Using the Ellipsoid Method to Study Relationships in Medical Data

Abstract

Deterioration of moral and psychological state on the background of a full–scale war is observed in many social groups. Timely detection of various types of pre–depressive states and appropriate therapy is a critically important task nowadays. In addition, an equally important task is to identify relationships between physical and psychological indicators of health. Establishing such regularities will allow detecting anxious states, avoiding direct profile testing of a patient. The article is devoted to construction of a mathematical apparatus for predicting psychological conclusions based on cardiological data. For this, a linear regression model and the ellipsoid method are used to determine its parameters with a criterion based on least moduli method (LMM), a feature selection procedure and a metric for assessing consistency of a data set. Material of the article is presented in 5 sections. Section 1 describes the ellipsoid method for finding parameters of linear regression with the least moduli method as a criterion in the power of p. Problem dimensions that can be successfully solved using the ellipsoid method on modern computers are indicated. The 2nd Section is devoted to Octave program emlmp, which implements the ellipsoid method, and the results of two computational experiments with its use. The obtained results demonstrate robustness of the obtained solutions when parameter p values are close to one. The 3rd Section describes mechanism of variable selection for the best prediction of psychological state of patients based on cardiological data. Variable selection was carried out using the Python Sequential Feature Selector procedure for predicting two psychological indicators – Beck's anxiety scale and psychologist's formalized conclusion. The 4th Section contains the results of a computational experiment using the emlmp program with LMM and least square method (LSM) criteria for predicting a psychologist’s formalized conclusion based on 84 selected patients and 22 parameters. Obtained solutions and forecasts for comparing criteria based on LMM and LSM are given. In the 5th Section, a metric for evaluation consistency of a data set is proposed, which allows to evaluate consistency for each parameter separately. A linear connection was found between 4 psychological parameters and the maximum accuracy of regression models with optimal number of parameters in specified models. Keywords: linear regression, convex function, ellipsoid method, least moduli method, data prediction, GNU Octave.