Reliable validation : new perspectives on adaptive data analysis and cross-validation

Validation refers to the challenge of assessing how well a learning algorithm performs after it has been trained on a given data set. It forms an important step in machine learning, as such assessments are then used to compare and choose between algorithms and provide reasonable approximations of their accuracy. In this thesis, we provide new approaches for addressing two common problems with validation. In the first half, we assume a simple validation framework, the holdout set, and address an important question of how many algorithms can be accurately assessed using the same holdout set, in the particular case where these algorithms are chosen adaptively. We do so by first critiquing the initial approaches to building a theory of adaptivity, then offering an alternative approach and preliminary results within this approach, all geared towards characterizing the inherent challenge of adaptivity. In the second half, we address the validation framework itself. Most common practice does not just use a single holdout set, but averages results from several, a family of techniques known as cross-validation. In this work, we offer several new cross-validation techniques with the common theme of utilizing training sets of varying sizes. This culminates in hierarchical cross-validation, a meta-technique for using cross-validation to choose the best cross-validation method.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Elder, Samuel Scott

Advisor dc:contributor.advisor

• Jonathan Kelner and Tamara Broderick.

• Mathematics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/120660

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/120660