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

Andrzej Piegat; Marek Landowski

International Journal of Applied Mathematics and Computer Science (2012)

  • Volume: 22, Issue: 3, page 629-645
  • ISSN: 1641-876X

Abstract

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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].

How to cite

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Andrzej Piegat, and Marek Landowski. "Optimal estimator of hypothesis probability for data mining problems with small samples." International Journal of Applied Mathematics and Computer Science 22.3 (2012): 629-645. <http://eudml.org/doc/244052>.

@article{AndrzejPiegat2012,
abstract = {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].},
author = {Andrzej Piegat, Marek Landowski},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {single-case problem; probability; probability estimation; frequency interpretation of probability; completeness interpretation of probability; uncertainty theory},
language = {eng},
number = {3},
pages = {629-645},
title = {Optimal estimator of hypothesis probability for data mining problems with small samples},
url = {http://eudml.org/doc/244052},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Andrzej Piegat
AU - Marek Landowski
TI - Optimal estimator of hypothesis probability for data mining problems with small samples
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 3
SP - 629
EP - 645
AB - 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].
LA - eng
KW - single-case problem; probability; probability estimation; frequency interpretation of probability; completeness interpretation of probability; uncertainty theory
UR - http://eudml.org/doc/244052
ER -

References

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