Paper Info
Title
Revisiting The Optimal Probability Estimator From Small Samples For Data Mining
Abstract
Estimation of probabilities from empirical data samples has drawn close attention in the scientific community and has been identified as a crucial phase in many machine learning and knowledge discovery research projects and applications. In addition to trivial and straightforward estimation with relative frequency, more elaborated probability estimation methods from small samples were proposed and applied in practice (e.g., Laplace's rule, the m-estimate). Piegat and Landowski (2012) proposed a novel probability estimation method from small samples Ep(h root 2) that is optimal according to the mean absolute error of the estimation result. In this paper we show that, even though the articulation of Piegat's formula seems different, it is in fact a special case of the m-estimate, where p(a) = 1/2 and m = root 2 the context of an experimental framework, we present an in-depth analysis of several probability estimation methods with respect to their mean absolute errors and demonstrate their potential advantages and disadvantages. We extend the analysis from single instance samples to samples with a moderate number of instances. We define small samples for the purpose of estimating probabilities as samples containing either less than four successes or less than four failures and justify the definition by analysing probability estimation errors on various sample sizes.
Year
DOI
Venue
2019
10.2478/amcs-2019-0058
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE
Keywords
DocType
Volume
probability estimation, small samples, minimal error, m-estimate
Journal
29
Issue
ISSN
Citations 
4
1641-876X
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Bojan Cestnik1716262.57