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Many existing covariate shift adaptation methods estimate sample weights tobe used in the risk estimation in order to mitigate the gap between the sourceand the target distribution. However, non-parametrically estimating the optimalweights typically involves computationally expensive hyper-parameter tuningthat is crucial to the final performance. In this paper, we propose a newnon-parametric approach to covariate shift adaptation which avoids estimatingweights and has no hyper-parameter to be tuned. Our basic idea is to labelunlabeled target data according to the $k$-nearest neighbors in the sourcedataset. Our analysis indicates that setting $k = 1$ is an optimal choice.Thanks to this property, there is no need to tune any hyper-parameters, unlikeother non-parametric methods. Moreover, our method achieves a running timequasi-linear in the sample size with a theoretical guarantee, for the firsttime in the literature to the best of our knowledge. Our results include sharprates of convergence for estimating the joint probability distribution of thetarget data. In particular, the variance of our estimators has the same rate ofconvergence as for standard parametric estimation despite their non-parametricnature. Our numerical experiments show that proposed method brings drasticreduction in the running time with accuracy comparable to that of thestate-of-the-art methods.

Scalable and hyper-parameter-free non-parametric covariate shift adaptation with conditional sampling