A Statistical Learning Theory Approach for the Analysis of the Trade-off Between Sample Size and Precision in Truncated Ordinary Least Squares

Giorgio Gnecco (), Fabio Raciti () and Daniela Selvi ()
Additional contact information
Giorgio Gnecco: AXES Research Unit, IMT School for Advanced Studies
Fabio Raciti: University of Catania
Daniela Selvi: Università di Firenze

A chapter in High-Dimensional Optimization and Probability, 2022, pp 241-252 from Springer

Abstract: Abstract This chapter deals with linear regression problems for which one has the possibility of varying the supervision cost per example, by controlling the conditional variance of the output given the feature vector. For a fixed upper bound on the total available supervision cost, the trade-off between the number of training examples and their precision of supervision is investigated, using a nonasymptotic data-independent bound from the literature in statistical learning theory. This bound is related to the truncated output of the ordinary least squares regression algorithm. The results of the analysis are also compared theoretically with the ones obtained in a previous work, based on a large-sample approximation of the untruncated output of ordinary least squares. Advantages and disadvantages of the investigated approach are discussed.

Keywords: Linear regression; Statistical learning theory; Supervision cost; Conditional variance (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spochp:978-3-031-00832-0_7

Ordering information: This item can be ordered from
http://www.springer.com/9783031008320

DOI: 10.1007/978-3-031-00832-0_7

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().