Optimal estimator of hypothesis probability for data mining problems with small samples

• Published in: International journal of applied mathematics and computer science 2012-09, Vol.22 (3), p.629-645
• Main Authors: Piegat, Andrzej, Landowski, Marek
• Format: Article
• Language: English
• Subjects: completeness interpretation of probability; frequency interpretation of probability; probability; probability estimation; single-case problem; uncertainty theory
• ISSN: 2083-8492; 1641-876X; 2083-8492
• DOI: 10.2478/v10006-012-0048-z

The paper presents a new (to the best of the authors’ knowledge) estimator of probability called the “Eph √ 2 completeness estimator” along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute errors).The estimator was compared with the universally used frequency estimator of probability and with Cestnik’s m-estimator with respect to accuracy. The comparison was realized both theoretically and experimentally. The results show the superiority of the Eph √ 2 completeness estimator over the frequency estimator for the probability interval p ∈ (0.1, 0.9). The frequency estimator is better for p ∈ [0, 0.1] and p ∈ [0.9, 1].