Using the Model of Continuous Dynamical System with Viscous Resistance Forces for Improving Distribution Prediction Based on Evolution of Quantiles

Abstract

The paper considers the problem of prediction of a probability distribution. We take into account an extrapolation model based on evolution of quantiles. We may use any concrete model which allows to track and extrapolate boundaries of buckets of an equi-height histogram. This histogram with p + 1 boundaries is equivalent to p-quantiles. Using such baseline extrapolation model we may obtain lines of locations of bucket boundaries that may intersect in future. To avoid intersections and to extend (in time) correctness of the results, we propose to use a model of continuous dynamical system with viscous resistance forces for obtaining improved lines of locations. The proposed model allows to obtain lines with unchanged shapes or very similar ones (comparing to the results from the baseline extrapolation model) but without any intersections. This approach will be helpful when a previously used baseline extrapolation model is too much time limited. The work was inspired by the problem of prediction of an attribute value distribution used for query selectivity estimation. However, the proposed method may be applied not only in query optimization problem.