A PARALLEL TO THE LEAST SQUARES FOR POSITIVE INVERSE PROBLEMS

Autor:	Kiyoshi Yoneda
Rok vydání:	2006
Předmět:	Combinatorics Quadratic growth Matrix (mathematics) General Decision Sciences Probability density function Function (mathematics) Management Science and Operations Research Inverse problem Convex function Stability (probability) Least squares Mathematics
Zdroj:	Journal of the Operations Research Society of Japan. 49:279-289
ISSN:	2188-8299 0453-4514
DOI:	10.15807/jorsj.49.279
Popis:	A new method is proposed to solve systems of linear approximate equations Xθ ≈ y where the unknowns θ and the data y are positive and the matrix X consists of nonnegative elements. Writing the i-th near-equality Xi ·θ/yi ≈ 1 the assumed model is Xi ·θ/yi = ζi with mutually independent positive errors ζi . The loss function is defined bywi(ζi − 1)log ζi in which wi is the importance weight for the i-th near-equality. A reparameterization reduces the method to unconstrained minimization of a smooth strictly convex function implying the unique existence of positive solution and the applicability of Newton's method that converges quadratically. The solution stability is controlled by weighting prior guesses of the unknowns θ. The method matches the maximum likelihood estimation if all weights wi are equal and ζi independently follow the probability density function ∝ t ω(1−t) ,0
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e1ca56c4a3604594f8aaeb089f00ffbf https://doi.org/10.15807/jorsj.49.279 Zobrazit plný text záznamu