

Statistical Performance Guarantee for Subgroup Identification with Generic Machine Learning

Michael Lingzhi Li·Kosuke Imai

View original source ↗Read source document ↗Export metadata ↓

Abstract

Across a wide array of disciplines, many researchers use machine learning (ML) algorithms to identify a subgroup of individuals who are likely to benefit from a treatment the most (``exceptional responders'') or those who are harmed by it. A common approach to this subgroup identification problem consists of two steps. First, researchers estimate the conditional average treatment effect (CATE) using an ML algorithm. Next, they use the estimated CATE to select those individuals who are predicted to be most affected by the treatment, either positively or negatively. Unfortunately, CATE estimates are often biased and noisy. In addition, utilizing the same data to both identify a subgroup and estimate its group average treatment effect results in a multiple testing problem. To address these challenges, we develop uniform confidence bands for estimation of the group average treatment effect sorted by generic ML algorithm (GATES). Using these uniform confidence bands, researchers can identify, with a statistical guarantee, a subgroup whose GATES exceeds a certain effect size, regardless of how this effect size is chosen. The validity of the proposed methodology depends solely on randomization of treatment and random sampling of units. Importantly, our method does not require modeling assumptions and avoids a computationally intensive resampling procedure. A simulation study shows that the proposed uniform confidence bands are reasonably informative and have an appropriate empirical coverage even when the sample size is as small as 100. We analyze a clinical trial of late-stage prostate cancer and find a relatively large proportion of exceptional responders.

Explore related subjects

stat.ME math.OC stat.AP stat.ML

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Michael Lingzhi Li, Kosuke Imai. 2025-08-31. Statistical Performance Guarantee for Subgroup Identification with Generic Machine Learning. https://arxiv.org/abs/2310.07973

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bias-Correction for Privacy-Protected Spatial Autoregressive Models with Application to Restaurant Network Analysis

Spatial autoregressive (SAR) models and their extensions are important tools for studying network effects. However, with an increasing emphasis on data privacy, data providers often implement protection measures that render standard SAR models inapplicable. In this study, we introduce a privacy-protected SAR model that incorporates noise into both the response and covariates to meet privacy requirements. With noise present in both components, the traditional quasi-maximum likelihood estimator becomes difficult to compute because the likelihood function cannot be directly formulated. To bypass this hurdle, we begin with a pseudo-likelihood approach, initially omitting the noise in the covariates. A Newton-Raphson algorithm is then applied to compute the estimator; however, the estimator is biased. To address this, we propose a bias-corrected Newton-Raphson-type algorithm that simultaneously accounts for noise in both the response and covariates. We further show, under appropriate regularity conditions, that the resulting estimator is consistent and asymptotically normal. To further enhance computational efficiency, we also develop a bias-corrected least squares estimator. Several extensions are discussed, and the finite-sample performance of the proposed methods is evaluated through extensive simulations. We apply the proposed methodology to restaurant transaction data from a third-party payment platform. Our method identifies a statistically significant competitive network effect among restaurants and further reveals meaningful restaurant-customer interaction patterns.

stat.ME↗

arXiv2026

A variational framework for modal estimation

Multivariate mode estimation arises in many statistical problems such as inverse problems, multimodal sampling, and density-based clustering, but becomes challenging in moderate to high dimensions, especially when the underlying density is not directly evaluable. We introduce GERVE (Gibbs-measure Entropy-Regularized Variational Estimation), a sample-based method for estimating multivariate modes by approximating Gibbs distributions directly from samples, without estimating or evaluating the density. GERVE uses Gaussian-mixture variational annealing and natural-gradient optimization, producing a mixture concentrated in high-density regions whose component responsibilities also provide a clustering of the observations. We prove theoretical guarantees in two regimes: as the Gibbs temperature goes to zero, the optimal variational mixture concentrates around the global modes of the population density; at fixed positive temperature, we prove existence, consistency, and asymptotic normality of empirical maximizers and propose a bootstrap procedure for uncertainty quantification. Simulations and a real-data experiment show that GERVE accurately recovers modes and produces meaningful clusters.

stat.ME↗

arXiv2026

Objective Model Prior Probabilities in Variable Selection

For many years it was routine to use equal model prior probabilities in Bayesian model uncertainty analysis. At least twenty years ago it became clear that this was problematic, leading to support of much too large models in the increasingly huge model spaces being considered in genomics and other fields. A popular replacement was to adopt a suggestion of Harold Jeffreys for the variable selection problem in which a total of $k$ possible variables are being considered for inclusion in the model: give the collection of all models containing $d$ variables ($d = 0, . . . , k$) prior probability $1/(k + 1)$ and then divide this prior probability equally among the models in the collection. Many other choices of model prior probabilities that impose severe parsimony have also been introduced. We begin by reviewing the problems with using equal model prior probabilities and then discuss some serious problems with the Jeffreys choice. Finally, we introduce and study a number of objective alternative choices of model prior probabilities, from both numerical and theoretical perspectives.

stat.ME↗