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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.

Note

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

Parameters

#	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.

Example

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

References

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