Interpreting Outliers: Localized Logistic Regression for Density Ratio Estimation

TL;DR

This paper introduces a localized logistic regression method for outlier detection that not only identifies outliers but also explains the features responsible, improving interpretability and detection accuracy in high-dimensional data.

Contribution

The paper presents a novel localized logistic regression algorithm for density ratio estimation, enabling outlier-specific feature selection and interpretability.

Findings

Successfully detects important features for outliers in synthetic data

Outperforms existing algorithms on benchmark datasets

Provides interpretable explanations for outlier detection

Abstract

We propose an inlier-based outlier detection method capable of both identifying the outliers and explaining why they are outliers, by identifying the outlier-specific features. Specifically, we employ an inlier-based outlier detection criterion, which uses the ratio of inlier and test probability densities as a measure of plausibility of being an outlier. For estimating the density ratio function, we propose a localized logistic regression algorithm. Thanks to the locality of the model, variable selection can be outlier-specific, and will help interpret why points are outliers in a high-dimensional space. Through synthetic experiments, we show that the proposed algorithm can successfully detect the important features for outliers. Moreover, we show that the proposed algorithm tends to outperform existing algorithms in benchmark datasets.