Convex-constrained Sparse Additive Modeling and Its Extensions
By Junming Yin, Yaoliang Yu. 2017
3 citations recorded by the source corpus.
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive models. The proposed sparse difference of convex additive models (SDCAM) can estimate most continuous functions without any a priori smoothness assumption. Motivated by a characterization of difference of convex functions, our method incorporates a natural regularization functional to avoid overfitting and to reduce model complexity. Computationally, we develop an efficient backfitting algorithm with linear per-iteration complexity. Experiments on both synthetic and real data verify that our method is competitive against state-of-the-art sparse additive models, with improved performance in most scenarios.
Subfields: Computer Vision and Pattern Recognition, Industrial and Manufacturing Engineering, Statistical Learning Theory, Mathematical Optimization
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Vision and Pattern Recognition
In Industrial and Manufacturing Engineering
In Statistical Learning Theory
In Mathematical Optimization
Citations in the corpus
- Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges (2021, methodology): “…functions are estimated by splines, many works apply convex regularizers (e.g., `1) to control both smoothness and sparsity (Lin et al., 2006; Ravikumar et al., 2009; Meier et al., 2009; Yin and Yu, 2017; Petersen et al., 2016; Lou et al., 2016; Sadhanala et al., 2019; Haris et al., 2019).”