Statistically Significant $k$NNAD by Selective Inference

In this paper, we investigate the problem of unsupervised anomaly detection using the k-Nearest Neighbor method. The k-Nearest Neighbor Anomaly Detection (kNNAD) is a simple yet effective approach for identifying anomalies across various domains and fields. A critical challenge in anomaly detection, including kNNAD, is appropriately quantifying the reliability of detected anomalies. To address this, we formulate kNNAD as a statistical hypothesis test and quantify the probability of false detection using $p$-values. The main technical challenge lies in performing both anomaly detection and statistical testing on the same data, which hinders correct $p$-value calculation within the conventional statistical testing framework. To resolve this issue, we introduce a statistical hypothesis testing framework called Selective Inference (SI) and propose a method named Statistically Significant NNAD (Stat-kNNAD). By leveraging SI, the Stat-kNNAD method ensures that detected anomalies are statistically significant with theoretical guarantees. The proposed Stat-kNNAD method is applicable to anomaly detection in both the original feature space and latent feature spaces derived from deep learning models. Through numerical experiments on synthetic data and applications to industrial product anomaly detection, we demonstrate the validity and effectiveness of the Stat-kNNAD method.

Time Series Anomaly Detection in the Frequency Domain with Statistical Reliability

Effective anomaly detection in complex systems requires identifying change points (CPs) in the frequency domain, as abnormalities often arise across multiple frequencies. This paper extends recent advancements in statistically significant CP detection, based on Selective Inference (SI), to the frequency domain. The proposed SI method quantifies the statistical significance of detected CPs in the frequency domain using $p$-values, ensuring that the detected changes reflect genuine structural shifts in the target system. We address two major technical challenges to achieve this. First, we extend the existing SI framework to the frequency domain by appropriately utilizing the properties of discrete Fourier transform (DFT). Second, we develop an SI method that provides valid $p$-values for CPs where changes occur across multiple frequencies. Experimental results demonstrate that the proposed method reliably identifies genuine CPs with strong statistical guarantees, enabling more accurate root-cause analysis in the frequency domain of complex systems.

si4onnx: A Python package for Selective Inference in Deep Learning Models

In this paper, we introduce si4onnx, a package for performing selective inference on deep learning models. Techniques such as CAM in XAI and reconstruction-based anomaly detection using VAE can be interpreted as methods for identifying significant regions within input images. However, the identified regions may not always carry meaningful significance. Therefore, evaluating the statistical significance of these regions represents a crucial challenge in establishing the reliability of AI systems. si4onnx is a Python package that enables straightforward implementation of hypothesis testing with controlled type I error rates through selective inference. It is compatible with deep learning models constructed using common frameworks such as PyTorch and TensorFlow.

Statistical Test for Data Analysis Pipeline by Selective Inference

A data analysis pipeline is a structured sequence of processing steps that transforms raw data into meaningful insights by effectively integrating various analysis algorithms. In this paper, we propose a novel statistical test designed to assess the statistical significance of data analysis pipelines. Our approach allows for the systematic development of valid statistical tests applicable to any data analysis pipeline configuration composed of a set of data analysis components. We have developed this framework by adapting selective inference, which has gained recent attention as a new statistical inference technique for data-driven hypotheses. The proposed statistical test is theoretically designed to control the type I error at the desired significance level in finite samples. As examples, we consider a class of pipelines composed of three missing value imputation algorithms, three outlier detection algorithms, and three feature selection algorithms. We confirm the validity of our statistical test through experiments with both synthetic and real data for this class of data analysis pipelines. Additionally, we present an implementation framework that facilitates testing across any configuration of data analysis pipelines in this class without extra implementation costs.