naive Bayes instrument
| Definition | A classifier that multiplies one-dimensional likelihoods and adds their logs, so that each feature's contribution is the same whatever the others are and it cannot read an interaction. Chapter 6. |
|---|---|
| Example | Two features with likelihood ratios 3 and 2 give a combined ratio of 6, whatever the other features are. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id naive-bayes, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/NaiveBayes.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A classifier that multiplies one-dimensional likelihoods and adds their logs. The log of the product is the sum of the logs, the log odds add across features, and one feature’s contribution is the same whatever the others are, so the score has no interaction terms and its Hessian is diagonal.
- What naive Bayes cannot read is the interaction, which is a limit of the model class rather than a direction in its kernel, and its read operator is still not diagonal in general because two sensitivities can rise and fall together across rows.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 6 section 6.1 of Data Mining as Observation, after TSK chapter 4.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/NaiveBayes.lean,
theorems log_likelihood_sum, log_odds_sum,
contribution_independent, at observation-data-mining
f3914f0; what the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation chapters 6.
Related
classifier; Hessian; confidence; logistic regression.
See also
Book equations stated beside the entry’s terms, not defining it: 6.1, 0.9.
Sources-table rows that share a record with the entry without naming it: chapter 2 section 2.3, chapter 6 section 6.1.
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.