# Making Sense of Dependence: Efficient Black-box Explanations Using Dependence Measure

arXiv: https://arxiv.org/abs/2206.06219 · HTML: https://mlsanity.com/paper/2206.06219/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 74 references that are in the map.
- First posted on arXiv 13 Jun 2022.

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

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (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)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (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)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Evaluating and Aggregating Feature-based Model Explanations](https://mlsanity.com/paper/2005.00631/) (2020)
- [Sanity Checks for Saliency Metrics](https://mlsanity.com/paper/1912.01451/) (2019)
- [XRAI: Better Attributions Through Regions](https://mlsanity.com/paper/1906.02825/) (2019)
- [Black-box Explanation of Object Detectors via Saliency Maps](https://mlsanity.com/paper/2006.03204/) (2020)
- [Look at the Variance! Efficient Black-box Explanations with Sobol-based Sensitivity Analysis](https://mlsanity.com/paper/2111.04138/) (2021)

## Built on by (most cited first, 30 of 33)

- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [A Holistic Approach to Unifying Automatic Concept Extraction and Concept Importance Estimation](https://mlsanity.com/paper/2306.07304/) (2023)
- [Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models](https://mlsanity.com/paper/2502.12892/) (2025)
- [Unlocking Feature Visualization for Deeper Networks with MAgnitude Constrained Optimization](https://mlsanity.com/paper/2306.06805/) (2023)
- [Interpreting Object-level Foundation Models via Visual Precision Search](https://mlsanity.com/paper/2411.16198/) (2024)
- [Block-Recurrent Dynamics in Vision Transformers](https://mlsanity.com/paper/2512.19941/) (2025)
- [Understanding Visual Feature Reliance through the Lens of Complexity](https://mlsanity.com/paper/2407.06076/) (2024)
- [Diffusion Models as Artists: Are we Closing the Gap between Humans and Machines?](https://mlsanity.com/paper/2301.11722/) (2023)
- [Local Concept Embeddings for Analysis of Concept Distributions in Vision DNN Feature Spaces](https://mlsanity.com/paper/2311.14435/) (2023)
- [Probabilistic Conceptual Explainers: Trustworthy Conceptual Explanations for Vision Foundation Models](https://mlsanity.com/paper/2406.12649/) (2024)
- [Assessment of the Reliablity of a Model's Decision by Generalizing Attribution to the Wavelet Domain](https://mlsanity.com/paper/2305.14979/) (2023)
- [Feature Accentuation: Revealing 'What' Features Respond to in Natural Images](https://mlsanity.com/paper/2402.10039/) (2024)
- [LibraGrad: Balancing Gradient Flow for Universally Better Vision Transformer Attributions](https://mlsanity.com/paper/2411.16760/) (2024)
- [Path Choice Matters for Clear Attribution in Path Methods](https://mlsanity.com/paper/2401.10442/) (2024)
- [Saliency strikes back: How filtering out high frequencies improves white-box explanations](https://mlsanity.com/paper/2307.09591/) (2023)
- [One Wave To Explain Them All: A Unifying Perspective On Feature Attribution](https://mlsanity.com/paper/2410.01482/) (2024)
- [Improving Perturbation-based Explanations by Understanding the Role of Uncertainty Calibration](https://mlsanity.com/paper/2511.10439/) (2025)
- [A Geometric Unification of Concept Learning with Concept Cones](https://mlsanity.com/paper/2512.07355/) (2025)
- [A Backdoor-based Explainable AI Benchmark for High Fidelity Evaluation of Attributions](https://mlsanity.com/paper/2405.02344/) (2024)
- [The Overfocusing Bias of Convolutional Neural Networks: A Saliency-Guided Regularization Approach](https://mlsanity.com/paper/2409.17370/) (2024)
- [Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI](https://mlsanity.com/paper/2411.15265/) (2024)
- [Where Not to Learn: Prior-Aligned Training with Subset-based Attribution Constraints](https://mlsanity.com/paper/2602.07008/) (2026)
- [SAfER: Layer-Level Sensitivity Assessment for Efficient and Robust Neural Network Inference](https://mlsanity.com/paper/2308.04753/) (2023)
- [Unlearning-based Neural Interpretations](https://mlsanity.com/paper/2410.08069/) (2024)
- [Back to the Baseline: Examining Baseline Effects on Explainability Metrics](https://mlsanity.com/paper/2512.11433/) (2025)
- [A Distributional View for Visual Mechanistic Interpretability: KL-Minimal Soft-Constraint Principle](https://mlsanity.com/paper/2605.17504/) (2026)
- [PhaseWin: An Efficient Search Algorithm for Faithful Visual Attribution](https://mlsanity.com/paper/2606.18008/) (2026)
- [Understanding Inhibition Through Maximally Tense Images](https://mlsanity.com/paper/2406.05598/) (2024)
- [Towards Robust and Generalizable Gerchberg Saxton based Physics Inspired Neural Networks for Computer Generated Holography: A Sensitivity Analysis Framework](https://mlsanity.com/paper/2505.00220/) (2025)
- [Why Uncertainty Calibration Matters for Reliable Perturbation-based Explanations](https://mlsanity.com/paper/2506.19630/) (2025)

## Abstract (arXiv)

This paper presents a new efficient black-box attribution method based on Hilbert-Schmidt Independence Criterion (HSIC), a dependence measure based on Reproducing Kernel Hilbert Spaces (RKHS). HSIC measures the dependence between regions of an input image and the output of a model based on kernel embeddings of distributions. It thus provides explanations enriched by RKHS representation capabilities. HSIC can be estimated very efficiently, significantly reducing the computational cost compared to other black-box attribution methods. Our experiments show that HSIC is up to 8 times faster than the previous best black-box attribution methods while being as faithful. Indeed, we improve or match the state-of-the-art of both black-box and white-box attribution methods for several fidelity metrics on Imagenet with various recent model architectures. Importantly, we show that these advances can be transposed to efficiently and faithfully explain object detection models such as YOLOv4. Finally, we extend the traditional attribution methods by proposing a new kernel enabling an ANOVA-like orthogonal decomposition of importance scores based on HSIC, allowing us to evaluate not only the importance of each image patch but also the importance of their pairwise interactions. Our implementation is available at https://github.com/paulnovello/HSIC-Attribution-Method.