# Attributing Cohen's d: Training Data Attribution for Disease-Related Effects in Normative Age Biomarkers

arXiv: https://arxiv.org/abs/2609.07729 · HTML: https://mlsanity.com/paper/2609.07729/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Datamodels: Predicting Predictions from Training Data](https://mlsanity.com/paper/2202.00622/) (2022)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Exploring Practitioner Perspectives On Training Data Attribution Explanations](https://mlsanity.com/paper/2310.20477/) (2023)
- [Towards User-Focused Research in Training Data Attribution for Human-Centered Explainable AI](https://mlsanity.com/paper/2409.16978/) (2024)

## Abstract (arXiv)

Normative age models are trained to predict chronological age in a nominally healthy cohort. Applied to patients, they deviate, and the gap between predicted and chronological age is read as disease risk. Here, we attribute the disease-related effect size of the age gap directly to individual training samples, rather than using a prediction-level loss as the attribution target. For Cohen's d, the resulting closed-form influence functional, validated against leave-one-out retraining, ranks training samples by their effect on held-out case-control separation. Across four diseases and two biomarker modalities in UK Biobank, removing the 10% most influential training samples raises held-out disease-related effect size in every seed. It more than doubles the metabolomic-age effect for type-2 diabetes and raises the brain-age effect for multiple sclerosis by roughly a third. Random removal leaves effect size flat even at 50% removal, confirming the gain comes from which samples are removed, not how many. Flagged subjects carry subclinical cardiometabolic burden that diagnosis-based exclusion misses, on markers the model never sees. For type-2 diabetes, where the method gains most, the marker recovered is HbA1c, the standard measure of blood sugar control. We release pyinfluence, our influence-function package, for reproducibility and reuse.