Akaike information criterion

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Akaike information criterion (AIC) (dibacana ah-kah-ee-keh), dimekarkeun Professor Hirotsugu Akaike (赤池 弘次) (1927-) dina 1971 sarta diusulkeun dina taun 1974, nyaeta model statistik ukuran fit. Model ieu ngitung goodness-of-fit relatif tina sababaraha model statistik nu aya samemehna numana sampel data geus aya. Model ieu make rarangka gawe analisa informasi nu taliti dumasar kana konsep entropy. Ide satukangeun AIC ieu nyaeta ku ayana karuwetan dina model nu babarengan jeung datangna data sejen kana model tur ngahadilkan ukuran diantara duanana.

Rumusan AIC nyaeta AIC=2k-2\ln(L), numana k nyaeta jumlah parameters, jeung L nyaeta fungsi likelihood.

Ilaharna, eror sebaran normal diasumsikeun sarta diitung make rumus AIC=2k+n\ln(RSS/n), numama n nyaeta lobana observasi jeung RSS nyaeta sesa kuadrat kasalahan.

Model nu loba parameterna bakal nembongkeun fit nu alus kana data, tapi bakal mibanda tingkat kabebasan nu saeutik tur pamakean nu heureut. Kasaimbangan ieu bakal nyababkeun overfitting. Dina kaayaan ieu leuwih hade dipilih model nu ngabogaan nilai AIC pangleutikna. Metode AIC nyoba keur nangtukeun model minimal nu nerangkeun data kalayan bener, nu mungkin beda jeung metoda nu leuwih tradisional dina nyieun model, saperto nu mimiti tina null hypothesis.

Variasi tina AIC kaasup AICc, QAIC, jeung QAICc.

AICc leuwih hade tinimbang AIC lamun ukuran sampel, n, saeutik. Rumus AICc nyaeta:

AICc = AIC + 2k(k + 1) / (n - k - 1), or

AICc = -2ln(L) + 2k(n / (n - k - 1)).

Sabab AICc konvergen jeung AIC keur n nu loba, disarankeun sacara praktis make AICc dina unggal kasus ( Burnham and Anderson, 2004).

QAIC dideukeutkeun keur over-dispersion atawa teu pas dina fit, saperti diartikeun:

QAIC = -[2ln(L)/c] + 2k,

numana c ngarupakeun faktor inflation.


Keur ukuran sample nu leutik QAIC nyaeta:

QAICc = QAIC + 2k(k + 1) / (n - k - 1).

Metoda ieu loba dimekarkeun di widang sejen saperti dina widang teknik sipil, upamana dina widang geoteknik, saperti Akaike Bayesian Information Criterion jeung Extended Bayesian Method.

Rujukan[édit | sunting sumber]

  • Akaike, Hirotugu (December 1974). "A new look at the statistical model identification". IEEE Transactions on Automatic Control 19 (6): 716–723.
  • Burnham, K.P., and D.R. Anderson. 2002. Model Selection and Multimodel Inference: A Practical-Theoretic Approach, 2nd Edition. Springer, New York. ISBN 0-387-95364-7.
  • Burnham, K.P., and D.R. Anderson. 2004. Multimodel Inference: understanding AIC and BIC in Model Selection, Amsterdam Workshop on Model Selection (available online: PDF)
  • Yusuke Honjo and Budhi Setiawan. 2004. On selection of a prior distribution in inverse analysis by Akaike Bayesian Information Criterion.Journal of Applied Mechanic JSCE, vol. 7. no. 1-2004 p.145 - 154 in Japanese

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