# A Bayesian Approach To Analysing Training Data Attribution In Deep Learning

arXiv: https://arxiv.org/abs/2305.19765 · HTML: https://mlsanity.com/paper/2305.19765/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 24 of 24)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Visual Transformers: Token-based Image Representation and Processing for Computer Vision](https://mlsanity.com/paper/2006.03677/) (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)
- [If Influence Functions are the Answer, Then What is the Question?](https://mlsanity.com/paper/2209.05364/) (2022)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [FastIF: Scalable Influence Functions for Efficient Model Interpretation and Debugging](https://mlsanity.com/paper/2012.15781/) (2020)
- [Understanding the Origins of Bias in Word Embeddings](https://mlsanity.com/paper/1810.03611/) (2018)
- [Input Similarity from the Neural Network Perspective](https://mlsanity.com/paper/2102.05262/) (2021)
- [Interpreting Black Box Predictions using Fisher Kernels](https://mlsanity.com/paper/1810.10118/) (2018)
- [Revisiting Methods for Finding Influential Examples](https://mlsanity.com/paper/2111.04683/) (2021)
- [Rethinking Influence Functions of Neural Networks in the Over-parameterized Regime](https://mlsanity.com/paper/2112.08297/) (2021)
- [Revisiting the Fragility of Influence Functions](https://mlsanity.com/paper/2303.12922/) (2023)
- [How Many and Which Training Points Would Need to be Removed to Flip this Prediction?](https://mlsanity.com/paper/2302.02169/) (2023)

## Built on by (most cited first, 11 of 11)

- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [Training Data Attribution via Approximate Unrolled Differentiation](https://mlsanity.com/paper/2405.12186/) (2024)
- [Better Training Data Attribution via Better Inverse Hessian-Vector Products](https://mlsanity.com/paper/2507.14740/) (2025)
- [Final-Model-Only Data Attribution with a Unifying View of Gradient-Based Methods](https://mlsanity.com/paper/2412.03906/) (2024)
- [Large Language Model Sourcing: A Survey](https://mlsanity.com/paper/2510.10161/) (2025)
- [Adversarial Attacks on Data Attribution](https://mlsanity.com/paper/2409.05657/) (2024)
- [Enhancing Interpretability in Generative AI Through Search-Based Data Influence Analysis](https://mlsanity.com/paper/2504.01771/) (2025)
- [A Bayesian Information-Theoretic Approach to Data Attribution](https://mlsanity.com/paper/2604.03858/) (2026)
- [TuCo: Measuring the Contribution of Fine-Tuning to Individual Responses of LLMs](https://mlsanity.com/paper/2506.23423/) (2025)
- [On the Fragility of Data Attribution When Learning Is Distributed](https://mlsanity.com/paper/2605.15520/) (2026)
- [Certified Approximation for Interpretable Representer Landmarks](https://mlsanity.com/paper/2609.38901/) (2026)

## Abstract (arXiv)

Training data attribution (TDA) techniques find influential training data for the model's prediction on the test data of interest. They approximate the impact of down- or up-weighting a particular training sample. While conceptually useful, they are hardly applicable to deep models in practice, particularly because of their sensitivity to different model initialisation. In this paper, we introduce a Bayesian perspective on the TDA task, where the learned model is treated as a Bayesian posterior and the TDA estimates as random variables. From this novel viewpoint, we observe that the influence of an individual training sample is often overshadowed by the noise stemming from model initialisation and SGD batch composition. Based on this observation, we argue that TDA can only be reliably used for explaining deep model predictions that are consistently influenced by certain training data, independent of other noise factors. Our experiments demonstrate the rarity of such noise-independent training-test data pairs but confirm their existence. We recommend that future researchers and practitioners trust TDA estimates only in such cases. Further, we find a disagreement between ground truth and estimated TDA distributions and encourage future work to study this gap. Code is provided at https://github.com/ElisaNguyen/bayesian-tda.