outlier concept
| Definition | A row the reader cannot place. The statistical detector calls a row an outlier when its distance from the mean in units of spread passes a threshold, and no more than one over the threshold squared of the weight can. Chapter 10. Also z-score. |
|---|---|
| Example | A row 3.6 spreads from the mean is an outlier at threshold 3, and by Chebyshev at most one ninth of the weight lies past 3 spreads. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id outlier, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Outlier.lean, lean/DataMiningAsObservation/Mahalanobis.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A row the reader cannot place. The statistical detector scores a row by its distance from the mean in units of spread, which is zero at the mean, unchanged when data, mean, and spread are rescaled and shifted together, and past a threshold t exactly when the row lies more than t spreads from the mean. By Chebyshev the weight of rows beyond t is at most the mean squared score over t squared.
- The four detector families read different coordinates, distance from the mean, distance to neighbours, density relative to neighbours, and cluster membership, and the observer’s outliers, the anti-hubs, are the rows no detector of the data alone can see.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 0 section 0.16 and chapter 10 section 10.1 of Data Mining
as Observation, after TSK chapter 9, with the hierarchical typing
in turboquant-pro/turboquant_pro/anatomy.py:98-170.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Outlier.lean,
theorems zscore_mean, zscore_affine,
outlier_iff, zscore_reflect,
chebyshev, at observation-data-mining f3914f0; what the
check covers is stated in the book’s appendix
C.
lean/DataMiningAsObservation/Mahalanobis.lean,
theorems dM2_nonneg, dM2_mean,
dM2_scale, dM2_eq_whitened,
dM2_antitone_in_variance, at observation-data-mining
f3914f0; what the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation primer S, chapters 0, 2, 3, 10.
Related
Mahalanobis distance; anti-hub; abstention; whitening; density.
See also
Book equations stated beside the entry’s terms, not defining it: 0.33, 10.3, 0.6.
Ledger rows that cite the entry’s records without naming it: NEG-14.
Sources-table rows that share a record with the entry without naming it: chapter 10 section 10.1, chapter 10 section 10.3.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.