# Deletion and Insertion Tests in Regression Models

arXiv: https://arxiv.org/abs/2205.12423 · HTML: https://mlsanity.com/paper/2205.12423/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 72 references that are in the map.
- First posted on arXiv 25 May 2022.

## Builds on (most cited first, 30 of 38)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Top-down Neural Attention by Excitation Backprop](https://mlsanity.com/paper/1608.00507/) (2016)
- [From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI](https://mlsanity.com/paper/2201.08164/) (2022)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Debugging Tests for Model Explanations](https://mlsanity.com/paper/2011.05429/) (2020)
- [Benchmarking and Survey of Explanation Methods for Black Box Models](https://mlsanity.com/paper/2102.13076/) (2021)
- [Explainable AI (XAI): A Systematic Meta-Survey of Current Challenges and Future Opportunities](https://mlsanity.com/paper/2111.06420/) (2021)
- [Human-Centered Explainable AI (XAI): From Algorithms to User Experiences](https://mlsanity.com/paper/2110.10790/) (2021)
- [Benchmarking Deep Learning Interpretability in Time Series Predictions](https://mlsanity.com/paper/2010.13924/) (2020)
- [Look at the Variance! Efficient Black-box Explanations with Sobol-based Sensitivity Analysis](https://mlsanity.com/paper/2111.04138/) (2021)
- [A Rigorous Study of Integrated Gradients Method and Extensions to Internal Neuron Attributions](https://mlsanity.com/paper/2202.11912/) (2022)
- [Visualizing Deep Networks by Optimizing with Integrated Gradients](https://mlsanity.com/paper/1905.00954/) (2019)
- [Evaluations and Methods for Explanation through Robustness Analysis](https://mlsanity.com/paper/2006.00442/) (2020)

## Built on by (most cited first, 14 of 14)

- [Decoupling Pixel Flipping and Occlusion Strategy for Consistent XAI Benchmarks](https://mlsanity.com/paper/2401.06654/) (2024)
- [Finer-CAM: Spotting the Difference Reveals Finer Details for Visual Explanation](https://mlsanity.com/paper/2501.11309/) (2025)
- [Class-Specific Explainability for Deep Time Series Classifiers](https://mlsanity.com/paper/2210.05411/) (2022)
- [Explaining Similarity in Vision-Language Encoders with Weighted Banzhaf Interactions](https://mlsanity.com/paper/2508.05430/) (2025)
- [EvalAttAI: A Holistic Approach to Evaluating Attribution Maps in Robust and Non-Robust Models](https://mlsanity.com/paper/2303.08866/) (2023)
- [Model free variable importance for high dimensional data](https://mlsanity.com/paper/2211.08414/) (2022)
- [Time series saliency maps: explaining models across multiple domains](https://mlsanity.com/paper/2505.13100/) (2025)
- [ShapBPT: Image Feature Attributions Using Data-Aware Binary Partition Trees](https://mlsanity.com/paper/2602.07047/) (2026)
- [XpertAI: uncovering regression model strategies for sub-manifolds](https://mlsanity.com/paper/2403.07486/) (2024)
- [Neural Dynamic Data Valuation via Stochastic State-Adjoint Trajectories](https://mlsanity.com/paper/2404.19557/) (2024)
- [PCIM: Learning Pixel Attributions via Pixel-wise Channel Isolation Mixing in High Content Imaging](https://mlsanity.com/paper/2412.02275/) (2024)
- [An Explainable Failure Prediction Framework for Neural Networks in Radio Access Networks](https://mlsanity.com/paper/2602.13231/) (2026)
- [Super Agents and Confounders: Influence of surrounding agents on vehicle trajectory prediction](https://mlsanity.com/paper/2604.03463/) (2026)
- [CAM-Guided Saliency Cutout and Image-Based Malware Classification](https://mlsanity.com/paper/2608.11634/) (2026)

## Abstract (arXiv)

A basic task in explainable AI (XAI) is to identify the most important features behind a prediction made by a black box function f. The insertion and deletion tests of Petsiuk et al. (2018) can be used to judge the quality of algorithms that rank pixels from most to least important for a classification. Motivated by regression problems we establish a formula for their area under the curve (AUC) criteria in terms of certain main effects and interactions in an anchored decomposition of f. We find an expression for the expected value of the AUC under a random ordering of inputs to f and propose an alternative area above a straight line for the regression setting. We use this criterion to compare feature importances computed by integrated gradients (IG) to those computed by Kernel SHAP (KS) as well as LIME, DeepLIFT, vanilla gradient and input×gradient methods. KS has the best overall performance in two datasets we consider but it is very expensive to compute. We find that IG is nearly as good as KS while being much faster. Our comparison problems include some binary inputs that pose a challenge to IG because it must use values between the possible variable levels and so we consider ways to handle binary variables in IG. We show that sorting variables by their Shapley value does not necessarily give the optimal ordering for an insertion-deletion test. It will however do that for monotone functions of additive models, such as logistic regression.