Algorithm for constructing fully interpretable segmented linear regressions

This article is devoted to the relevant scientific field – interpretable machine learning. Previously, the author introduced the concept of «fully interpretable linear regression», which is constructed using ordinary least squares for the entire set of statistical data. In this article, this concept is generalized to segmented linear regression, in which data is first divided into segments, and then its own linear regression is constructed on each of them. An algorithm for constructing fully interpretable segmented linear regressions has been developed. Its peculiarity is that, firstly, the division of the predictor space into segments is carried out using logical activation functions for the arguments of binary operations min. Secondly, paired regression is construct in each segment, which completely solves the problem of multicollinearity. Using the developed algorithm, a segmented linear regression of concrete compressive strength was constructed based on a sample of 1030 observations. In all its eight segments, the values of the linear regression determination coefficients do not exceed 0.8, which indicates the presence of unaccounted-for factors, so the constructed model cannot be strictly attributed to fully interpretable ones. However, all other interpretability conditions are met. In addition, the segmented model turned out to be much better in terms of approximation quality than simple linear regression.

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