Wave regression: nonlinear cognitive heuristic

Bogdanov P.I., Surov I.A. Wave regression: nonlinear cognitive heuristic. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2025, vol. 25, no. 5, pp. 979–987 (in Russian). doi: 10.17586/2226-1494-2025-25-5-979-987

The quality of regression is determined by the choice of an approximation function, more or less accurately reflecting the process which generated the data. An important class of such processes is cognitive processes of largely wave nature. Here, the corresponding wave-like calculus is used in the new method of behavioral regression. We generalize classical linear regression from real weights to complex-valued amplitudes the modules and phases of which encode the amplification and delay of cognitive waves. The target feature then emerges as squared module of total amplitude influences of all basis features. The obtained regression models are tested on the data of academic performance of the study group in comparison with linear regressions of the same number of parameters. When using all basis features, the accuracy of wave regression is close to the accuracy of linear models. With fewer basis features the quality of linear regression degrades, while the performance of wave regression improves. The largest difference is observed in triadic regime when the target feature is produced by two basis features. In this case, the error of three-parameter wave regression is 2.5 % lower than that of full linear regression with 21 parameters. This dramatic improvement is due to a special nonlinearity of wave regression, typical to pragmatic heuristics of natural thinking. This nonlinearity takes advantage of semantic correlations of features missed by classical regressions. The wave-like reduction of computational complexity opens up ways for developing more efficient and nature-like algorithms of data analysis and artificial intelligence.

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