Faithful Variable Screening for High-Dimensional Convex Regression
By Min Xu, Minhua Chen, John D. Lafferty. 2014
29 citations recorded by the source corpus.
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the relevant variables. Our approach is a two-stage quadratic programming method that estimates a sum of one-dimensional convex functions, followed by one-dimensional concave regression fits on the residuals. In contrast to previous methods for sparse additive models, the optimization is finite dimensional and requires no tuning parameters for smoothness. Under appropriate assumptions, we prove that the procedure is faithful in the population setting, yielding no false negatives. We give a finite sample statistical analysis, and introduce algorithms for efficiently carrying out the required quadratic programs. The approach leads to computational and statistical advantages over fitting a full model, and provides an effective, practical approach to variable screening in convex regression.
Subfields: Statistics and Probability
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In Statistics and Probability
- Yining Chen
- Richard J. Samworth
- Junming Yin
- Yaoliang Yu
- Arlene K. H. Kim
- Bodhisattva Sen
- John D. Lafferty
- Minhua Chen
Citations in the corpus
- Convex-constrained Sparse Additive Modeling and Its Extensions (2017, methodology): “…note in passing that a similar model to (7) (with group `∞ norm instead) appeared as the first stage of the screening procedure in the recent work of Xu et al. (2016), Following the discussion from §2.1, we can simplify the infinite-dimensional problem (7) by first sorting each of the p…”
- Generalized additive and index models with shape constraints (2014, background): “In other cases, as pointed out by Xu et al. (2014), shape restrictions are attractive as tractable non-parametric relaxations of linear models.”