# Post-Transfer Learning Statistical Inference in High-Dimensional Regression

arXiv: https://arxiv.org/abs/2504.18212 · HTML: https://mlsanity.com/paper/2504.18212/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 25 Apr 2025.

## Builds on (most cited first, 14 of 14)

- [Deep Convolutional Neural Networks for Computer-Aided Detection: CNN Architectures, Dataset Characteristics and Transfer Learning](https://mlsanity.com/paper/1602.03409/) (2016)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [More powerful post-selection inference, with application to the Lasso](https://mlsanity.com/paper/1801.09037/) (2018)
- [Selective Inference for Group-Sparse Linear Models](https://mlsanity.com/paper/1607.08211/) (2016)
- [A significance test for forward stepwise model selection](https://mlsanity.com/paper/1405.3920/) (2014)
- [TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression](https://mlsanity.com/paper/2404.01153/) (2024)
- [A Study of Error Variance Estimation in Lasso Regression](https://mlsanity.com/paper/1311.5274/) (2013)
- [CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference](https://mlsanity.com/paper/2310.14608/) (2023)
- [Statistical Inference for Feature Selection after Optimal Transport-based Domain Adaptation](https://mlsanity.com/paper/2410.15022/) (2024)

## Abstract (arXiv)

Transfer learning (TL) for high-dimensional regression (HDR) is an important problem in machine learning, particularly when dealing with limited sample size in the target task. However, there currently lacks a method to quantify the statistical significance of the relationship between features and the response in TL-HDR settings. In this paper, we introduce a novel statistical inference framework for assessing the reliability of feature selection in TL-HDR, called PTL-SI (Post-TL Statistical Inference). The core contribution of PTL-SI is its ability to provide valid p-values to features selected in TL-HDR, thereby rigorously controlling the false positive rate (FPR) at desired significance level α (e.g., 0.05). Furthermore, we enhance statistical power by incorporating a strategic divide-and-conquer approach into our framework. We demonstrate the validity and effectiveness of the proposed PTL-SI through extensive experiments on both synthetic and real-world high-dimensional datasets, confirming its theoretical properties and utility in testing the reliability of feature selection in TL scenarios.