Varying Parameter in Classification Based on Imprecise Probabilities

Summary. We shall present a first explorative study of the variation of the parameter s of the imprecise Dirichlet model when it is used to build classification trees. In the method to build classification trees we use uncertainty measures on closed and convex sets of probability distributions, otherwise known as credal sets. We will use the imprecise Dirichlet model to obtain a credal set from a sample, where the set of probabilities obtained depends on s. According to the characteristics of the dataset used, we will see that the results can be improved varying the values of s.

[1]  Marco Zaffalon A Credal Approach to Naive Classification , 1999, ISIPTA.

[2]  A. Ramer Uniqueness of information measure in the theory of evidence , 1987 .

[3]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[4]  Serafín Moral,et al.  A non-specificity measure for convex sets of probability distributions , 2000 .

[5]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

[6]  George J. Klir,et al.  On Measuring Uncertainty and Uncertainty-Based Information: Recent Developments , 2001, Annals of Mathematics and Artificial Intelligence.

[7]  George J. Klir,et al.  Uncertainty-Based Information , 1999 .

[8]  Serafín Moral,et al.  Maximum of Entropy for Credal Sets , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[9]  Serafín Moral,et al.  Building classification trees using the total uncertainty criterion , 2003, Int. J. Intell. Syst..

[10]  Jean-Marc Bernard,et al.  An introduction to the imprecise Dirichlet model for multinomial data , 2005, Int. J. Approx. Reason..

[11]  Serafín Moral,et al.  Difference of entropies as a non-specificity function on credal sets† , 2005, Int. J. Gen. Syst..

[12]  S. Moral,et al.  COMPLETING A TOTAL UNCERTAINTY MEASURE IN THE DEMPSTER-SHAFER THEORY , 1999 .

[13]  Alberto Maria Segre,et al.  Programs for Machine Learning , 1994 .

[14]  P. Walley Statistical Reasoning with Imprecise Probabilities , 1990 .

[15]  Leo Breiman,et al.  Classification and Regression Trees , 1984 .

[16]  P. Walley Inferences from Multinomial Data: Learning About a Bag of Marbles , 1996 .

[17]  G. Klir Uncertainty and Information: Foundations of Generalized Information Theory , 2005 .

[18]  George J. Klir,et al.  Disaggregated total uncertainty measure for credal sets , 2006, Int. J. Gen. Syst..

[19]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[20]  Serafín Moral,et al.  Upper entropy of credal sets. Applications to credal classification , 2005, Int. J. Approx. Reason..

[21]  Joaquín Abellán,et al.  Uncertainty measures on probability intervals from the imprecise Dirichlet model , 2006, Int. J. Gen. Syst..

[22]  Serafín Moral,et al.  An Algorithm to Compute the Upper Entropy for Order-2 Capacities , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..