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

• Published in: International journal of applied mathematics and computer science Vol. 22; no. 3; pp. 629 - 645
• Main Authors: Piegat Andrzej, Landowski Marek
• Format: Journal Article
• Language: English
• Published: Sciendo 01-09-2012
• Subjects: completeness interpretation of probability; frequency interpretation of probability; probability; probability estimation; single-case problem; uncertainty theory
• ISSN: 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 ph ∈ (0.1, 0.9). The frequency estimator is better for ph ∈ [0, 0.1] and ph ∈ [0.9, 1].