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StandardAbsoluteDeviation

Standard Absolute Deviation (SAD).

SAD is the model that calculates the anomaly score by using the deviation from the mean/median, divided by the standard deviation of all the points seen within the data stream. The idea of this model is based on the \(3 \times \sigma\) rule described in 1.

This implementation is adapted from the implementation within PySAD (Python Streaming Anomaly Detection) 2.

As a univariate anomaly detection algorithm, this implementation is adapted to River in a similar way as that of the GaussianScorer algorithm, with the variable taken into the account at the learning phase and scoring phase under variable y, ignoring x.

Parameters

  • sub_stat

    Typestats.base.Univariate

    DefaultNone

    The statistic to be subtracted, then divided by the standard deviation for scoring. Defaults to stats.Mean()`.

Examples

import random
from river import anomaly
from river import stats
from river import stream

rng = random.Random(42)

model = anomaly.StandardAbsoluteDeviation(sub_stat=stats.Mean())

for _ in range(150):
    y = rng.gauss(0, 1)
    model = model.learn_one(None, y)

model.score_one(None, 2)
2.057...

model.score_one(None, 0)
0.084...

model.score_one(None, 1)
0.986...

Methods

learn_one

Update the model.

Parameters

  • x'dict'
  • y'base.typing.Target'

Returns

SupervisedAnomalyDetector: self

score_one

Return an outlier score.

A high score is indicative of an anomaly. A low score corresponds a normal observation.

Parameters

  • x'dict'
  • y'base.typing.Target'

Returns

float: An anomaly score. A high score is indicative of an anomaly. A low score corresponds a


  1. Hochenbaum, J., Vallis, O.S., Kejariwal, A., 2017. Automatic Anomaly Detection in the Cloud Via Statistical Learning. https://doi.org/10.48550/ARXIV.1704.07706. 

  2. Yilmaz, S.F., Kozat, S.S., 2020. PySAD: A Streaming Anomaly Detection Framework in Python. https://doi.org/10.48550/ARXIV.2009.02572.