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Robust Z-Score#

A statistical anomaly detector that uses modified Z-Scores that are robust to preexisting outliers in the training set. The modified Z-Score is defined as the feature value minus the median over the median absolute deviation (MAD). Anomalies are flagged if their final weighted Z-Score exceeds a user-defined threshold.


A beta value of 1 means the estimator only considers the maximum absolute Z-Score, whereas a setting of 0 indicates that only the average Z-Score factors into the final score.

Interfaces: Estimator, Learner, Scoring, Persistable

Data Type Compatibility: Continuous


# Name Default Type Description
1 threshold 3.5 float The minimum Z-Score to be flagged as an anomaly.
2 beta 0.5 float The weight of the maximum Z-Score in the overall anomaly score.
3 smoothing 1e-9 float The amount of epsilon smoothing added to the MAD of each feature.


use Rubix\ML\AnomalyDetectors\RobustZScore;

$estimator = new RobustZScore(3.5, 0.25, 1e-6);

Additional Methods#

Return the median of each feature column in the training set:

public medians() : float[]|null

Return the median absolute deviation (MAD) of each feature column in the training set:

public mads() : float[]|null


  1. B. Iglewicz et al. (1993). How to Detect and Handle Outliers.