Revisiting the optimal probability estimator from small samples for data mining

Cestnik, Bojan

doi:10.2478/amcs-2019-0058

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Tytuł artykułu

Revisiting the optimal probability estimator from small samples for data mining

Autorzy

Cestnik Bojan

Treść / Zawartość

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13_cestnik_revisiting_the_optimal_probability_estimator_2019_4.pdf

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DOI

10.2478/amcs-2019-0058

Warianty tytułu

Języki publikacji

Abstrakty

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√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 = √2. In 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.

Słowa kluczowe

probability estimation small sample minimal error m-estimate

estymacja prawdopodobieństwa mała próbka błąd minimalny

Wydawca

Oficyna Wydawnicza Uniwersytetu Zielonogórskiego

Czasopismo

International Journal of Applied Mathematics and Computer Science

Rocznik

2019

Tom

Vol. 29, no. 4

Strony

783--796

Opis fizyczny

Bibliogr. 36 poz., rys., tab., wykr.

Twórcy

autor

Cestnik Bojan

bojan.cestnik@temida.si

Department of Knowledge Technologies, Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia; Temida d.o.o., Dunajska cesta 51, 1000 Ljubljana, Slovenia

Bibliografia

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[29] Piegat, A. and Landowski, M. (2012). Optimal estimator of hypothesis probability for data mining problems with small samples, International Journal of Applied Mathematics and Computer Science 22(3): 629–645, DOI: 10.2478/v10006-012-0048-z.
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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

Typ dokumentu

Bibliografia

Identyfikator YADDA

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