A. A. Dokukin

A system for computer-assisted design of inorganic compounds based on computer training

A system for computer-assisted design of inorganic compounds, with an integrated complex of databases for the properties of inorganic substances and materials, a subsystem for the analysis of data, based on computer training, a knowledge base, a predictions base, and a managing subsystem, has been developed. The methodology of integration of software products for data analysis, built upon different algorithms of computer training, has been devised. In many instances the employment of the developed system makes it possible to predict new inorganic compounds and estimate various properties of those without experimental synthesis.

Optimal convex correcting procedures in problems of high dimension

The properties of convex correcting procedures (CCPs) over sets of predictors are examined. It is shown that the minimization of the generalized error in a CCP is reduced to a quadratic programming problem. The conditions are studied under which a set of predictors cannot be reduced without degrading the accuracy of the corresponding optimal CCP. Experimental studies of the prognostic properties of CCPs for samples of one-dimensional linear regressions showed that CCP optimization can be an effective tool for regression variable selection.

Practical algorithms for algebraic and logical correction in precedent-based recognition problems

Practical precedent-based recognition algorithms relying on logical or algebraic correction of various heuristic recognition algorithms are described. The recognition problem is solved in two stages. First, an arbitrary object is recognized independently by algorithms from a group. Then a final collective solution is produced by a suitable corrector. The general concepts of the algebraic approach are presented, practical algorithms for logical and algebraic correction are described, and results of their comparison are given.

Algorithms for algebraic and logical correction and their applications

Practical algorithms for precedent-based recognit ion are considered that are based on the logical or algebraic correction of various heuristic algorithms or models of recognition. The recognition problem is solved in two stages. First, algorithms from a certain group are independently applied to recognition of an arbitrary object, and then an appropriate corrector is used to calculate the final collective solution. General concepts of the algebraic approach, descriptions of practical algorithms for logical and algebraic correction, and the results of comparison of these algorithms are presented.

On the construction of samples for testing approximate optimization methods for estimate calculation algorithms

To validate approximate optimization schemes for estimate calculation algorithms (ECAs), it is necessary to compute the optimal height, which cannot be done in a reasonable amount of time. A variety of samples are built for which the optimal height of the ECAs is known by construction.

A method for constructing an optimal estimate calculation algorithm

The problem of searching for an optimal procedure for constructing the best (in a certain sense) algorithm in the family of estimate calculation algorithms is considered. Such a procedure is designed, and upper bounds for its complexity are derived. The case of a two-dimensional feature space is analyzed in detail.

Methods for discrete analysis of medical data on the basis of recognition theory and some of their applications

Methods for the analysis of medical data and the results of their application to the treatment of a number of socially important diseases in important medical areas (cardiology, neurology, surgery, and oncology) are considered. The precedent approach is investigated. Practical methods of discrete analysis of training data, logical and statistical methods for searching logical regularities in data, combinatorial logic and logical statistical classification methods, and methods for estimating models and searching for “nonstandard” descriptions are presented. The results of experiments on real data are demonstrated.

Regression model based on convex combinations best correlated with response

A new regression method based on constructing optimal convex combinations of simple linear regressions of the least squares method (LSM regressions) built from original regressors is presented. It is shown that, in fact, this regression method is equivalent to a modification of the LSM including the additional requirement of the coincidence of the sign of the regression parameter with that of the correlation coefficient between the corresponding regressor and the response. A method for constructing optimal convex combinations based on the concept of nonexpandable irreducible ensembles is described. Results of experiments comparing the developed method with the known glmnet algorithm are presented, which confirm the efficiency of the former.

Design of inorganic compounds with the use of precedent-based pattern recognition methods

The possibility of searching for classification regularities in large arrays of chemical information with the use precedent-based recognition methods is discussed. The results of application of these regularities to the computer-assisted design of inorganic compounds promising for the search for new materials for electronics are presented.

Generalization of the method for constructing maximum-height estimate-calculating algorithms to recognition problems

Yu. I. Zhuravlev proved the existence of a correct algorithm for a regular recognition problem, which is a polynomial on the family of estimate-calculating algorithms (ECAs). At a certain stage, the search for a correct polynomial can be reduced to the search for optimal terms (i.e., ECAs possessing the best properties) in this family. An optimal approach to constructing the maximum-height algorithm for certain families of ECAs is described.