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Journal articles on the topic 'Piecewise linear regression'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Nakamura, Tsuyoshi. "BMDP program for piecewise linear regression." Computer Methods and Programs in Biomedicine 23, no. 1 (1986): 53–55. http://dx.doi.org/10.1016/0169-2607(86)90080-5.

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2

Noskov, Sergey I. "Estimating the parameters of simple nested piecele-linear regression with a linear component." Yugra State University Bulletin 20, no. 1 (2024): 19–21. http://dx.doi.org/10.18822/byusu20240119-21.

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Subject of research: the problem of estimating the parameters of a simple nested piecewise linear regression with a linear component. Purpose of research: to apply an effective linear-Boolean programming apparatus to solve this problem. Methods and objects of research: the object of research is the minimization of approximation errors of simple nested piecewise linear regression with a linear component, methods – linear regression analysis and mathematical programming apparatus. Main results of research: an approach to determining parameter estimates for simple nested piecewise linear regressi

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3

Носков, Сергей Иванович, and Б. Даниил Е. "Construction of a piecewise linear regression model with linear combinations of grouped predictors." Scientific works of KubSTU, no. 1 (June 6, 2024): 57–64. http://dx.doi.org/10.26297/2312-9409.2024.1.7.

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В работе приведен краткий обзор результатов по применению более сложных по сравнению с линейными форм связи между переменными в математических моделях регрессионного типа. Это, в частности, робастная модель кусочно-линейной регрессии с неизвестным количеством точек переключения; полуконтролируемый классификатор, основанный на модели кусочно-линейной регрессии; метод автоматического построения управляемых моделей энергетических систем; алгоритм решения задач многомерной регрессии и классификации с использованием кусочно-линейных предикторов над многогранным разбиением пространства пр

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4

Yang, Xubing, Hongxin Yang, Fuquan Zhang, et al. "Piecewise Linear Regression Based on Plane Clustering." IEEE Access 7 (2019): 29845–55. http://dx.doi.org/10.1109/access.2019.2902620.

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5

Krotov, Sergey V., Dmitriy P. Kononov, and Alexander P. Buynosov. "Piecewise linear regression for estimating slip zones." Transport of the Urals, no. 1 (2024): 30–34. http://dx.doi.org/10.20291/1815-9400-2024-1-30-34.

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A strong connection between a wheel and an axle is an important parameter for the load-bearing capacity of a wheelset. While operating mutual slip zones of the wheel and axle reduce the reliability of the connection and their direct measurement is not possible. The article examines the admissibility of using piecewise linear regression with a breakpoint to predict the state of a press connection in which slip zones can reach significant values. This is a danger for traffic safety especially while running rolling stock with increased axle loads. The wheelset parameter is calculated using the fi

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6

Yang, Lingjian, Songsong Liu, Sophia Tsoka, and Lazaros G. Papageorgiou. "Mathematical programming for piecewise linear regression analysis." Expert Systems with Applications 44 (February 2016): 156–67. http://dx.doi.org/10.1016/j.eswa.2015.08.034.

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7

Gopalswamy, Karthick, Yahya Fathi, and Reha Uzsoy. "Valid inequalities for concave piecewise linear regression." Operations Research Letters 47, no. 1 (2019): 52–58. http://dx.doi.org/10.1016/j.orl.2018.12.004.

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8

Noskov, S. I., and A. S. Vergasov. "PIECEWISE LINEAR REGRESSION MODEL OF ROAD CONSTRUCTION." Advances and Applications in Discrete Mathematics 39, no. 1 (2023): 117–24. http://dx.doi.org/10.17654/0974165823040.

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9

Zhang, Tianyi. "Statistical Estimation in Piecewise Linear Regression Models." Asian Research Journal of Mathematics 21, no. 4 (2025): 39–45. https://doi.org/10.9734/arjom/2025/v21i4909.

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The kink regression model assumes that linear regression forms are separately modelled on two sides of an unknown threshold but still continuous at the threshold. This paper considers statistical estimation for piecewise linear regression models which are widely used in various fields to capture nonlinear relationships between variables. The estimators for the kink locations and regression coefficients are obtained by using the least squares method, a detailed explanation of the estimation process is provided. Furthermore, the proposed methodology is validated through an illustrative example u

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10

Debarre, Thomas, Quentin Denoyelle, Michael Unser, and Julien Fageot. "Sparsest piecewise-linear regression of one-dimensional data." Journal of Computational and Applied Mathematics 406 (May 2022): 114044. http://dx.doi.org/10.1016/j.cam.2021.114044.

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11

Cologne, John, and Richard Sposto. "Smooth piecewise linear regression splines with hyperbolic covariates." Journal of Applied Statistics 21, no. 4 (1994): 221–33. http://dx.doi.org/10.1080/757583867.

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12

Vieth, E. "Fitting piecewise linear regression functions to biological responses." Journal of Applied Physiology 67, no. 1 (1989): 390–96. http://dx.doi.org/10.1152/jappl.1989.67.1.390.

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An iterative approach was achieved for fitting piecewise linear functions to nonrectilinear responses of biological variables. This algorithm is used to estimate the parameters of the two (or more) regression functions and the separation point(s) (thresholds, sensitivities) by statistical approximation. Although it is often unknown whether the response of a biological variable is adequately described by one rectilinear regression function or by piecewise linear regression function(s) with separation point(s), an F test is proposed to determine whether one regression line is the optimal fitted

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13

Zubrilin, K. M. "Paired piecewise linear regression model with fixed nodes." Economics and Mathematical Methods 60, no. 4 (2024): 113–24. http://dx.doi.org/10.31857/s0424738824040103.

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In this paper we develop a method for constructing a paired regression model in the class of piecewise linear continuous functions with fixed nodes. The concept of linear division of the correlation field, its partial sections and its nodes is introduced into consideration. Using the linear division of the correlation field, a class of piecewise linear functions with fixed nodes is determined. The linear division is revealed during the visual analysis of the correlation field. Using the least squares method, a system of linear equations is compiled to find point estimates of the parameters of

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14

Ndlovu, P., and J. Preater. "CALIBRATION USING A PIECEWISE SIMPLE LINEAR REGRESSION MODEL." Communications in Statistics - Theory and Methods 30, no. 2 (2001): 229–42. http://dx.doi.org/10.1081/sta-100002027.

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15

Cardoso-Silva, Jonathan, Lazaros G. Papageorgiou, and Sophia Tsoka. "Network-based piecewise linear regression for QSAR modelling." Journal of Computer-Aided Molecular Design 33, no. 9 (2019): 831–44. http://dx.doi.org/10.1007/s10822-019-00228-6.

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Abstract Quantitative Structure-Activity Relationship (QSAR) models are critical in various areas of drug discovery, for example in lead optimisation and virtual screening. Recently, the need for models that are not only predictive but also interpretable has been highlighted. In this paper, a new methodology is proposed to build interpretable QSAR models by combining elements of network analysis and piecewise linear regression. The algorithm presented, modSAR, splits data using a two-step procedure. First, compounds associated with a common target are represented as a network in terms of their

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16

Cardoso‐Silva, Jonathan, George Papadatos, Lazaros G. Papageorgiou, and Sophia Tsoka. "Optimal Piecewise Linear Regression Algorithm for QSAR Modelling." Molecular Informatics 38, no. 3 (2018): 1800028. http://dx.doi.org/10.1002/minf.201800028.

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17

Noskov, Sergey I. "Identification of parameters of a combined piece-linear regression model." Yugra State University Bulletin 18, no. 4 (2023): 115–19. http://dx.doi.org/10.18822/byusu202204115-119.

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Subject of research: the problem of estimating the parameters of a combined piecewise linear regression model. Purpose of research: to apply the apparatus of linear Boolean programming to identify its parameters.  Methods and objects of research: the object of research is a set of indicators of inventive activity in the Russian Federation, the methods are regression analysis and mathematical programming. Main results of research: an approach to estimating the parameters of a combined piecewise linear regression model by using the method of least modules is described, which ma

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18

Noskov, Sergey I. "Construction of a piece-linear autoregression model of an arbitrary order." Yugra State University Bulletin 18, no. 2 (2022): 89–94. http://dx.doi.org/10.18822/byusu20220289-94.

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The relevance of the study is due to the need to expand the arsenal of forms of communication between variables in regression models. Object: piecewise linear autoregressive model of arbitrary order. Subject: computing apparatus for solving problems of linear-Boolean programming. Purpose: development of an algorithm for estimating the parameters of piecewise linear regression. Methods: regression analysis, mathematical programming. Results: the paper formulated the problem of constructing a piecewise linear autoregressive model of an arbitrary order based on the m

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19

Noskov, Sergey I. "Construction of a piece-linear autoregression model of an arbitrary order." Yugra State University Bulletin 18, no. 2 (2022): 89–94. http://dx.doi.org/10.18822/byusu20220289-94.

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The relevance of the study is due to the need to expand the arsenal of forms of communication between variables in regression models. Object: piecewise linear autoregressive model of arbitrary order. Subject: computing apparatus for solving problems of linear-Boolean programming. Purpose: development of an algorithm for estimating the parameters of piecewise linear regression. Methods: regression analysis, mathematical programming. Results: the paper formulated the problem of constructing a piecewise linear autoregressive model of an arbitrary order based on the m

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20

Noskov, Sergeу I., and Aleksandra R. Chekalova. "CONSTRUCTION OF A HOMOGENEOUS NESTED PIECEWISE LINEAR REGRESSION WITH LAGGING VARIABLES." Vestnik Chuvashskogo universiteta, no. 4 (December 25, 2024): 75–83. https://doi.org/10.47026/1810-1909-2024-4-75-83.

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When constructing regression models of objects of any nature, it is often necessary to use nonlinear approximating constructions, including piecewise linear ones, while the process under study can have a pronounced dynamic nature, therefore, lagging (lag) variables can be used as regressors. The research purpose is to develop an algorithmic method of identifying the parameters of a homogeneous nested piecewise linear regression with lagging variables. Materials and methods. To achieve the goal, the methods of reducing the problems of estimating the parameters of nested piecewise linear models

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21

Keshvari, Abolfazl. "Segmented concave least squares: A nonparametric piecewise linear regression." European Journal of Operational Research 266, no. 2 (2018): 585–94. http://dx.doi.org/10.1016/j.ejor.2017.10.006.

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22

Martinez, Nadia, Hadis Anahideh, Jay M. Rosenberger, Diana Martinez, Victoria C. P. Chen, and Bo Ping Wang. "Global optimization of non-convex piecewise linear regression splines." Journal of Global Optimization 68, no. 3 (2017): 563–86. http://dx.doi.org/10.1007/s10898-016-0494-5.

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23

Noskov, S. I., and S. I. Belinskaya. "Computing Parameter Estimates of a Homogeneous Nested Piecewise Linear Regression." Herald of Dagestan State Technical University. Technical Sciences 50, no. 4 (2024): 115–20. http://dx.doi.org/10.21822/2073-6185-2023-50-4-115-120.

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Objective. The aim of the study is to develop an algorithm for identifying the parameters of a homogeneous nested piecewise linear regression model of the first type by the method of least modules. Method. Estimation of its unknown parameters is carried out with the help of reduction to the problem of linear Boolean programming. Its solution should not cause computational difficulties due to a significant number of effective software tools - for example, the well-established and freely available program LPsolve on the Internet. Result. The generated linear programming problem has an acceptable

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24

Zhang, Shunpu, Kent M. Eskridge, Stephen D. Kachman, Yumou Qiu, and Tami M. Brown-Brandl. "Comparing Piecewise Regression and Hysteresis Models in Assessing Beef Cattle Heat Stress." Transactions of the ASABE 62, no. 2 (2019): 549–59. http://dx.doi.org/10.13031/trans.12910.

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Abstract. Climate change may generate more frequent heat waves, resulting in substantial cattle production losses through increased heat stress. Time lags between air temperature and an animal’s body temperature have been recognized as valuable measures of heat stress, and developing methods for detecting time lags is important. Existing hysteresis models are useful for estimating air-body temperature time lags, especially when the air temperature follows a consistent diurnal sinusoidal function, such as when animals are housed in a controlled environment. However, in cattle feedlot or pasture

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25

Artemenko, Vladislav, and Volodymyr Petrovych. "Features of the application of the method of quantile regression in problems of hydroecology." Automobile Roads and Road Construction, no. 110 (2021): 90–98. http://dx.doi.org/10.33744/0365-8171-2021-110-090-098.

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Such perspective method of the analysis of the natural time series is considered in article as method of quantile regression. They are discussed imperfection existing methods of the analysis of the natural processes (least square method and the method of linear robust regression). It is shown that transition towards quantile regression allows greatly to raise efficiency of the investigations of the natural time series. Main gоal of the work consists in practical applications of the quantile regression method for decision of the different problemsof the hydroecology. Hydrochemical time series w

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26

Takeuchi, Ichiro, Kaname Nomura, and Takafumi Kanamori. "Nonparametric Conditional Density Estimation Using Piecewise-Linear Solution Path of Kernel Quantile Regression." Neural Computation 21, no. 2 (2009): 533–59. http://dx.doi.org/10.1162/neco.2008.10-07-628.

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The goal of regression analysis is to describe the stochastic relationship between an input vector x and a scalar output y. This can be achieved by estimating the entire conditional density p(y ∣ x). In this letter, we present a new approach for nonparametric conditional density estimation. We develop a piecewise-linear path-following method for kernel-based quantile regression. It enables us to estimate the cumulative distribution function of p(y ∣ x) in piecewise-linear form for all x in the input domain. Theoretical analyses and experimental results are presented to show the effectiveness o

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27

Mythili, S., R. Pradeep Kumar, and P. Nagabhushan. "Knowledge Discovery in Learning Management System Using Piecewise Linear Regression." Circuits and Systems 07, no. 11 (2016): 3862–73. http://dx.doi.org/10.4236/cs.2016.711322.

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28

Bagirov, Adil, Sona Taheri, and Soodabeh Asadi. "A difference of convex optimization algorithm for piecewise linear regression." Journal of Industrial & Management Optimization 15, no. 2 (2019): 909–32. http://dx.doi.org/10.3934/jimo.2018077.

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29

Jin, Ran, and Jianjun Shi. "Reconfigured piecewise linear regression tree for multistage manufacturing process control." IIE Transactions 44, no. 4 (2012): 249–61. http://dx.doi.org/10.1080/0740817x.2011.564603.

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30

Yu, Jing-Rung, Gwo-Hshiung Tzeng, and Han-Lin Li. "A general piecewise necessity regression analysis based on linear programming." Fuzzy Sets and Systems 105, no. 3 (1999): 429–36. http://dx.doi.org/10.1016/s0165-0114(97)00223-6.

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31

Shi, Shurong, Yi Li, and Chuang Wan. "Robust continuous piecewise linear regression model with multiple change points." Journal of Supercomputing 76, no. 5 (2018): 3623–45. http://dx.doi.org/10.1007/s11227-018-2597-x.

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32

Ren, Yanni, Weite Li, and Jinglu Hu. "A semisupervised classifier based on piecewise linear regression model using gated linear network." IEEJ Transactions on Electrical and Electronic Engineering 15, no. 7 (2020): 1048–56. http://dx.doi.org/10.1002/tee.23149.

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33

Saishu, Hiroki, Kota Kudo, and Yuichi Takano. "Sparse Poisson regression via mixed-integer optimization." PLOS ONE 16, no. 4 (2021): e0249916. http://dx.doi.org/10.1371/journal.pone.0249916.

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We present a mixed-integer optimization (MIO) approach to sparse Poisson regression. The MIO approach to sparse linear regression was first proposed in the 1970s, but has recently received renewed attention due to advances in optimization algorithms and computer hardware. In contrast to many sparse estimation algorithms, the MIO approach has the advantage of finding the best subset of explanatory variables with respect to various criterion functions. In this paper, we focus on a sparse Poisson regression that maximizes the weighted sum of the log-likelihood function and the L2-regularization t

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34

Godoy, C., and J. C. A. Batista. "Adhesion Evaluation of Plasma Sprayed Coatings Using Piecewise Linear Regression Analysis." Journal of Thermal Spray Technology 8, no. 4 (1999): 531–36. http://dx.doi.org/10.1361/105996399770350214.

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35

Launay, Tristan, Anne Philippe, and Sophie Lamarche. "Consistency of the posterior distribution and MLE for piecewise linear regression." Electronic Journal of Statistics 6 (2012): 1307–57. http://dx.doi.org/10.1214/12-ejs713.

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36

Pakdaman Naeini, Mahdi, and Gregory F. Cooper. "Binary classifier calibration using an ensemble of piecewise linear regression models." Knowledge and Information Systems 54, no. 1 (2017): 151–70. http://dx.doi.org/10.1007/s10115-017-1133-2.

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37

Luo, Jingjing, Xianfang Sun, Man Lung Yiu, Longcun Jin, and Xinyi Peng. "Piecewise linear regression-based single image super-resolution via Hadamard transform." Information Sciences 462 (September 2018): 315–30. http://dx.doi.org/10.1016/j.ins.2018.06.030.

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38

Teeter, Rebecca A. "The Application of Linear Piecewise Regression to Basal Body Temperature Data." Biometrical Journal 27, no. 7 (1985): 759–73. http://dx.doi.org/10.1002/bimj.4710270707.

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39

Zern, Artjom, Klaus Broelemann, and Gjergji Kasneci. "Interventional SHAP Values and Interaction Values for Piecewise Linear Regression Trees." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 9 (2023): 11164–73. http://dx.doi.org/10.1609/aaai.v37i9.26322.

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In recent years, game-theoretic Shapley values have gained increasing attention with respect to local model explanation by feature attributions. While the approach using Shapley values is model-independent, their (exact) computation is usually intractable, so efficient model-specific algorithms have been devised including approaches for decision trees or their ensembles in general. Our work goes further in this direction by extending the interventional TreeSHAP algorithm to piecewise linear regression trees, which gained more attention in the past few years. To this end, we introduce a decompo

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40

Moreno-Carbonell, Santiago, and Eugenio F. Sánchez-Úbeda. "A Piecewise Linear Regression Model Ensemble for Large-Scale Curve Fitting." Algorithms 17, no. 4 (2024): 147. http://dx.doi.org/10.3390/a17040147.

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The Linear Hinges Model (LHM) is an efficient approach to flexible and robust one-dimensional curve fitting under stringent high-noise conditions. However, it was initially designed to run in a single-core processor, accessing the whole input dataset. The surge in data volumes, coupled with the increase in parallel hardware architectures and specialised frameworks, has led to a growth in interest and a need for new algorithms able to deal with large-scale datasets and techniques to adapt traditional machine learning algorithms to this new paradigm. This paper presents several ensemble alternat

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41

Носков, С. И., and А. Н. Знайдюк. "CALCULATING PARAMETERS OF A SIMPLE NESTED PIECEWISE LINEAR REGRESSION USING MIXED ESTIMATION." Proceedings in Cybernetics 23, no. 1 (2024): 54–59. http://dx.doi.org/10.35266/1999-7604-2024-1-7.

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The article describes an algorithm for calculating numerical estimates of the parameters of a simple nested piecewise linear regression using mixed estimation. The algorithm aims at simultaneous identifi cation using methods of least modules and antirobust estimation, both of which operate on certain subsamplings from the initial sampling. The approach comes to solving the problem of linear Boolean programming. A numerical problem has been solved.

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42

Bartlett, Peter L., Vitaly Maiorov, and Ron Meir. "Almost Linear VC-Dimension Bounds for Piecewise Polynomial Networks." Neural Computation 10, no. 8 (1998): 2159–73. http://dx.doi.org/10.1162/089976698300017016.

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We compute upper and lower bounds on the VC dimension and pseudodimension of feedforward neural networks composed of piecewise polynomial activation functions. We show that if the number of layers is fixed, then the VC dimension and pseudo-dimension grow as W log W, where W is the number of parameters in the network. This result stands in opposition to the case where the number of layers is unbounded, in which case the VC dimension and pseudo-dimension grow as W2. We combine our results with recently established approximation error rates and determine error bounds for the problem of regression

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43

Lu, Kang-Ping, and Shao-Tung Chang. "An Advanced Segmentation Approach to Piecewise Regression Models." Mathematics 11, no. 24 (2023): 4959. http://dx.doi.org/10.3390/math11244959.

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Two problems concerning detecting change-points in linear regression models are considered. One involves discontinuous jumps in a regression model and the other involves regression lines connected at unknown places. Significant literature has been developed for estimating piecewise regression models because of their broad range of applications. The segmented (SEG) regression method with an R package has been employed by many researchers since it is easy to use, converges fast, and produces sufficient estimates. The SEG method allows for multiple change-points but is restricted to continuous mo

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Shi, Hon-Yi, Hao-Hsien Lee, Meng-Han Tsai, Chong-Chi Chiu, Yih-Huei Uen, and King-Teh Lee. "Long-term outcomes of laparoscopic cholecystectomy: a prospective piecewise linear regression analysis." Surgical Endoscopy 25, no. 7 (2010): 2132–40. http://dx.doi.org/10.1007/s00464-010-1508-x.

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45

Noskov, Sergey I. "PARAMETER IDENTIFICATION OF THE SIMPLE FORM OF A NESTED PIECEWISE LINEAR REGRESSION." Scholarly Notes of Komsomolsk-na-Amure State Technical University, no. 3 (2023): 57–61. http://dx.doi.org/10.17084/20764359-2023-67-57.

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46

YU, JING-RUNG, GWO-HSHIUNG TZENG, and HAN-LIN LI. "INTERVAL PIECEWISE REGRESSION MODEL WITH AUTOMATIC CHANGE-POINT DETECTION BY QUADRATIC PROGRAMMING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 13, no. 03 (2005): 347–61. http://dx.doi.org/10.1142/s0218488505003503.

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To handle large variation data, an interval piecewise regression method with automatic change-point detection by quadratic programming is proposed as an alternative to Tanaka and Lee's method. Their unified quadratic programming approach can alleviate the phenomenon where some coefficients tend to become crisp in possibilistic regression by linear programming and also obtain the possibility and necessity models at one time. However, that method can not guarantee the existence of a necessity model if a proper regression model is not assumed especially with large variations in data. Using automa

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47

Gao, Qingjia, Chong Wang, Xiaoming Wang, et al. "Pointing Error Correction for Vehicle-Mounted Single-Photon Ranging Theodolite Using a Piecewise Linear Regression Model." Sensors 24, no. 10 (2024): 3192. http://dx.doi.org/10.3390/s24103192.

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Pointing error is a critical performance metric for vehicle-mounted single-photon ranging theodolites (VSRTs). Achieving high-precision pointing through processing and adjustment can incur significant costs. In this study, we propose a cost-effective digital correction method based on a piecewise linear regression model to mitigate this issue. Firstly, we introduce the structure of a VSRT and conduct a comprehensive analysis of the factors influencing its pointing error. Subsequently, we develop a physically meaningful piecewise linear regression model that is both physically meaningful and ca

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48

Paweł, Kałużny, and Bobrowski Leon. "Linear Regression Modeling of Interval-censored Survival Times Based on a Convex Piecewise-linear Criterion Function." Biocybernetics and Biomedical Engineering 32, no. 3 (2012): 69–78. http://dx.doi.org/10.1016/s0208-5216(12)70043-8.

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49

Samosir, Perak, Rulyenzi Rasyid, Felisitas Serena Nomer, and Bethran Christofer. "Analisis Statistik Bauran Energi Terbarukan Indonesia Tahun 2015-2022." Jurnal Mekanik Terapan 4, no. 3 (2024): 127–37. http://dx.doi.org/10.32722/jmt.v4i3.5856.

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Berdasarkan data Badan Pusat Statistik dan Kementerian Energi dan Sumber Daya Mineral Republik Indonesia, sejak tahun 2015 bauran energi terbarukan (%) Indonesia mengalami peningkatan. Hal ini sejalan dengan pidato Presiden Republik Indonesia pada Conference of Parties (COP) 26 United Nations Framework Convention on Climate Change (UNFCCC) di Glasgow Inggris bulan Nopember tahun 2021, bahwa Indonesia berkomitmen untuk ikut melakukan penurunan emisi. Indonesia dapat berkontribusi untuk mencapai net-zero emission dunia. Salah satu langkah yang dapat dilakukan adalah dengan melakukan diversifikas

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50

Todorovski, Ljupčo, Sašo Džeroski, and Peter Ljubič. "Discovery of polynomial equations for regression." Advances in Methodology and Statistics 1, no. 1 (2004): 131–42. http://dx.doi.org/10.51936/uogl8142.

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Abstract:

Both equation discovery and regression methods aim at inducing models of numerical data. While the equation discovery methods are usually evaluated in terms of comprehensibility of the induced model, the emphasis of the regression methods evaluation is on their predictive accuracy. In this paper, we present Ciper, an efficient method for discovery of polynomial equations and empirically evaluate its predictive performance on standard regression tasks. The evaluation shows that polynomials compare favorably to linear and piecewise regression models, induced by the existing state-of-the-art regr

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