ИСТИНА

Feature selection problems are intensively studied on the borderline of mathematical statistics and machine learning, see, e.g., [1] and [2]. The main problem in this research domain can be described as follows. There is a response variable which depends on a collection of factors. One has to identify a subcollection of relevant (in a sense) factors. Such problem is of great importance for applications, e.g., in medicine and biology. We concentrate on conditional central limit theorem arising in the framework of nonlinear regression analysis. The goal is to compare the response variable predictions involving different subcollections of factors. Some extensions of recent results [3] are obtained. We also discuss certain problems concerning the MDR-EFE method developed in [4]. REFERENCES [1] V.Bol\'on-Canedo, N.S\'anchez-Maro$\tilde{{\rm n}}$o and A.Alonso-Betanzos. Feature Selection for High Dimensional Data. Springer, Cham, 2015. [2] G.James, D.Witten, T.Hastie and R.Tibshirani. In Introduction to Statistical Learning with Applications in R. Springer, New York, 2013. [3] L.Gy\"{o}rfi and H.Walk. On the asymptotic normality of an estimate of a regression functional. J. of Machine Learning Research, 2015, v.16, 1863-1877. [4] A.Bulinski and A.Rakitko. MDR method for nonbinary response variable. J. of Multivariate Analysis. 2015, v. 135, 22-45.