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Constrained LeastSquares DensityDifference Estimation
Tuan Duong NGUYEN Marthinus Christoffel DU PLESSIS Takafumi KANAMORI Masashi SUGIYAMA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E97D
No.7
pp.18221829 Publication Date: 2014/07/01 Online ISSN: 17451361
DOI: 10.1587/transinf.E97.D.1822 Type of Manuscript: PAPER Category: Artificial Intelligence, Data Mining Keyword: density difference, asymptotic variance, L^{2}distance, bias, classbalance change, twosample homogeneity test,
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Summary:
We address the problem of estimating the difference between two probability densities. A naive approach is a twostep procedure that first estimates two densities separately and then computes their difference. However, such a twostep procedure does not necessarily work well because the first step is performed without regard to the second step and thus a small error in the first stage can cause a big error in the second stage. Recently, a singleshot method called the leastsquares densitydifference (LSDD) estimator has been proposed. LSDD directly estimates the density difference without separately estimating two densities, and it was demonstrated to outperform the twostep approach. In this paper, we propose a variation of LSDD called the constrained leastsquares densitydifference (CLSDD) estimator, and theoretically prove that CLSDD improves the accuracy of density difference estimation for correctly specified parametric models. The usefulness of the proposed method is also demonstrated experimentally.


