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Controllable RANSAC-based Anomaly Detection via Hypothesis Testing

Le Hong Phong, Ho Ngoc Luat, Vo Nguyen Le Duy

TL;DR

This paper proposes CTRL‐RANSAC (controllable RANSAC), a novel statistical method for testing the AD results obtained from RANSAC in linear regression tasks, and proves that achieving controllable RANSAC is indeed feasible.

Abstract

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.

Controllable RANSAC-based Anomaly Detection via Hypothesis Testing

TL;DR

This paper proposes CTRL‐RANSAC (controllable RANSAC), a novel statistical method for testing the AD results obtained from RANSAC in linear regression tasks, and proves that achieving controllable RANSAC is indeed feasible.

Abstract

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 (e.g., ). 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.

Paper Structure

This paper contains 28 sections, 5 theorems, 51 equations, 10 figures, 3 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. RANSAC-based Anomaly Detection
  4. Statistical Inference and Decision Making
  5. The null and alternative hypotheses.
  6. Test statistic.
  7. Compute $p$-value and decision making.
  8. Difficulty in computing a valid $p$-value.
  9. PROPOSED CTRL-RANSAC
  10. The valid p-value in CTRL-RANSAC
  11. Conditional Data Space Characterization
  12. Reformulation of the selective p-value computation with ${\mathcal{Z}}$.
  13. Identification of Truncation Region ${\mathcal{Z}}$
  14. Solving of each sub-problem.
  15. Experiment
  16. ...and 13 more sections

Key Result

Lemma 1

The selective $p$-value in (eq:selective_p) is a valid $p$-value that satisfies the following property:

Figures (10)

  • Figure 1: Illustration of the proposed CTRL-RANSAC method. Performing AD without inference produces wrong anomalies (B, D). The naive $p$-values are even small for falsely detected anomalies. With the $p$-value provided by CTRL-RANSAC, we can identify both false positive (FP) and true positive (TP) detections, i.e., large p-values for FPs and small p-values for TPs.
  • Figure 2: A schematic illustration of the proposed method. By applying RANSAC to the observed data, we obtain a set of anomalies. Then, we parametrize the data with a scalar parameter $z$ in the direction of the test statistic to identify the truncation region ${\mathcal{Z}}$ whose data have the same result of AD as the observed data. Finally, the inference is conducted conditional on ${\mathcal{Z}}$. We employ the "divide-and-conquer" strategy and introduce an efficient method for characterizing the truncation region ${\mathcal{Z}}$.
  • Figure 3: FPR Comparison
  • Figure 4: TPR Comparison
  • Figure 5: Average running time in 100 trials
  • ...and 5 more figures

Theorems & Definitions (14)

  • Example 1
  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Remark 2
  • Lemma 3
  • proof
  • Lemma 4
  • ...and 4 more