# Measuring the Effect of Training Data on Deep Learning Predictions via Randomized Experiments

arXiv: https://arxiv.org/abs/2206.10013 · HTML: https://mlsanity.com/paper/2206.10013/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 92 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Targeted Backdoor Attacks on Deep Learning Systems Using Data Poisoning](https://mlsanity.com/paper/1712.05526/) (2017)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [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)
- [Poison Frogs! Targeted Clean-Label Poisoning Attacks on Neural Networks](https://mlsanity.com/paper/1804.00792/) (2018)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Spectral Signatures in Backdoor Attacks](https://mlsanity.com/paper/1811.00636/) (2018)
- [STRIP: A Defence Against Trojan Attacks on Deep Neural Networks](https://mlsanity.com/paper/1902.06531/) (2019)
- [Detecting Backdoor Attacks on Deep Neural Networks by Activation Clustering](https://mlsanity.com/paper/1811.03728/) (2018)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Manipulating Machine Learning: Poisoning Attacks and Countermeasures for Regression Learning](https://mlsanity.com/paper/1804.00308/) (2018)
- [Datamodels: Predicting Predictions from Training Data](https://mlsanity.com/paper/2202.00622/) (2022)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Counterfactual Memorization in Neural Language Models](https://mlsanity.com/paper/2112.12938/) (2021)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [Stronger Data Poisoning Attacks Break Data Sanitization Defenses](https://mlsanity.com/paper/1811.00741/) (2018)
- [SPECTRE: Defending Against Backdoor Attacks Using Robust Statistics](https://mlsanity.com/paper/2104.11315/) (2021)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Demon in the Variant: Statistical Analysis of DNNs for Robust Backdoor Contamination Detection](https://mlsanity.com/paper/1908.00686/) (2019)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)

## Built on by (most cited first, 30 of 50)

- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [OpenDataVal: a Unified Benchmark for Data Valuation](https://mlsanity.com/paper/2306.10577/) (2023)
- [Intriguing Properties of Data Attribution on Diffusion Models](https://mlsanity.com/paper/2311.00500/) (2023)
- [The Journey, Not the Destination: How Data Guides Diffusion Models](https://mlsanity.com/paper/2312.06205/) (2023)
- [Data-OOB: Out-of-bag Estimate as a Simple and Efficient Data Value](https://mlsanity.com/paper/2304.07718/) (2023)
- [Rethinking Data Shapley for Data Selection Tasks: Misleads and Merits](https://mlsanity.com/paper/2405.03875/) (2024)
- [Unleashing the Power of Data Tsunami: A Comprehensive Survey on Data Assessment and Selection for Instruction Tuning of Language Models](https://mlsanity.com/paper/2408.02085/) (2024)
- [DataMIL: Selecting Data for Robot Imitation Learning with Datamodels](https://mlsanity.com/paper/2505.09603/) (2025)
- [On the Variance of Neural Network Training with respect to Test Sets and Distributions](https://mlsanity.com/paper/2304.01910/) (2023)
- [Diffusion Attribution Score: Evaluating Training Data Influence in Diffusion Models](https://mlsanity.com/paper/2410.18639/) (2024)
- [Causal Estimation of Memorisation Profiles](https://mlsanity.com/paper/2406.04327/) (2024)
- [Threshold KNN-Shapley: A Linear-Time and Privacy-Friendly Approach to Data Valuation](https://mlsanity.com/paper/2308.15709/) (2023)
- [Regression-adjusted Monte Carlo Estimators for Shapley Values and Probabilistic Values](https://mlsanity.com/paper/2506.11849/) (2025)
- [Efficient Data Shapley for Weighted Nearest Neighbor Algorithms](https://mlsanity.com/paper/2401.11103/) (2024)
- [An Economic Solution to Copyright Challenges of Generative AI](https://mlsanity.com/paper/2404.13964/) (2024)
- [Data Valuation and Detections in Federated Learning](https://mlsanity.com/paper/2311.05304/) (2023)
- [Rethinking Backdoor Attacks](https://mlsanity.com/paper/2307.10163/) (2023)
- [Data Attribution for Diffusion Models: Timestep-induced Bias in Influence Estimation](https://mlsanity.com/paper/2401.09031/) (2024)
- [A Note on "Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms"](https://mlsanity.com/paper/2304.04258/) (2023)
- [Selectivity Drives Productivity: Efficient Dataset Pruning for Enhanced Transfer Learning](https://mlsanity.com/paper/2310.08782/) (2023)
- [XInsight: eXplainable Data Analysis Through The Lens of Causality](https://mlsanity.com/paper/2207.12718/) (2022)
- [Towards Explainable Artificial Intelligence (XAI): A Data Mining Perspective](https://mlsanity.com/paper/2401.04374/) (2024)
- [One Sample Fits All: Approximating All Probabilistic Values Simultaneously and Efficiently](https://mlsanity.com/paper/2410.23808/) (2024)
- [2D-Shapley: A Framework for Fragmented Data Valuation](https://mlsanity.com/paper/2306.10473/) (2023)
- [Fast Data Attribution for Text-to-Image Models](https://mlsanity.com/paper/2511.10721/) (2025)
- [Data Optimization in Deep Learning: A Survey](https://mlsanity.com/paper/2310.16499/) (2023)
- [Sparse, Efficient and Explainable Data Attribution with DualXDA](https://mlsanity.com/paper/2402.12118/) (2024)
- [Task-Oriented GNNs Training on Large Knowledge Graphs for Accurate and Efficient Modeling](https://mlsanity.com/paper/2403.05752/) (2024)

## Abstract (arXiv)

We develop a new, principled algorithm for estimating the contribution of training data points to the behavior of a deep learning model, such as a specific prediction it makes. Our algorithm estimates the AME, a quantity that measures the expected (average) marginal effect of adding a data point to a subset of the training data, sampled from a given distribution. When subsets are sampled from the uniform distribution, the AME reduces to the well-known Shapley value. Our approach is inspired by causal inference and randomized experiments: we sample different subsets of the training data to train multiple submodels, and evaluate each submodel's behavior. We then use a LASSO regression to jointly estimate the AME of each data point, based on the subset compositions. Under sparsity assumptions (k ll N datapoints have large AME), our estimator requires only O(klog N) randomized submodel trainings, improving upon the best prior Shapley value estimators.