# Anomaly Detection in the Presence of Missing Values

arXiv: https://arxiv.org/abs/1809.01605 · HTML: https://mlsanity.com/paper/1809.01605/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2018.

## Built on by (most cited first, 6 of 6)

- [Greedy structure learning from data that contain systematic missing values](https://mlsanity.com/paper/2107.04184/) (2021)
- [Anomaly Attribution with Likelihood Compensation](https://mlsanity.com/paper/2208.10679/) (2022)
- [Marginalizable Density Models](https://mlsanity.com/paper/2106.04741/) (2021)
- [Reconstruction of Sentinel-2 Time Series Using Robust Gaussian Mixture Models -- Application to the Detection of Anomalous Crop Development in wheat and rapeseed crops](https://mlsanity.com/paper/2110.11780/) (2021)
- [A Study imbalance handling by various data sampling methods in binary classification](https://mlsanity.com/paper/2105.10959/) (2021)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)

## Abstract (arXiv)

Standard methods for anomaly detection assume that all features are observed at both learning time and prediction time. Such methods cannot process data containing missing values. This paper studies five strategies for handling missing values in test queries: (a) mean imputation, (b) MAP imputation, (c) reduction (reduced-dimension anomaly detectors via feature bagging), (d) marginalization (for density estimators only), and (e) proportional distribution (for tree-based methods only). Our analysis suggests that MAP imputation and proportional distribution should give better results than mean imputation, reduction, and marginalization. These hypotheses are largely confirmed by experimental studies on synthetic data and on anomaly detection benchmark data sets using the Isolation Forest (IF), LODA, and EGMM anomaly detection algorithms. However, marginalization worked surprisingly well for EGMM, and there are exceptions where reduction works well on some benchmark problems. We recommend proportional distribution for IF, MAP imputation for LODA, and marginalization for EGMM.