Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inference

TL;DR

This paper introduces a statistical framework for deep k-nearest neighbor anomaly detection that quantifies the significance of anomalies using p-values, addressing uncertainty estimation and false positive control in industrial applications.

Contribution

It develops a novel selective inference approach to quantify anomaly significance in deep kNN AD, managing selection bias and enabling reliable uncertainty estimation.

Findings

Provides a method to compute p-values for anomalies

Demonstrates reliable false positive control in industrial datasets

Enhances interpretability and trustworthiness of deep kNN AD

Abstract

In real-world applications, anomaly detection (AD) often operates without access to anomalous data, necessitating semi-supervised methods that rely solely on normal data. Among these methods, deep k-nearest neighbor (deep kNN) AD stands out for its interpretability and flexibility, leveraging distance-based scoring in deep latent spaces.Despite its strong performance, deep kNN lacks a mechanism to quantify uncertainty-an essential feature for critical applications such as industrial inspection. To address this limitation, we propose a statistical framework that quantifies the significance of detected anomalies in the form of p-values, thereby enabling control over false positive rates at a user-specified significance level (e.g.,0.05). A central challenge lies in managing selection bias, which we tackle using Selective Inference-a principled method for conducting inference conditioned on data-driven selections. We evaluate our method on diverse datasets and demonstrate that it provides reliable AD well-suited for industrial use cases.