# Valid P-Value for Deep Learning-Driven Salient Region

arXiv: https://arxiv.org/abs/2301.02437 · HTML: https://mlsanity.com/paper/2301.02437/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 42 references that are in the map.
- First posted on arXiv 6 Jan 2023.

## Builds on (most cited first, 30 of 34)

- [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)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [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)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Inverting Visual Representations with Convolutional Networks](https://mlsanity.com/paper/1506.02753/) (2015)
- [Fooling Neural Network Interpretations via Adversarial Model Manipulation](https://mlsanity.com/paper/1902.02041/) (2019)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Association of genomic subtypes of lower-grade gliomas with shape features automatically extracted by a deep learning algorithm](https://mlsanity.com/paper/1906.03720/) (2019)
- [Interpretable Deep Learning under Fire](https://mlsanity.com/paper/1812.00891/) (2018)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Valid Inference Corrected for Outlier Removal](https://mlsanity.com/paper/1711.10635/) (2017)
- [Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programming](https://mlsanity.com/paper/2002.09132/) (2020)
- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [Computing Valid p-values for Image Segmentation by Selective Inference](https://mlsanity.com/paper/1906.00629/) (2019)
- [More powerful post-selection inference, with application to the Lasso](https://mlsanity.com/paper/1801.09037/) (2018)
- [Selective Inference for Group-Sparse Linear Models](https://mlsanity.com/paper/1607.08211/) (2016)
- [Quantifying Statistical Significance of Neural Network-based Image Segmentation by Selective Inference](https://mlsanity.com/paper/2010.01823/) (2020)
- [Post-Selection Inference for Changepoint Detection Algorithms with Application to Copy Number Variation Data](https://mlsanity.com/paper/1812.03644/) (2018)
- [Selective Sequential Model Selection](https://mlsanity.com/paper/1512.02565/) (2015)
- [Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation](https://mlsanity.com/paper/2104.10840/) (2021)

## Built on by (most cited first, 17 of 17)

- [CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference](https://mlsanity.com/paper/2310.14608/) (2023)
- [Statistical Test for Anomaly Detections by Variational Auto-Encoders](https://mlsanity.com/paper/2402.03724/) (2024)
- [Statistical Test for Attention Map in Vision Transformer](https://mlsanity.com/paper/2401.08169/) (2024)
- [Selective Inference for Changepoint detection by Recurrent Neural Network](https://mlsanity.com/paper/2311.14964/) (2023)
- [Statistical Test for Auto Feature Engineering by Selective Inference](https://mlsanity.com/paper/2410.19768/) (2024)
- [Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inference](https://mlsanity.com/paper/2502.12978/) (2025)
- [Controllable RANSAC-based Anomaly Detection via Hypothesis Testing](https://mlsanity.com/paper/2410.15133/) (2024)
- [Change Point Detection in the Frequency Domain with Statistical Reliability](https://mlsanity.com/paper/2502.03062/) (2025)
- [Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptation](https://mlsanity.com/paper/2508.07049/) (2025)
- [Bounded P-values in Parametric Programming-based Selective Inference](https://mlsanity.com/paper/2307.11351/) (2023)
- [Statistical Test for Diffusion-Based Anomaly Localization via Selective Inference](https://mlsanity.com/paper/2402.11789/) (2024)
- [Statistical Test for Saliency Maps of Graph Neural Networks via Selective Inference](https://mlsanity.com/paper/2505.16893/) (2025)
- [Statistical testing on generative AI anomaly detection tools in Alzheimer's Disease diagnosis](https://mlsanity.com/paper/2410.13363/) (2024)
- [Statistical Inference for Clustering-based Anomaly Detection](https://mlsanity.com/paper/2504.18633/) (2025)
- [Automatic Statistical Test for Rationally Expressible Algorithms by Selective Inference, with Applications to Feature Selection](https://mlsanity.com/paper/2608.04667/) (2026)
- [Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathology](https://mlsanity.com/paper/2609.31712/) (2026)
- [Post-Anomaly Detection Inference for Deep SVDD](https://mlsanity.com/paper/2609.37935/) (2026)

## Abstract (arXiv)

Various saliency map methods have been proposed to interpret and explain predictions of deep learning models. Saliency maps allow us to interpret which parts of the input signals have a strong influence on the prediction results. However, since a saliency map is obtained by complex computations in deep learning models, it is often difficult to know how reliable the saliency map itself is. In this study, we propose a method to quantify the reliability of a salient region in the form of p-values. Our idea is to consider a salient region as a selected hypothesis by the trained deep learning model and employ the selective inference framework. The proposed method can provably control the probability of false positive detections of salient regions. We demonstrate the validity of the proposed method through numerical examples in synthetic and real datasets. Furthermore, we develop a Keras-based framework for conducting the proposed selective inference for a wide class of CNNs without additional implementation cost.