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In counterfactual learning to rank (CLTR) user interactions are used as a source of supervision. Since user interactions come with bias, an important focus of research in this field lies in developing methods to correct for the bias of interactions. Inverse propensity scoring (IPS) is a popular method suitable for correcting position bias. Affine correction (AC) is a generalization of IPS that corrects for position bias and trust bias. IPS and AC provably remove bias, conditioned on an accurate estimation of the bias parameters. Estimating the bias parameters, in turn, requires an accurate estimation of the relevance probabilities. This cyclic dependency introduces practical limitations in terms of sensitivity, convergence and efficiency. We propose a new correction method for position and trust bias in CLTR in which, unlike the existing methods, the correction does not rely on relevance estimation. Our proposed method, mixture-based correction (MBC), is based on the assumption that the distribution of the CTRs over the items being ranked is a mixture of two distributions: the distribution of CTRs for relevant items and the distribution of CTRs for non-relevant items. We prove that our method is unbiased. The validity of our proof is not conditioned on accurate bias parameter estimation. Our experiments show that MBC, when used in different bias settings and accompanied by different LTR algorithms, outperforms AC, the state-of-the-art method for correcting position and trust bias, in some settings, while performing on par in other settings. Furthermore, MBC is orders of magnitude more efficient than AC in terms of the training time., Comment: CIKM 2021

In the course of this work, experiments were carried out to simulate the deflection of the composite tape between two supports under the action of gravity without load and under load. The position was approximated during deformation of a given object accounting its individual properties. As an example of this problem, we proposed an approach that allows us to take into account the individual features of a real object without complicating the differential structure of the model using real measurements. The differential model itself describes a narrow class of objects that are similar in some properties and can give a poor forecasting result for specific real objects. Accounting measurements allows extremely well consider the individual characteristics of the simulated object without complicating the differential structure. In the proposed neural network approach, the loss function is composed so that to take into account the differential structure, boundary conditions, and measurement data. The loss function is represented as a sum, each term of which is a weighted functional. One functional is responsible for satisfying the differential structure of the model, another for boundary conditions, and a third for the quality of the description of real measurements. The role of the weights is to align of all terms in a series. The application of global minimum search methods for such a loss function allows one to obtain reliable results even in the case of using an unsuitable differential model.