# 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

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topAndrzej 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 -

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