The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R d . Namely, the mixed-pair model (X, Y ) is considered where X and Y take values in R d and an arbitrary finite set, respectively. Such models include, for instance, the famous logistic regression. In contrast to the well-known Kozachenko -Leonenko estimates of unconditional entropy the proposed estimates are constructed by means of the certain spacial order statistics (or k-nearest neighbor statistics where k = k n depends on amount of observations n) and a random number of i.i.d. observations contained in the balls of specified random radii. The asymptotic unbiasedness and L 2 -consistency of the new estimates are established under simple conditions. The obtained results can be applied to the feature selection problem which is important, e.g., for medical and biological investigations.

One of the problems on the way to successful implementation of neural networks is the quality of annotation. For instance, different annotators can annotate images in a different way and very often their decisions do not match exactly and in extreme cases are even mutually exclusive which results in noisy annotations and, consequently, inaccurate predictions.To avoid that problem in the task of computed tomography (CT) imaging segmentation we propose a clearing algorithm for annotations 1 . It consists of 3 stages:• annotators scoring, which assigns a higher confidence level to better annotators;• nodules scoring, which assigns a higher confidence level to nodules confirmed by good annotators;• nodules merging, which aggregates annotations according to nodules confidence.In general, the algorithm can be applied to many different tasks (namely, binary and multi-class semantic segmentation, and also with trivial adjustments to classification and regression) where there are several annotators labeling each image. *

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