Support vector regression for polyhedral and missing data

Gianluca Gazzola () and Myong K. Jeong ()
Additional contact information
Gianluca Gazzola: Rutgers University
Myong K. Jeong: Rutgers University

Annals of Operations Research, 2021, vol. 303, issue 1, No 20, 483-506

Abstract: Abstract We introduce “Polyhedral Support Vector Regression” (PSVR), a regression model for data represented by arbitrary convex polyhedral sets. PSVR is derived as a generalization of support vector regression, in which the data is represented by individual points along input variables $$X_1$$ X 1 , $$X_2$$ X 2 , $$\ldots $$ … , $$X_p$$ X p and output variable Y, and extends a support vector classification model previously introduced for polyhedral data. PSVR is in essence a robust-optimization model, which defines prediction error as the largest deviation, calculated along Y, between an interpolating hyperplane and all points within a convex polyhedron; the model relies on the affine Farkas’ lemma to make this definition computationally tractable within the formulation. As an application, we consider the problem of regression with missing data, where we use convex polyhedra to model the multivariate uncertainty involving the unobserved values in a data set. For this purpose, we discuss a novel technique that builds on multiple imputation and principal component analysis to estimate convex polyhedra from missing data, and on a geometric characterization of such polyhedra to define observation-specific hyper-parameters in the PSVR model. We show that an appropriate calibration of such hyper-parameters can have a significantly beneficial impact on the model’s performance. Experiments on both synthetic and real-world data illustrate how PSVR performs competitively or better than other benchmark methods, especially on data sets with high degree of missingness.

Keywords: Regression; Uncertainty; Missing data; Convex polyhedron; Farkas’ lemma (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10479-020-03799-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:303:y:2021:i:1:d:10.1007_s10479-020-03799-y

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-020-03799-y

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().