# U-learning for Prediction Inference via Combinatory Multi-Subsampling: With Applications to LASSO and Neural Networks

arXiv: https://arxiv.org/abs/2407.15301 · HTML: https://mlsanity.com/paper/2407.15301/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 69 references that are in the map.
- First posted on arXiv 22 Jul 2024.

## Builds on (most cited first, 21 of 21)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Optimal Approximation with Sparsely Connected Deep Neural Networks](https://mlsanity.com/paper/1705.01714/) (2017)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models](https://mlsanity.com/paper/1412.8765/) (2014)
- [Asymptotics of Wide Convolutional Neural Networks](https://mlsanity.com/paper/2008.08675/) (2020)
- [Post-Selection Inference for Generalized Linear Models with Many Controls](https://mlsanity.com/paper/1304.3969/) (2013)
- [Linear Hypothesis Testing in Dense High-Dimensional Linear Models](https://mlsanity.com/paper/1610.02987/) (2016)
- [Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach](https://mlsanity.com/paper/1903.04408/) (2019)
- [Inference for the Case Probability in High-dimensional Logistic Regression](https://mlsanity.com/paper/2012.07133/) (2020)
- [High-dimensional Inference for Dynamic Treatment Effects](https://mlsanity.com/paper/2110.04924/) (2021)
- [Inference for High Dimensional Censored Quantile Regression](https://mlsanity.com/paper/2107.10959/) (2021)

## Built on by (most cited first, 1 of 1)

- [Can Tabular Foundation Models Amortize Statistical Inference?](https://mlsanity.com/paper/2609.33114/) (2026)

## Abstract (arXiv)

Epigenetic aging clocks play a pivotal role in estimating an individual's biological age through the examination of DNA methylation patterns at numerous CpG (Cytosine-phosphate-Guanine) sites within their genome. However, making valid inferences on predicted epigenetic ages, or more broadly, on predictions derived from high-dimensional inputs, presents challenges. We introduce a novel U-learning approach via combinatory multi-subsampling for making ensemble predictions and constructing confidence intervals for predictions of continuous outcomes when traditional asymptotic methods are not applicable. More specifically, our approach conceptualizes the ensemble estimators within the framework of generalized U-statistics and invokes the H'ajek projection for deriving the variances of predictions and constructing confidence intervals with valid conditional coverage probabilities. We apply our approach to two commonly used predictive algorithms, Lasso and deep neural networks (DNNs), and illustrate the validity of inferences with extensive numerical studies. We have applied these methods to predict the DNA methylation age (DNAmAge) of patients with various health conditions, aiming to accurately characterize the aging process and potentially guide anti-aging interventions.