Generalized additive and index models with shape constraints

By Yining Chen, Richard J. Samworth. 2014

88 citations recorded by the source corpus.

We study generalized additive models, with shape restrictions (e.g. monotonicity, convexity and concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a non‐parametric estimator of each additive component, obtained by maximizing the likelihood. The procedure is free of tuning parameters and under mild conditions is proved to be uniformly consistent on compact intervals. More generally, our methodology can be applied to generalized additive index models. Here again, the procedure can be justified on theoretical grounds and, like the original algorithm, has highly competitive finite sample performance. Practical utility is illustrated through the use of these methods in the analysis of two real data sets. Our algorithms are publicly available in the R package scar, short for shape‐constrained additive regression.

Subfields: Artificial Intelligence, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals (2018, background): “…(1972); Groeneboom and Jongbloed (2014); Gupta et al. (2016); Canini et al. (2016); Luss and Rosset (2017); You et al. (2017); Bonakdarpour et al. (2018)), or other shapes (e.g. Chetverikov et al. (2018); Pya and Wood (2015); Chen and Samworth (2016); Gupta et al. (2018); Cotter et al. (2019b)).”
Recent Progress in Log-Concave Density Estimation (2017, background): “There is a large literature on estimating m under different shape constraints (e.g. van Eeden, 1958; Groeneboom, Jongbloed and Wellner, 2001; Han and Wellner, 2016b; Chen and Samworth, 2016).”
Least squares estimation in the monotone single index model (2016, methodology): “The monotone single index model is also closely related to the model considered by Chen and Samworth (2016), who in contrast to the approach followed here, assume that the conditional distribution of Y given X takes the form (1.2). Chen and Samworth (2016) also consider additive index models where, ”
Nonparametric Shape-Restricted Regression (2017, background): “Shape-restricted additive and single-index regression models offer flexible, yet interpretable, statistical procedures for handling multidimensional covariates, and have been extensively used in econometrics, epidemiology and other fields (see [35, 82, 113] and the references therein).”
Faithful Variable Screening for High-Dimensional Convex Regression (2014, methodology): “We also include an extra boundedness constraint to use new bracketing number results (Kim and Samworth, 2014).”