The Baker-Akhiezer function and factorization of the Chebotarev-Khrapkov matrix

A new technique is proposed for the solution of the Riemann-Hilbert problem with the Chebotarev-Khrapkov matrix coefficient $G(t)=\alpha_1(t)I+\alpha_2(t)Q(t)$, $\alpha_1(t), \alpha_2(t)\in H(L)$, $Q(t)$ is a $2\times 2$ zero-trace polynomial matrix, and $I$ is the unit matrix. This problem has numerous applications in elasticity and diffraction theory. The main feature of the method is the removal of the essential singularities of the solution to the associated homogeneous scalar Riemann-Hilbert problem on the hyperelliptic surface of an algebraic function by means of the Baker-Akhiezer function. The consequent application of this function for the derivation of the general solution to the vector Riemann-Hilbert problem requires finding of the $\rho$ zeros of the Baker-Akhiezer function ($\rho$ is the genus of the surface). These zeros are recovered through the solution to the associated Jacobi problem of inversion of abelian integrals or, equivalently, the determination of the zeros of the associated degree-$\rho$ polynomial and solution of a certain linear algebraic system of $\rho$ equations.Comment: 17 pages, 1 figur

Applying CHAID for logistic regression diagnostics and classification accuracy improvement

In this study a CHAID-based approach to detecting classification accuracy heterogeneity across segments of observations is proposed. This helps to solve some important problems, facing a model-builder: 1. How to automatically detect segments in which the model significantly underperforms? 2. How to incorporate the knowledge about classification accuracy heterogeneity across segments to partition observations in order to achieve better predictive accuracy? The approach was applied to churn data from the UCI Repository of Machine Learning Databases. By splitting the dataset into 4 parts, which are based on the decision tree, and building a separate logistic regression scoring model for each segment we increased the accuracy by more than 7 percentage points on the test sample. Significant increase in recall and precision was also observed. It was shown that different segments may have absolutely different churn predictors. Therefore such a partitioning gives a better insight into factors influencing customer behavior.CHAID; logistic regression; churn prediction; performance improvement; segmentwise prediction; decision tree; classification tree

Applying a CART-based approach for the diagnostics of mass appraisal models

In this paper an approach for automatic detection of segments where a regression model significantly underperforms and for detecting segments with systematically under- or overestimated prediction is introduced. This segmentational approach is applicable to various expert systems including, but not limited to, those used for the mass appraisal. The proposed approach may be useful for various regression analysis applications, especially those with strong heteroscedasticity. It helps to reveal segments for which separate models or appraiser assistance are desirable. The segmentational approach has been applied to a mass appraisal model based on the Random Forest algorithm.CART, model diagnostics, mass appraisal, real estate, Random forest, heteroscedasticity

Mass appraisal of residential apartments: An application of Random forest for valuation and a CART-based approach for model diagnostics

To the best knowledge of authors, the use of Random forest as a potential technique for residential estate mass appraisal has been attempted for the first time. In the empirical study using data on residential apartments the method performed better than such techniques as CHAID, CART, KNN, multiple regression analysis, Artificial Neural Networks (MLP and RBF) and Boosted Trees. An approach for automatic detection of segments where a model significantly underperforms and for detecting segments with systematically under- or overestimated prediction is introduced. This segmentational approach is applicable to various expert systems including, but not limited to, those used for the mass appraisal.Random forest, mass appraisal, CART, model diagnostics, real estate, automatic valuation model