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Information Geometry of Self-organizing maximum likelihood

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Presentation Transcript

Bernoulli 2000 Conference at Riken on 27 October, 2000

Information Geometry of

Self-organizing maximum likelihood

Shinto Eguchi ISM, GUAS

This talk is based on joint research with

Dr Yutaka Kano, Osaka Univ

Consider a statistical model:

Maximum Likelihood Estimation (MLE)

( Fisher, 1922),

Consistency, efficiency sufficiency, unbiasedness invariance, information

Take an increasing function .

-MLE

Differential geometry of

Riemann metric

Affine connection

Conjugate

affine connection

Ciszsar’s divergence

-divergence

Amari’s -divergence

Another definition of Y-likelihood

Take a positive function k(x, q) and define

Y-likelihood equation is a weighted score with integrabity.

Fisher consistency

e -contamination model of

Influence function

Asymptotic efficiency

Robustness or Efficiency

Bernoulli regression

Logistic regression

Input

Output

Maximum likelihood

-maximum likelihood

Classic procedure

Self-organizing procedure

Concluding remark

Bias potential function

Y-sufficiency

Y-factoriziable

Y-exponential family

Y-EM algorithm

Y-Regression analysis

Y-Discriminant analysis

Y-PCA

Y-ICA

?

!

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