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AIC,BIC and the new CIC http://omega.albany.edu:8008/CIC copyMEright by C. Rodriguez. Please copy me! Carlos Rodriguez SUNY Albany. Model: { p(x|q)} Truth: t(x) t q* Geometrization of Inference Embedding in Hilbert Space Fisher Information metric automagically induced on the tangent bundle ! 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: Volumes of Bitnets = dags of bits Maple Module vTool http://omega.albany.edu:8008/bitnets Complete Bitnets 3 p3 3 t3 t2 p p1 2 t1 1 Constant Ricci Scalar 2 x3 x2 x1 3 + ( Ground 0 Where does it ALL come from? 42 (joke) 110 (funny but no joke) 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 NEED http://omega.albany.edu:8008/ ignorance ) Model Selection from Data Naïve approach Given Data: iid Regular model: Most likely M is asymptotically given my minimizing the MDL score. Model Selection Close to the Vacuum Choose among Complete bitnets: For given data sequence: MLE,MDL,AIC,BIC and… Worse < BIC < AIC < CIC < Best % of correct segmentations v/s N. Based on 100 reps for each N. Params at ramdom each time. CIC movie Moving window of 640 bits over sound file.aiff .jpg .aiff .txt .gz The Iliad: BOOK I + CIC + Sing, O goddess, the anger of Achilles son of Peleus, that brought countless ills upon the Achaeans. Many a brave soul did it send hurrying down 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 son of Atreus, king of men, and great Achilles, first fell out with one another………… + 01100…0 . end