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After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety.
This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry.
This is an openaccess book.
After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety.
This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry.
This is an openaccess book.
Preface.- Historical Snapshot.- Critical Equations.- Computations.- Polar Degrees.- Wasserstein Distance.- Curvature.- Reach and Offset.- Voronoi Cells.- Condition Numbers.- Machine Learning.- Maximum Likelihood.- Tensors.- Computer Vision.- Volumes of Semialgebraic Sets.- Sampling.- References.
Erscheinungsjahr: | 2024 |
---|---|
Fachbereich: | Arithmetik & Algebra |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
Seiten: | 232 |
Reihe: | Oberwolfach Seminars |
Inhalt: |
xiv
215 S. |
ISBN-13: | 9783031514616 |
ISBN-10: | 3031514610 |
Sprache: | Englisch |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: |
Breiding, Paul
Sturmfels, Bernd Kohn, Kathlén |
Auflage: | 2024 |
Hersteller: |
Springer Nature Switzerland
Springer International Publishing Oberwolfach Seminars |
Maße: | 240 x 168 x 13 mm |
Von/Mit: | Paul Breiding (u. a.) |
Erscheinungsdatum: | 28.02.2024 |
Gewicht: | 0,397 kg |
Preface.- Historical Snapshot.- Critical Equations.- Computations.- Polar Degrees.- Wasserstein Distance.- Curvature.- Reach and Offset.- Voronoi Cells.- Condition Numbers.- Machine Learning.- Maximum Likelihood.- Tensors.- Computer Vision.- Volumes of Semialgebraic Sets.- Sampling.- References.
Erscheinungsjahr: | 2024 |
---|---|
Fachbereich: | Arithmetik & Algebra |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
Seiten: | 232 |
Reihe: | Oberwolfach Seminars |
Inhalt: |
xiv
215 S. |
ISBN-13: | 9783031514616 |
ISBN-10: | 3031514610 |
Sprache: | Englisch |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: |
Breiding, Paul
Sturmfels, Bernd Kohn, Kathlén |
Auflage: | 2024 |
Hersteller: |
Springer Nature Switzerland
Springer International Publishing Oberwolfach Seminars |
Maße: | 240 x 168 x 13 mm |
Von/Mit: | Paul Breiding (u. a.) |
Erscheinungsdatum: | 28.02.2024 |
Gewicht: | 0,397 kg |