AIC,BIC and the new CIC Carlos Rodriguez SUNY Albany. copyMEright by C. Rodriguez. Please copy me!
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Transcript of AIC,BIC and the new CIC Carlos Rodriguez SUNY Albany. copyMEright by C. Rodriguez. Please copy me!
AIC,BIC and the new CIC
http://omega.albany.edu:8008/CIC
Carlos Rodriguez SUNY Albany.
copyMEright by C. Rodriguez. Please copy me!
The Volume Form as Prior
A hypothesis space M is said to be regular when (M,g) is a smooth orientable riemannian manifold. A k-dim regular M has volume form:
In arbitrary (orientation preserving) theta coordinates the volume of (M,g) is:
MDL bold pragmatism
Forget about the data being generated by a probability distribution. This is just a
CODING GAME!! Best model is the one
providing the shortest code for the observed data. Data is all there is!
Есть Проблема
The shortest description length of a sequence is NON-COMPUTABLE!!
And can only be approximated with
MODELS.
Data and Theory are Entangled
There is no data in the vacuum.Data is a logical proposition with truth values only
relative to a given domain of discourse.A sequence 0110011110… is NOT DATA as the
number 2.4 is not data unless is understood as “the result of such and such experiment is 2.4”.
Data is theory laden.
Theory is data laden.
IMHO
Model Selection from DataNaïve approach
Given Data: iid
Regular model:
Most likely M is asymptotically given my minimizing the MDL score.
Worse < BIC < AIC < CIC < Best
% of correct segmentations v/s N. Based on 100 reps for each N. Params at ramdom each time.
The Iliad: BOOK I
Sing, O goddess, the anger of Achilles son of Peleus, that broughtcountless ills upon the Achaeans. Many a brave soul did it send hurryingdown to Hades, and many a hero did it yield a prey to dogs and vultures,for so were the counsels of Jove fulfilled from the day on which the sonof Atreus, king of men, and great Achilles, first fell out with oneanother…………
++
+ 01100…0
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CIC