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!

t

Truth: t(x)

Model: { p(x|)}

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

How2use.mw

http://omega.albany.edu:8008/bitnets

CompleteBitnets

1

2

t

t

t1

2

3

x

x

x

1

2

3

pp

p

1

2

3

3 3

3+

Constant Ricci Scalar

(

Ground 0Ground 0Where 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/ignoranceignorance

)

Model Selection from DataNaïve 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

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

.aiff .jpg.txt

.gz

CIC

.end