Moment-Based Anomaly Detection in High-Dimensional Mixed Data
Abstract
We propose an anomaly detection method for high-dimensional mixed-type data that maps heterogeneous features to a common scale via standardized moment-based transformations, yielding interpretable feature-level anomaly scores. These scores are combined through a dependence-aware aggregation step to construct the Mixed-data Influence (MDI) score, accounting for correlations across features and providing a unified measure of how strongly an observation departs from the reference data distribution. By incorporating higher-order moments, the MDI can detect anomalies that arise not only from location shifts, but also from changes in variability, skewness, and other distributional characteristics. The aggregation mechanism allows our method to capture both sparse anomalies concentrated in a small number of features and weak, coordinated deviations distributed across many features. We empirically investigate the distribution and thresholding behavior of the MDI score across different sample sizes, dimensions, dependence structures, and data types. Simulation experiments and two real-data applications, to multi-omics and ESG data, evaluate finite-sample calibration, detection performance, and feature-level interpretability.
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BibTeX
@misc{ferrari2026momentbased,
title = {{Moment-Based Anomaly Detection in High-Dimensional Mixed Data}},
author = {Davide Ferrari and Andrea Nicolodi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16285},
eprint = {2610.16285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16285},
}
RIS
TY - UNPB
TI - Moment-Based Anomaly Detection in High-Dimensional Mixed Data
AU - Davide Ferrari
AU - Andrea Nicolodi
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16285
UR - https://arxiv.org/abs/2610.16285
AB - We propose an anomaly detection method for high-dimensional mixed-type data that maps heterogeneous features to a common scale via standardized moment-based transformations, yielding interpretable feature-level anomaly scores. These scores are combined through a dependence-aware aggregation step to construct the Mixed-data Influence (MDI) score, accounting for correlations across features and providing a unified measure of how strongly an observation departs from the reference data distribution. By incorporating higher-order moments, the MDI can detect anomalies that arise not only from location shifts, but also from changes in variability, skewness, and other distributional characteristics. The aggregation mechanism allows our method to capture both sparse anomalies concentrated in a small number of features and weak, coordinated deviations distributed across many features. We empirically investigate the distribution and thresholding behavior of the MDI score across different sample sizes, dimensions, dependence structures, and data types. Simulation experiments and two real-data applications, to multi-omics and ESG data, evaluate finite-sample calibration, detection performance, and feature-level interpretability.
ER -