Knot optimization for multivariate adaptive regression splines

Xinglong Ju, Victoria C.P. Chen, Jay M. Rosenberger, Feng Liu

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    1 Scopus citations

    Abstract

    Multivariate adaptive regression splines (MARS) is a popular statistical modeling method. In the MARS model building process, knot positioning is a critical aspect that potentially affects the accuracy of the final MARS model. However, identifying well-positioned knots requires assessing the quality of many knots in each model building iteration, creating a time-consuming process. By exploring the change in residual sum of squares (?RSS) function within MARS, we find that local optima from previous model building iterations are very close to those of the current iteration. In our approach, this prior ?RSS information is used to "warm start" an optimization algorithm for knot positioning. We propose two methods for MARS knot positioning. The first method is a fixed step hill climbing method (FSHC), which assumes a fixed step size in the search algorithm and ignores prior ?RSS information. The second method is FSHC using prior ?RSS information. Numerical experiments are conducted on data with up to 30 dimensions. Our results show that both versions of FSHC outperform the original MARS knot selection method. Further, FSHC using prior ?RSS information performs best in both accuracy and computational speed.

    Original languageEnglish
    Title of host publicationIISE Annual Conference and Expo 2019
    ISBN (Electronic)9781713814092
    StatePublished - 2019
    Event2019 Institute of Industrial and Systems Engineers Annual Conference and Expo, IISE 2019 - Orlando, United States
    Duration: 18 May 201921 May 2019

    Publication series

    NameIISE Annual Conference and Expo 2019

    Conference

    Conference2019 Institute of Industrial and Systems Engineers Annual Conference and Expo, IISE 2019
    Country/TerritoryUnited States
    CityOrlando
    Period18/05/1921/05/19

    Keywords

    • Hill Climbing
    • Knot Optimization
    • Knot Positioning
    • MARS
    • Regression

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