C.2.8:4.6 - Relation to epiplexity and MDL

A formal structural-information estimate is useful when a mathematical model can represent the selected account, observer and extraction question. Use C.29 for that correspondence and its preserved and lost structure.

Finzi et al.’s computational epiplexity selects a time-bounded probabilistic program by a two-part coding criterion:

P* = argmin over P in P_T of ( |P| + E[-log2 P(X)] )
S_T(X) = |P*|
H_T(X) = E[-log2 P*(X)]

Ties select the shorter program. The model term describes structural information; the residual is time-bounded entropy. Conditional versions allow side information, and practical estimators have their own assumptions. The execution bound and the effort of finding or estimating a model are distinct costs. Finzi et al., v2, §3–4

For an ESI estimate, explain how the episteme and expression map to X, how the model class represents the observer’s available operations, and which selected structure the model term estimates. State how prior knowledge is represented. Conditional model description given side information need not count all familiar structure a reader can recover.

Use epiplexity as a formal specialization where that correspondence holds. Otherwise it motivates the structural-information question without supplying its value. Total code length, text length and arbitrary model size are not interchangeable ESI measures. Ordinary description comparisons may use an adequate domain method without a coding model.