# Controllable RANSAC-based Anomaly Detection via Hypothesis Testing

arXiv: https://arxiv.org/abs/2410.15133 · HTML: https://mlsanity.com/paper/2410.15133/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 19 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [MODS: Fast and Robust Method for Two-View Matching](https://mlsanity.com/paper/1503.02619/) (2015)
- [Valid Inference Corrected for Outlier Removal](https://mlsanity.com/paper/1711.10635/) (2017)
- [Testing for a Change in Mean After Changepoint Detection](https://mlsanity.com/paper/1910.04291/) (2019)
- [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)
- [Valid P-Value for Deep Learning-Driven Salient Region](https://mlsanity.com/paper/2301.02437/) (2023)
- [Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation](https://mlsanity.com/paper/2104.10840/) (2021)
- [Efficient Initial Pose-graph Generation for Global SfM](https://mlsanity.com/paper/2011.11986/) (2020)
- [Selective Inference for Change Point Detection in Multi-dimensional Sequences](https://mlsanity.com/paper/1706.00514/) (2017)
- [Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference](https://mlsanity.com/paper/2110.08989/) (2021)
- [CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference](https://mlsanity.com/paper/2310.14608/) (2023)
- [Statistical Test for Attention Map in Vision Transformer](https://mlsanity.com/paper/2401.08169/) (2024)

## Built on by (most cited first, 2 of 2)

- [Statistical Inference for Clustering-based Anomaly Detection](https://mlsanity.com/paper/2504.18633/) (2025)
- [Post-Anomaly Detection Inference for Deep SVDD](https://mlsanity.com/paper/2609.37935/) (2026)

## Abstract (arXiv)

Detecting the presence of anomalies in regression models is a crucial task in machine learning, as anomalies can significantly impact the accuracy and reliability of predictions. Random Sample Consensus (RANSAC) is one of the most popular robust regression methods for addressing this challenge. However, this method lacks the capability to guarantee the reliability of the anomaly detection (AD) results. In this paper, we propose a novel statistical method for testing the AD results obtained by RANSAC, named CTRL-RANSAC (controllable RANSAC). The key strength of the proposed method lies in its ability to control the probability of misidentifying anomalies below a pre-specified level α (e.g., α = 0.05). By examining the selection strategy of RANSAC and leveraging the Selective Inference (SI) framework, we prove that achieving controllable RANSAC is indeed feasible. Furthermore, we introduce a more strategic and computationally efficient approach to enhance the true detection rate and overall performance of the CTRL-RANSAC. Experiments conducted on synthetic and real-world datasets robustly support our theoretical results, showcasing the superior performance of the proposed method.