Computational complexity of learning algebraic varieties

DOI10.1016/j.aam.2020.102100zbMath1506.13046arXiv1910.03305OpenAlexW3056277354MaRDI QIDQ2221768

Oliver Gäfvert

Publication date: 2 February 2021

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.03305

Mathematics Subject Classification ID

General nonlinear regression (62J02) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Uses Software

• Macaulay2
• Bertini
• LearningAlgebraicVarieties

Cites Work

• Critical points via monodromy and local methods
• Chern classes and characteristic cycles of determinantal varieties
• The Euclidean distance degree of smooth complex projective varieties
• Learning algebraic varieties from samples
• Regeneration homotopies for solving systems of polynomials
• Nonlinear Dimensionality Reduction
• Understanding Machine Learning
• The elements of statistical learning. Data mining, inference, and prediction
• The Euclidean distance degree of an algebraic variety
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