liveBook · Manning

Mean of squared scores

As explained in Outlier Detection in Python

The mean of squared scores is an aggregation technique that averages detector scores after squaring them, giving greater weight to larger scores.

The mean of squared scores aggregates detector scores by averaging their squares. Squaring preserves every score while making larger values contribute disproportionately to the final score. section 14.6.3

Use the method to:

  • Emphasize detectors assigning unusually high scores without discarding lower scores. section 14.6.3
  • Compare alternative power-based aggregations, such as cubing scores to emphasize extremes further or using power 1.5 for a milder effect. section 14.6.3

Detector-score comparison

For five rows scored by four detectors, the mean of squared scores is 14.40, 57.49, 62.49, 2.29, and 12.08. Rows 3 and 2 therefore receive the highest aggregate scores, while a single high detector score can strongly influence the ranking.

How Outlier Detection in Python covers it

How deep it goes
Explains the weighting rationale and compares powers, but stops short of deriving calibration or threshold-selection procedures.
Examples
Uses four detector scores across five rows and compares squared, cubed, and thresholded mean aggregations.
What it assumes
Assumes multiple detector scores for each row and familiarity with thresholding and z-score-scaled scores.
What you can do after
Evaluate alternative detector-score aggregations by observing how power transformations change row rankings.
How it connects
Connects detector ensembles with outlier scores, thresholding, z-score scaling, and power-based aggregation.
Cover of Outlier Detection in Python
liveBookmanning.com
Read Outlier Detection in Python on liveBook Get the book at manning.com

Related concepts

This explainer was generated by Manning's knowledge graph from the text of Outlier Detection in Python. The section links point to the parts of the book it draws on.