The Observation Theory EncyclopediaFrom TSKAboutBy kindBy chapterBy Lean fileLedgerProvenance

entropy concept

DefinitionThe expected surprise of a distribution, the bits needed per outcome under the best code, at most the log base two of the number of outcomes. Primer S, equation S.19.
ExampleA fair die has entropy log2 of 6, about 2.585 bits, and (0.5, 0.25, 0.25) has 1.5 bits.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id entropy, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equation

Book equation S.19.

Assumptions and scopenone
Prior artnone recorded
Evidencenone
Reviewedsemantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page.

Equation

Book equation S.19.

\[H(p)=-\sum_i p_i\log_2 p_i.\]

Conditions

none

Ledger

none

First stated

Primer S section S.10 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix C covers it at length.

Measurements

none

Failures and corrections

none

Invariance envelope

none declared

Machine checked

none

Used in

Data Mining as Observation primer S.

Related

surprise; cross-entropy; KL divergence; perplexity; bit.

See also

none

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.

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