Use of Kullback–Leibler divergence for forgetting

0315684 - ÚTIA 2009 RIV GB eng J - Journal Article
Kárný, Miroslav - Andrýsek, Josef
Use of Kullback–Leibler divergence for forgetting.
[Použití Kullback–Leibler divergence pro zapomínání.]
International Journal of Adaptive Control and Signal Processing. Roč. 23, č. 1 (2009), s. 1-15. ISSN 0890-6327. E-ISSN 1099-1115
R&D Projects: GA MŠMT 2C06001; GA MŠMT 1M0572; GA ČR GA102/08/0567
Institutional research plan: CEZ:AV0Z10750506
Keywords : Bayesian estimation * Kullback–Leibler divergence * functional approximation of estimation * parameter tracking by stabilized forgetting * ARX model
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 1.347, year: 2009
http://library.utia.cas.cz/separaty/2008/AS/karny-use%20of%20kullback-leibler%20divergence%20for%20forgetting.pdf

Non-symmetric Kullback–Leibler divergence (KLD) measures proximity of probability density functions (pdfs). Bernardo (Ann. Stat. 1979; 7(3):686–690) had shown its unique role in approximation of pdfs. The order of the KLD arguments is also implied by his methodological result. Functional approximation of estimation and stabilized forgetting, serving for tracking of slowly varying parameters, use the reversed order. This choice has the pragmatic motivation: recursive estimator often approximates the parametric model by a member of exponential family (EF) as it maps prior pdfs from the set of conjugate pdfs (CEF) back to the CEF. Approximations based on the KLD with the reversed order of arguments preserves this property. In the paper, the approximation performed within the CEF but with the proper order of arguments of the KLD is advocated. It is applied to the parameter tracking and performance improvements are demonstrated.

Nesymetrická Kullback-Leiblerova divergence (KLD) měří blízkost pravděpodobnostních hustot. Dá se ukázat, že jedna z jejich verzí je teoreticky lepší. Článek popisuje využití této skutečnosti ke zlepšení techniky zapomínání.
Permanent Link: http://hdl.handle.net/11104/0165815