# Understanding Instance-based Interpretability of Variational Auto-Encoders

arXiv: https://arxiv.org/abs/2105.14203 · HTML: https://mlsanity.com/paper/2105.14203/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 29 May 2021.

## Builds on (most cited first, 27 of 27)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [Data Valuation using Reinforcement Learning](https://mlsanity.com/paper/1909.11671/) (2019)
- [On Second-Order Group Influence Functions for Black-Box Predictions](https://mlsanity.com/paper/1911.00418/) (2019)
- [Data Cleansing for Models Trained with SGD](https://mlsanity.com/paper/1906.08473/) (2019)
- [A Non-Parametric Test to Detect Data-Copying in Generative Models](https://mlsanity.com/paper/2004.05675/) (2020)
- [Interpreting Black Box Predictions using Fisher Kernels](https://mlsanity.com/paper/1810.10118/) (2018)
- [RelatIF: Identifying Explanatory Training Examples via Relative Influence](https://mlsanity.com/paper/2003.11630/) (2020)
- [Evaluating the Interpretability of Generative Models by Interactive Reconstruction](https://mlsanity.com/paper/2102.01264/) (2021)
- [Multi-Stage Influence Function](https://mlsanity.com/paper/2007.09081/) (2020)
- [Estimating informativeness of samples with Smooth Unique Information](https://mlsanity.com/paper/2101.06640/) (2021)
- [Teaching a GAN What Not to Learn](https://mlsanity.com/paper/2010.15639/) (2020)
- [Optimal Sub-sampling with Influence Functions](https://mlsanity.com/paper/1709.01716/) (2017)
- [Influence Estimation for Generative Adversarial Networks](https://mlsanity.com/paper/2101.08367/) (2021)
- [Out-of-Distribution Generalization Analysis via Influence Function](https://mlsanity.com/paper/2101.08521/) (2021)
- [Data Cleansing for Deep Neural Networks with Storage-efficient Approximation of Influence Functions](https://mlsanity.com/paper/2103.11807/) (2021)

## Built on by (most cited first, 21 of 21)

- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [On Memorization in Probabilistic Deep Generative Models](https://mlsanity.com/paper/2106.03216/) (2021)
- [Intriguing Properties of Data Attribution on Diffusion Models](https://mlsanity.com/paper/2311.00500/) (2023)
- [Rethinking Influence Functions of Neural Networks in the Over-parameterized Regime](https://mlsanity.com/paper/2112.08297/) (2021)
- [Diffusion Attribution Score: Evaluating Training Data Influence in Diffusion Models](https://mlsanity.com/paper/2410.18639/) (2024)
- [An Empirical Study of Memorization in NLP](https://mlsanity.com/paper/2203.12171/) (2022)
- [Adapting and Evaluating Influence-Estimation Methods for Gradient-Boosted Decision Trees](https://mlsanity.com/paper/2205.00359/) (2022)
- [Label-Free Explainability for Unsupervised Models](https://mlsanity.com/paper/2203.01928/) (2022)
- [Data Attribution for Diffusion Models: Timestep-induced Bias in Influence Estimation](https://mlsanity.com/paper/2401.09031/) (2024)
- [Towards Explainable Artificial Intelligence (XAI): A Data Mining Perspective](https://mlsanity.com/paper/2401.04374/) (2024)
- [TracInAD: Measuring Influence for Anomaly Detection](https://mlsanity.com/paper/2205.01362/) (2022)
- [Error Discovery by Clustering Influence Embeddings](https://mlsanity.com/paper/2312.04712/) (2023)
- [Prototypical Self-Explainable Models Without Re-training](https://mlsanity.com/paper/2312.07822/) (2023)
- [Exploring Latent Pathways: Enhancing the Interpretability of Autonomous Driving with a Variational Autoencoder](https://mlsanity.com/paper/2404.01750/) (2024)
- [GMValuator: Similarity-based Data Valuation for Generative Models](https://mlsanity.com/paper/2304.10701/) (2023)
- [Approximate Data Deletion in Generative Models](https://mlsanity.com/paper/2206.14439/) (2022)
- [Trainable and Explainable Simplicial Map Neural Networks](https://mlsanity.com/paper/2306.00010/) (2023)
- [Differential Privacy, Linguistic Fairness, and Training Data Influence: Impossibility and Possibility Theorems for Multilingual Language Models](https://mlsanity.com/paper/2308.08774/) (2023)
- [A Comparative Analysis of Influence Signals for Data Debugging](https://mlsanity.com/paper/2506.11584/) (2025)
- [IFFair: Influence Function-driven Sample Reweighting for Fair Classification](https://mlsanity.com/paper/2512.07249/) (2025)
- [Distilling Diffusion Score Discrepancy for Efficient Training Data Attribution](https://mlsanity.com/paper/2609.38776/) (2026)

## Abstract (arXiv)

Instance-based interpretation methods have been widely studied for supervised learning methods as they help explain how black box neural networks predict. However, instance-based interpretations remain ill-understood in the context of unsupervised learning. In this paper, we investigate influence functions [Koh and Liang, 2017], a popular instance-based interpretation method, for a class of deep generative models called variational auto-encoders (VAE). We formally frame the counter-factual question answered by influence functions in this setting, and through theoretical analysis, examine what they reveal about the impact of training samples on classical unsupervised learning methods. We then introduce VAE- TracIn, a computationally efficient and theoretically sound solution based on Pruthi et al. [2020], for VAEs. Finally, we evaluate VAE-TracIn on several real world datasets with extensive quantitative and qualitative analysis.