Toric Fiber Products in Geometric Modeling

• Type: Article in International Conference Proceedings Book
• Date: 2023

Authors

Duarte, E (Author) FCUP; Hollering, B (Author) Other; Wiesmann, M (Author) Other

Conference proceedings International

Title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Pages: 494-503

The 6th International Conference on Geometric Science of Information, GSI 2023

St. Malo, 30 August 2023 through 1 September 2023

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Scopus - 0 Citations

Other information

Authenticus ID: P-00Z-4T7

DOI: 10.1007/978-3-031-38271-0_49

Abstract (EN): An important challenge in Geometric Modeling is to classify polytopes with rational linear precision. Equivalently, in Algebraic Statistics one is interested in classifying scaled toric varieties, also known as discrete exponential families, for which the maximum likelihood estimator can be written in closed form as a rational function of the data (rational MLE). The toric fiber product (TFP) of statistical models is an operation to iteratively construct new models with rational MLE from lower dimensional ones. In this paper we introduce TFPs to the Geometric Modeling setting to construct polytopes with rational linear precision and give explicit formulae for their blending functions. A special case of the TFP is taking the Cartesian product of two polytopes and their blending functions. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 9