Blow-up Algorithm for Sum-of-Products Polynomials and Real Log Canonical Thresholds

• URL: http://arxiv.org/abs/2303.11619v1
• Date: Tue, 21 Mar 2023 06:40:06 GMT
• Title: Blow-up Algorithm for Sum-of-Products Polynomials and Real Log Canonical Thresholds
• Authors: Joe Hirose
• Abstract summary: Papers replace a mean error function with a relatively simple log canonical threshold (RLCT) They obtain its RLCT by resolving its singularities through an operation called blow-up. This paper considers the blow-up algorithm for the iterationss called sum-of-products (sop)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: When considering a real log canonical threshold (RLCT) that gives a Bayesian generalization error, in general, papers replace a mean error function with a relatively simple polynomial whose RLCT corresponds to that of the mean error function, and obtain its RLCT by resolving its singularities through an algebraic operation called blow-up. Though it is known that the singularities of any polynomial can be resolved by a finite number of blow-up iterations, it is not clarified whether or not it is possible to resolve singularities of a specific polynomial by applying a specific blow-up algorithm. Therefore this paper considers the blow-up algorithm for the polynomials called sum-of-products (sop) polynomials and its RLCT.

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