Density-Based Partitioning for K-Fold Cross-Validation

• Activity Number: 627
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Lulu Kang*+
• Companies: Illinois Institute of Technology-Department of Applied Mathematics
• Keywords: Cross Validation ; K-fold ; kernel density estimation ; optimal band-width

Abstract

Cross-validation, sometimes called rotation estimation, is a technique for assessing how the results of a statistical analysis will generalize to an independent data set. K-fold cross-validation is the most commonly used cross-validation method. Typically in K-fold cross-validation, the original sample is randomly partitioned into K sub-samples. In this paper, we propose a new sampling method to partition the complete data set into K folds such that the probability distribution within each fold is similar to the probability distribution of the complete date set. The L2-norm of the difference between the empirical kernel density functions of the within-fold data and the complete data the measure is used here as objective function to search for the optimal partition of the K folds. Numerical examples are shown to compare the proposed cross-validation methods and the conventional ones.