Tropical Geometric Tools for Machine Learning: the TML package
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Authors
Barnhill, David
Yoshida, Ruriko
Aliatimis, Georgios
Miura, Keiji
Subjects
Advisors
Date of Issue
2023
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Abstract
In the last decade, developments in tropical geometry have provided a
number of uses directly applicable to problems in statistical learning. The
TML package is the first R package which contains a comprehensive set
of tools and methods used for basic computations related to tropical convexity,
visualization of tropically convex sets, as well as supervised and
unsupervised learning models using the tropical metric under the max-plus
algebra over the tropical projective torus. Primarily, the TML package
employs a Hit and Run Markov chain Monte Carlo sampler in conjunction
with the tropical metric as its main tool for statistical inference. In addition
to basic computation and various applications of the tropical HAR
sampler, we also focus on several supervised and unsupervised methods
incorporated in the TML package including tropical principal component
analysis, tropical logistic regression and tropical kernel density estimation.
Type
Preprint
Description
The article of record as published may be found at http://dx.doi.org/10.
RY and DB are partially supported from NSF DMS 1916037. KM is partially supported by JSPS KAKENHI Grant Numbers JP22K19816, JP22H02364.
RY and DB are partially supported from NSF DMS 1916037. KM is partially supported by JSPS KAKENHI Grant Numbers JP22K19816, JP22H02364.
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Naval Postgraduate School
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GA is funded by EPSRC through the STOR-i Centre for Doctoral Training
under grant EP/L015692/1.
Format
43 p.
Citation
Barnhill, David, et al. "Tropical Geometric Tools for Machine Learning: the TML package." arXiv preprint arXiv:2309.01082 (2023).
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States