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We introduce a general constructive setting of the density ratio estimation problem as a solution of a (multidimensional) integral equation.
A correspondence between Bayesian estimation on stochastic processes and smoothing by splines
Kimeldorf, G., Wahba, G.: · 1970
Earlier work this paper cites.
Nonparametric methods for estimating probability densities
Vapnik, V.N., Stefanyuk, A.R.: · 1978
Earlier work this paper cites.
Estimation of the likelihood ratio function in the “disorder” problem of random processes
Stefanyuk, A.R.: · 1986
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Statistical Learning Theory
Vapnik, V.N.: · 1998
Earlier work this paper cites.
Improving predictive inference under covariate shift by weighting the log-likelihood function
Shimodaira, H.: · 2000
Earlier work this paper cites.
Estimating divergence functionals and the likelihood ratio by penalized convex risk minimization
Nguyen, X., Wainwright, M., Jordan, M.: · 2008
Cited alongside, same era.
Direct Importance Estimation with Model Selection and Its Application to Covariate Shift Adaptation
Sugiyama, M., Nakajima, S., Kashima, H., von Bünau, P., Kawanabe, M.: · 2008
Cited alongside, same era.
Mutual information approximation via maximum likelihood estimation of density ratio
Suzuki, T., Sugiyama, M., Tanaka, T.: · 2009
Cited alongside, same era.
Change-point detection in time-series data by direct density-ratio estimation
Kawahara, Y., Sugiyama, M.: · 2009
Cited alongside, same era.
In: Covariate Shift by Kernel Mean Matching. MIT Press (2009) 131–160
Gretton, A., Smola, A., Huang, J., Schmittfull, M., Borgwardt, K., Scholkopf, B · 2009
Cited alongside, same era.
A least-squares approach to direct importance estimation
Kanamori, T., Hido, S., Sugiyama, M.: · 2009
Later among the works it cites.
Estimating divergence functionals and the likelihood ratio by convex risk minimization
Nguyen, X., Wainwright, M., Jordan, M.: · 2010
Later among the works it cites.
Density Ratio Estimation in Machine Learning
Sugiyama, M., Suzuki, T., Kanamori, T.: · 2011
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Machine Learning in Non-Stationary Environments: Introduction to Covariate Shift Adaptation
Sugiyama, M., Kawanabe, M.: · 2012
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