¹Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation

It is generally assumed (and in practice this is most often true) that with increasing complexity of the method, the bias component monotonically decreases, and the variance component increases. The conducted research shows that in some cases this behavior is violated.

In this paper, we obtain an expression for the variance component for the kNN method for the linear regression problem in the formulation when the “explanatory” features are random variables. In contrast to the well-known result obtained for non-random “explanatory” variables, in the considered case, the variance may increase with the growth of 𝑘.

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