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

2. 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

3. 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

4. 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).

5. Summary of NCC2 procedures - Learning

6. Summary of NCC2 procedures

7. Introducing NCC2 The probability for class C M Likelihood function

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

9. Probability of the Next Class

10. Dominance tests with an imprecise prior

11. Incomplete, non-MAR, learning set

12. Summary of NCC2 procedures

13. Experiments on 18 UCI data sets

14. 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.