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

Mizuki Niihori, Shuichi Nishino, Teruyuki Katsuoka, Tomohiro Shiraishi, Kouichi Taji, Ichiro Takeuchi

Keywords: Anomaly Detection, k-Nearest Neighbors, Statistical Test, Selective Inference, Deep Learning

TL;DR: We propose a method to quantify the statistical significance of anomalies detected by deep k-nearest neighbor approach.

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 $k$NN) AD stands out for its interpretability and flexibility, leveraging distance-based scoring in deep latent spaces.
Despite its strong performance, deep $k$NN 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.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 25480