Information geometry and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Tokyo
Springer
[2016]
|
| Series: | Applied mathematical sciences
volume 194 |
| Subjects: | |
| Online Access: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UBY01 UEI01 UPA01 Volltext Abstract Inhaltsverzeichnis |
| Physical Description: | 1 Online Ressource (XIII, 373 Seiten, 94 illus) |
| ISBN: | 9784431559788 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-4-431-55978-8 |
Staff View
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Record in the Search Index
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| adam_text | INFORMATION GEOMETRY AND ITS APPLICATIONS
/ AMARI, SHUN-ICHI
: 2016
ABSTRACT / INHALTSTEXT
THIS IS THE FIRST COMPREHENSIVE BOOK ON INFORMATION GEOMETRY, WRITTEN BY
THE FOUNDER OF THE FIELD. IT BEGINS WITH AN ELEMENTARY INTRODUCTION TO
DUALISTIC GEOMETRY AND PROCEEDS TO A WIDE RANGE OF APPLICATIONS,
COVERING INFORMATION SCIENCE, ENGINEERING, AND NEUROSCIENCE. IT CONSISTS
OF FOUR PARTS, WHICH ON THE WHOLE CAN BE READ INDEPENDENTLY. A MANIFOLD
WITH A DIVERGENCE FUNCTION IS FIRST INTRODUCED, LEADING DIRECTLY TO
DUALISTIC STRUCTURE, THE HEART OF INFORMATION GEOMETRY. THIS PART (PART
I) CAN BE APPREHENDED WITHOUT ANY KNOWLEDGE OF DIFFERENTIAL GEOMETRY. AN
INTUITIVE EXPLANATION OF MODERN DIFFERENTIAL GEOMETRY THEN FOLLOWS IN
PART II, ALTHOUGH THE BOOK IS FOR THE MOST PART UNDERSTANDABLE WITHOUT
MODERN DIFFERENTIAL GEOMETRY. INFORMATION GEOMETRY OF STATISTICAL
INFERENCE, INCLUDING TIME SERIES ANALYSIS AND SEMIPARAMETRIC ESTIMATION
(THE NEYMAN–SCOTT PROBLEM), IS DEMONSTRATED CONCISELY IN PART III.
APPLICATIONS ADDRESSED IN PART IV INCLUDE HOT CURRENT TOPICS IN MACHINE
LEARNING, SIGNAL PROCESSING, OPTIMIZATION, AND NEURAL NETWORKS. THE BOOK
IS INTERDISCIPLINARY, CONNECTING MATHEMATICS, INFORMATION SCIENCES,
PHYSICS, AND NEUROSCIENCES, INVITING READERS TO A NEW WORLD OF
INFORMATION AND GEOMETRY. THIS BOOK IS HIGHLY RECOMMENDED TO GRADUATE
STUDENTS AND RESEARCHERS WHO SEEK NEW MATHEMATICAL METHODS AND TOOLS
USEFUL IN THEIR OWN FIELDS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
INFORMATION GEOMETRY AND ITS APPLICATIONS
/ AMARI, SHUN-ICHI
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
1 MANIFOLD, DIVERGENCE AND DUALLY FLAT STRUCTURE
2 EXPONENTIAL FAMILIES AND MIXTURE FAMILIES OF PROBABILITY
3 INVARIANT GEOMETRY OF MANIFOLD OF PROBABILITY
4 Α-GEOMETRY, TSALLIS Q-ENTROPY AND POSITIVE-DEFINITE
5 ELEMENTS OF DIFFERENTIAL GEOMETRY
6 DUAL AFFINE CONNECTIONS AND DUALLY FLAT MANIFOLD
7 ASYMPTOTIC THEORY OF STATISTICAL INFERENCE
8 ESTIMATION IN THE PRESENCE OF HIDDEN VARIABLES
9 NEYMAN–SCOTT PROBLEM
10 LINEAR SYSTEMS AND TIME SERIES
11 MACHINE LEARNING
12 NATURAL GRADIENT LEARNING AND ITS DYNAMICS IN SINGULAR
13 SIGNAL PROCESSING AND OPTIMIZATION
INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Amari, Shun'ichi 1936- |
| author_GND | (DE-588)1055752951 |
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| author_role | aut |
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| author_variant | s a sa |
| building | Verbundindex |
| bvnumber | BV043423061 |
| callnumber-first | Q - Science |
| callnumber-label | QA1-939 |
| callnumber-raw | QA1-939 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)943763469 (DE-599)BVBBV043423061 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-4-431-55978-8 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:25:30Z |
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| isbn | 9784431559788 |
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| spelling | Amari, Shun'ichi 1936- Verfasser (DE-588)1055752951 aut Information geometry and its applications Shun-ichi Amari Tokyo Springer [2016] © 2016 1 Online Ressource (XIII, 373 Seiten, 94 illus) txt rdacontent c rdamedia cr rdacarrier Applied mathematical sciences volume 194 0066-5452 Mathematics Computer science / Mathematics Computer mathematics Differential geometry Statistics Differential Geometry Mathematical Applications in Computer Science Statistical Theory and Methods Informatik Mathematik Statistik Informationsgeometrie (DE-588)1029624550 gnd rswk-swf Informationsgeometrie (DE-588)1029624550 s DE-604 Erscheint auch als Druckausgabe 978-4-431-55977-1 Applied mathematical sciences volume 194 (DE-604)BV040244599 194 https://doi.org/10.1007/978-4-431-55978-8 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840953&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840953&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Amari, Shun'ichi 1936- Information geometry and its applications Applied mathematical sciences Mathematics Computer science / Mathematics Computer mathematics Differential geometry Statistics Differential Geometry Mathematical Applications in Computer Science Statistical Theory and Methods Informatik Mathematik Statistik Informationsgeometrie (DE-588)1029624550 gnd |
| subject_GND | (DE-588)1029624550 |
| title | Information geometry and its applications |
| title_auth | Information geometry and its applications |
| title_exact_search | Information geometry and its applications |
| title_full | Information geometry and its applications Shun-ichi Amari |
| title_fullStr | Information geometry and its applications Shun-ichi Amari |
| title_full_unstemmed | Information geometry and its applications Shun-ichi Amari |
| title_short | Information geometry and its applications |
| title_sort | information geometry and its applications |
| topic | Mathematics Computer science / Mathematics Computer mathematics Differential geometry Statistics Differential Geometry Mathematical Applications in Computer Science Statistical Theory and Methods Informatik Mathematik Statistik Informationsgeometrie (DE-588)1029624550 gnd |
| topic_facet | Mathematics Computer science / Mathematics Computer mathematics Differential geometry Statistics Differential Geometry Mathematical Applications in Computer Science Statistical Theory and Methods Informatik Mathematik Statistik Informationsgeometrie |
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