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Knotilus: A Differentiable Piecewise Linear Regression Framework

Gormley, Nolan D
http://orcid.org/0000-0002-9336-4043
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1617222994436272

Abstract Details

2021, Master of Science (MS), Bowling Green State University, Computer Science.
Methods of piecewise linear regression (PLR) generally use a max function in their objective function for optimization. It is also common to use gradient-based methods to solve optimization problems. As the max function is not differentiable at a point, an exact gradient and hessian cannot be directly calculated on an objective function that contains it. In order to address this issue, this thesis proposes and evaluates a modified method of PLR called Knotilus. The modifications to the PLR method includes the use of a proposed polynomial approximation of a max function called SofterMax. This function is twice continuously differentiable on all real numbers, allowing for gradient based algorithms to be used on objective functions that contain SofterMax. Results demonstrate that despite the intuition that a twice differentiable max function for knot selection in PLR would lead to improved optimization and computational performance, they are not necessary and do not have a significant impact on computational performance or accuracy.
Robert Green, PhD (Committee Chair)
Ian Deters, PhD (Committee Member)
Michael Decker, PhD (Committee Member)
64 p.
Computer Science; Statistics
Piecewise Linear Regression; Regression; Optimization

Recommended Citations

Citations

  • Gormley, N. D. (2021). Knotilus: A Differentiable Piecewise Linear Regression Framework [Master's thesis, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1617222994436272

    APA Style (7th edition)

  • Gormley, Nolan. Knotilus: A Differentiable Piecewise Linear Regression Framework. 2021. Bowling Green State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1617222994436272.

    MLA Style (8th edition)

  • Gormley, Nolan. "Knotilus: A Differentiable Piecewise Linear Regression Framework." Master's thesis, Bowling Green State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1617222994436272

    Chicago Manual of Style (17th edition)

bgsu1617222994436272
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This open access ETD is published by Bowling Green State University and OhioLINK.