Piecewise polynomial regression trees

By Probal Chaudhuri, Min-Ching Huang, W. Loh, Ruji Yao. 1994

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Citations in the corpus

Toward Interpretable Deep Reinforcement Learning with Linear Model U-Trees (2018, background): “than simple constants. Being strictly more expressive than a regression tree, a linear model tree can also approximate a continuous function arbitrarily closely, with typically with many fewer leaves [4]. Smaller trees are more interpretable, and therefore more suitable for mimic learning. As shown ”
Supervised Neighborhoods for Distributed Nonparametric Regression (2016, methodology): “, tree-based piecewise polynomials models [13], and multivariate adaptive regression splines [14].”
Semiconvex Regression for Metamodeling-Based Optimization (2014, methodology): “1 is similar to Theorem 1 of [19]; to prove our theorem, we modify parts of the proof in [19] that rely on a fixed number of polyhedral faces and account for the error introduced through the varying-coefficient model.”
Regression trees for longitudinal and multiresponse data (2012, background): “The conditions generalize those for univariate responses in Chaudhuri et al. (1994, 1995), Chaudhuri and Loh (2002) and Kim et al. (2007).”
Fifty Years of Classification and Regression Trees (2014, background): “Smoothed and Unsmoothed Piecewise POlynomial Regression Trees (SUPPORT) (Chaudhuri et al., 1994) uses a different approach that applies classification tree techniques to the residuals.”
Multivariate convex regression with adaptive partitioning (2011, methodology): “Algorithmic methods for solving the quadratic program were given in Wu (1982), Dykstra (1983) and Fraser & Massam (1989).”
Learning model trees from evolving data streams (2010, methodology): “The RA splitting rule comes from SUPPORT (Chaudhuri et al. 1994).”
Gaining insight with recursive partitioning of generalized linear models (2013, methodology): “Furthermore, MOB provides functionality for many diﬀerent type of node models that even exceeds the versatility of SUPPORT and GUIDE.”
REGRESSION TREES WITH UNBIASED VARIABLE SELECTION AND INTERACTION DETECTION (2002, methodology): “Chaudhuri et al. (1994) use the data to illustrate the SUPPORT method.”
Expert Systems With Applications (unknown): “…reduction by predicting of mean output values in two child nodes ( Breiman et al., 1984; Quinlan, 1992; Wang & Witten, 1997 ), or examining distribution of sample deviations from ﬁtting one linear regression function to all the samples in the parent node ( Chaudhuri et al., 1994; Loh, 2002 ).”
Visualizable and interpretable regression models with good prediction power (2007, unknown): “Now, following the ideas in the proof of Theorem 1 in Chaudhuri, Huang, Loh and Yao (1994) ,”
Bayesian Treed Generalized Linear Models (2003, methodology): “Several papers have suggested such a strategy: Karali‚c (1992) for multiple regression models, Alexander and Grimshaw (1996) for simple linear regression models, and Chaudhuri, Huang, Loh and Yao (1994) for multiple polynomial regression models.”