On the Properties of Bias-Variance Decomposition for kNN Regression

When choosing the optimal complexity of the method for constructing decision functions, an important tool is the decomposition of the quality criterion into bias and variance. 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 $k$

On the Maximization of Quadratic Weighted Kappa

An analytical expression for the optimal estimation of the numerical dependence by the criterion of a quadratic weighted kappa and also the expression for the optimal value of this criterion were obtained. It is shown that the optimal decision function is obtained from the regression function by a linear transformation. The coefficients of this transformation can be found from the condition of equality of mathematical expectations and variances of the predicted value and its estimate. The quadratic weighted kappa coefficient was originally proposed as an alternative to the correlation coefficient to reflect the strength of dependence between two characteristics, but recently it has been widely used as a criterion for the quality of the forecast in the problem of recovery of dependencies (regression analysis). At the same time, the properties of this coefficient in this context are still poorly understood. The properties of the quadratic weighted kappa criterion revealed in the work allow us to conclude that the expediency of using it as a criterion for the quality of the decision function in most cases raises doubts. This criterion provides a solution that is actually based on the regression function, but the variance of the forecast is artificially made equal to the variance of the original value. This distorts the forecast without improving the statistical properties of the decision function

On Evaluation of Statistical Regularities in Seismic Data

A method for short-term prediction of earthquakes based on Markov time scale is investigated. The results show that the noise added to a signal when sensors are placed on the ground dramatically weakens the predictability. Additionally, a method for testing the statistical dependency between earthquakes on neighbouring regions is proposed. This method uses a certain model of earthquake influence propagation