NAÏVE CREDAL CLASSIFIER 2 : AN EXTENSION OF NAÏVE BAYES FOR DELIVERING ROBUST CLASSIFICATIONS 2012.05.23. 이아람.

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Presentation transcript:

NAÏVE CREDAL CLASSIFIER 2 : AN EXTENSION OF NAÏVE BAYES FOR DELIVERING ROBUST CLASSIFICATIONS 이아람

Set up MP : Missing process MAR : missing at Random Learnining set = Training set 1, …, N The units to classify = Test set M := N+1 Latent : complete yet not observable variables Manifest : incomplete variables

Set up C i : set of latent classes A ij : set of latent attributes - Affected by an unknown MP A il : set of latent attributes - Affected by a MAR MP Vector C := (C 1,…, C N ) Matrix X i : = (X 1,…,X N ) Matrix D i : = (C i, X i ) O : Manifest variables

Set up Class C i dominates C j if P(C i ) > P(C j ) in any distribution of posterior credal set. If no class dominates C i, then C i is non-dominated. (1) is the general form of the test of dominance for any classifier based on conservative inference rule(CIR).

Summary of NCC2 procedures - Learning

Summary of NCC2 procedures

Introducing NCC2 The probability for class C M Likelihood function

Imprecise prior ( prior credal set ) Conjugate to the likelihood. We want the prior to be imprecise, to be set of prior.

Probability of the Next Class

Dominance tests with an imprecise prior

Incomplete, non-MAR, learning set

Summary of NCC2 procedures

Experiments on 18 UCI data sets

Conclusions NCC2 extends Naïve Bayes to imprecise probabilities, to robustly deal with small data sets and missing data. NCC2 becomes indeterminate on instances whose classification is doubtful indeed. Indeterminate classifications preserve the classifier’ reliability while conveying sensible information.