# Out-of-Distribution Generalization Analysis via Influence Function

arXiv: https://arxiv.org/abs/2101.08521 · HTML: https://mlsanity.com/paper/2101.08521/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 21 Jan 2021.

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

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Adversarial Domain Adaptation with Domain Mixup](https://mlsanity.com/paper/1912.01805/) (2019)
- [Causality matters in medical imaging](https://mlsanity.com/paper/1912.08142/) (2019)
- [Invariant Risk Minimization Games](https://mlsanity.com/paper/2002.04692/) (2020)
- [Improve Unsupervised Domain Adaptation with Mixup Training](https://mlsanity.com/paper/2001.00677/) (2020)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Heterogeneous Domain Generalization via Domain Mixup](https://mlsanity.com/paper/2009.05448/) (2020)
- [Detecting Adversarial Samples Using Influence Functions and Nearest Neighbors](https://mlsanity.com/paper/1909.06872/) (2019)
- [Influence Function based Data Poisoning Attacks to Top-N Recommender Systems](https://mlsanity.com/paper/2002.08025/) (2020)
- [Stable Prediction with Model Misspecification and Agnostic Distribution Shift](https://mlsanity.com/paper/2001.11713/) (2020)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [CCMI : Classifier based Conditional Mutual Information Estimation](https://mlsanity.com/paper/1906.01824/) (2019)
- [Risk Variance Penalization](https://mlsanity.com/paper/2006.07544/) (2020)
- [Explaining Latent Factor Models for Recommendation with Influence Functions](https://mlsanity.com/paper/1811.08120/) (2018)

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

- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Towards a Theoretical Framework of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.04496/) (2021)
- [Understanding Instance-based Interpretability of Variational Auto-Encoders](https://mlsanity.com/paper/2105.14203/) (2021)
- [A Review of Causality for Learning Algorithms in Medical Image Analysis](https://mlsanity.com/paper/2206.05498/) (2022)
- [Label Smoothing Improves Machine Unlearning](https://mlsanity.com/paper/2406.07698/) (2024)
- [When Graph Neural Network Meets Causality: Opportunities, Methodologies and An Outlook](https://mlsanity.com/paper/2312.12477/) (2023)
- [Evaluating the Impact of Local Differential Privacy on Utility Loss via Influence Functions](https://mlsanity.com/paper/2309.08678/) (2023)
- [Causal Transfer in Medical Image Analysis](https://mlsanity.com/paper/2603.24388/) (2026)
- [PLSP (Pre-hoc Liminal Space Profiling): OOD Prediction over Detection -- An Anticipatory Approach for Machine Learning Model Reliability](https://mlsanity.com/paper/2609.12225/) (2026)
- [Can Circuit Alignment Predict OOD Generalization?](https://mlsanity.com/paper/2609.31996/) (2026)

## Abstract (arXiv)

The mismatch between training and target data is one major challenge for current machine learning systems. When training data is collected from multiple domains and the target domains include all training domains and other new domains, we are facing an Out-of-Distribution (OOD) generalization problem that aims to find a model with the best OOD accuracy. One of the definitions of OOD accuracy is worst-domain accuracy. In general, the set of target domains is unknown, and the worst over target domains may be unseen when the number of observed domains is limited. In this paper, we show that the worst accuracy over the observed domains may dramatically fail to identify the OOD accuracy. To this end, we introduce Influence Function, a classical tool from robust statistics, into the OOD generalization problem and suggest the variance of influence function to monitor the stability of a model on training domains. We show that the accuracy on test domains and the proposed index together can help us discern whether OOD algorithms are needed and whether a model achieves good OOD generalization.