A unified approach to outlier identification for mixed-type data

2026-06-24

AI Summary

This study addresses the lack of a unified anomaly detection framework for mixed-type data comprising both continuous and ordinal categorical variables. The authors propose a robust approach based on a latent Gaussian variable model, wherein non-anomalous observations are assumed to follow a multivariate Gaussian distribution, and ordinal variables are represented through underlying latent Gaussian variables. Parameter estimation is performed using the Minimum Covariance Determinant (MCD) estimator, explicitly accounting for potential incompleteness in the observed ordinal information. Theoretical analysis demonstrates that the method effectively identifies extreme outliers and maintains robustness even under data contamination. Empirical evaluations on synthetic datasets show high detection rates coupled with low false alarm rates, and the method’s practical utility is further validated through application to real-world Airbnb listing data.

Abstract

We present an outlier identification method for mixed type data sets comprising continuous and ordinal variables. We define outliers based on using a multivariate Gaussian distribution as reference distribution for non-outliers, with a latent Gaussian assumed for ordinal variables. The proposed algorithm is based on the robust Minimum Covariance Determinant estimator for estimating the parameters of the multivariate Gaussian for the non-outliers. This is extended to account for the fact that the full Gaussian information underlying the ordinal variables is not observed. A breakdown theorem shows that replacing observations will noty stop extreme enough outliers from being identified. The effectiveness of our approach is demonstrated via simulations on synthetic data with various types of contamination, achieving high detection and low false positive rates. Practical relevance is illustrated through an application to Airbnb listing data containing both continuous and ordinal attributes.

Problem

• outlier identification
• mixed-type data
• ordinal variables
• continuous variables
• anomaly detection

Innovation

• mixed-type data
• outlier detection
• latent Gaussian model
• Minimum Covariance Determinant
• robust estimation