Warped Metrics for Location-Scale Models View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2017-10-24

AUTHORS

Salem Said , Yannick Berthoumieu

ABSTRACT

This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results: (i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invariance condition, (ii) the analytic expression of the sectional curvature of this metric, (iii) the exact analytic solution of the geodesic equation of this metric. The paper applies these new results to several examples of interest, where it shows that warped metrics turn location-scale models into complete Riemannian manifolds of negative sectional curvature. This is a very suitable situation for developing algorithms which solve problems of classification and on-line estimation. Thus, by revealing the connection between warped metrics and location-scale models, the present paper paves the way to the introduction of new efficient statistical algorithms. More... »

PAGES

631-638

References to SciGraph publications

Book

TITLE

Geometric Science of Information

ISBN

978-3-319-68444-4
978-3-319-68445-1

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-68445-1_73

DOI

http://dx.doi.org/10.1007/978-3-319-68445-1_73

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1092381058


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Bordeaux", 
          "id": "https://www.grid.ac/institutes/grid.412041.2", 
          "name": [
            "Laboratoire IMS (CNRS - UMR 5218), Universit\u00e9 de Bordeaux, Bordeaux, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Said", 
        "givenName": "Salem", 
        "id": "sg:person.016161076243.21", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016161076243.21"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Bordeaux", 
          "id": "https://www.grid.ac/institutes/grid.412041.2", 
          "name": [
            "Laboratoire IMS (CNRS - UMR 5218), Universit\u00e9 de Bordeaux, Bordeaux, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Berthoumieu", 
        "givenName": "Yannick", 
        "id": "sg:person.010636166221.26", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010636166221.26"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1032041249", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-18855-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032041249", 
          "https://doi.org/10.1007/978-3-642-18855-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-18855-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032041249", 
          "https://doi.org/10.1007/978-3-642-18855-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tit.2017.2653803", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1084206540"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tit.2017.2713829", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1085953112"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4757-2201-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1109705737", 
          "https://doi.org/10.1007/978-1-4757-2201-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4757-2201-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1109705737", 
          "https://doi.org/10.1007/978-1-4757-2201-7"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2017-10-24", 
    "datePublishedReg": "2017-10-24", 
    "description": "This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results: (i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invariance condition, (ii) the analytic expression of the sectional curvature of this metric, (iii) the exact analytic solution of the geodesic equation of this metric. The paper applies these new results to several examples of interest, where it shows that warped metrics turn location-scale models into complete Riemannian manifolds of negative sectional curvature. This is a very suitable situation for developing algorithms which solve problems of classification and on-line estimation. Thus, by revealing the connection between warped metrics and location-scale models, the present paper paves the way to the introduction of new efficient statistical algorithms.", 
    "editor": [
      {
        "familyName": "Nielsen", 
        "givenName": "Frank", 
        "type": "Person"
      }, 
      {
        "familyName": "Barbaresco", 
        "givenName": "Fr\u00e9d\u00e9ric", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-319-68445-1_73", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": {
      "isbn": [
        "978-3-319-68444-4", 
        "978-3-319-68445-1"
      ], 
      "name": "Geometric Science of Information", 
      "type": "Book"
    }, 
    "name": "Warped Metrics for Location-Scale Models", 
    "pagination": "631-638", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-319-68445-1_73"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "9db0074d7c1742438d83e3834a0054a4c5bb3232f11c95b19d168c87299c2d12"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1092381058"
        ]
      }
    ], 
    "publisher": {
      "location": "Cham", 
      "name": "Springer International Publishing", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-319-68445-1_73", 
      "https://app.dimensions.ai/details/publication/pub.1092381058"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-16T05:01", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000325_0000000325/records_100801_00000000.jsonl", 
    "type": "Chapter", 
    "url": "https://link.springer.com/10.1007%2F978-3-319-68445-1_73"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-68445-1_73'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-68445-1_73'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-68445-1_73'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-68445-1_73'


 

This table displays all metadata directly associated to this object as RDF triples.

93 TRIPLES      23 PREDICATES      31 URIs      19 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-319-68445-1_73 schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author N721e74bfb8e848dcb93c8e1677e132fc
4 schema:citation sg:pub.10.1007/978-1-4757-2201-7
5 sg:pub.10.1007/978-3-642-18855-8
6 https://app.dimensions.ai/details/publication/pub.1032041249
7 https://doi.org/10.1109/tit.2017.2653803
8 https://doi.org/10.1109/tit.2017.2713829
9 schema:datePublished 2017-10-24
10 schema:datePublishedReg 2017-10-24
11 schema:description This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results: (i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invariance condition, (ii) the analytic expression of the sectional curvature of this metric, (iii) the exact analytic solution of the geodesic equation of this metric. The paper applies these new results to several examples of interest, where it shows that warped metrics turn location-scale models into complete Riemannian manifolds of negative sectional curvature. This is a very suitable situation for developing algorithms which solve problems of classification and on-line estimation. Thus, by revealing the connection between warped metrics and location-scale models, the present paper paves the way to the introduction of new efficient statistical algorithms.
12 schema:editor N2fc2bd9cefec4ba9855afce8f30077ad
13 schema:genre chapter
14 schema:inLanguage en
15 schema:isAccessibleForFree true
16 schema:isPartOf Nfe2560e15acf4df7952ed5a18b9710e2
17 schema:name Warped Metrics for Location-Scale Models
18 schema:pagination 631-638
19 schema:productId N48cdef94e7484582acb4cd7b7c67eb15
20 Ne566b309e4eb4a26b4c740924c6e7c8a
21 Nf09977c2be284ed790ef99e05855d3b5
22 schema:publisher Ndfbb84a73a5d4da0b8f75c226071bacb
23 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092381058
24 https://doi.org/10.1007/978-3-319-68445-1_73
25 schema:sdDatePublished 2019-04-16T05:01
26 schema:sdLicense https://scigraph.springernature.com/explorer/license/
27 schema:sdPublisher N728f7533328f4639a502b21ea5025612
28 schema:url https://link.springer.com/10.1007%2F978-3-319-68445-1_73
29 sgo:license sg:explorer/license/
30 sgo:sdDataset chapters
31 rdf:type schema:Chapter
32 N170d33c5216c425785ad1fe70d3a76d5 rdf:first N9252156fb2fc4e4b9d78172dd825bcbb
33 rdf:rest rdf:nil
34 N2fc2bd9cefec4ba9855afce8f30077ad rdf:first Nc629aa8628f34379bfa694bb5f8406ce
35 rdf:rest N170d33c5216c425785ad1fe70d3a76d5
36 N48cdef94e7484582acb4cd7b7c67eb15 schema:name doi
37 schema:value 10.1007/978-3-319-68445-1_73
38 rdf:type schema:PropertyValue
39 N4cf7f6f8d1ab4e55ab56aaf57f226323 rdf:first sg:person.010636166221.26
40 rdf:rest rdf:nil
41 N721e74bfb8e848dcb93c8e1677e132fc rdf:first sg:person.016161076243.21
42 rdf:rest N4cf7f6f8d1ab4e55ab56aaf57f226323
43 N728f7533328f4639a502b21ea5025612 schema:name Springer Nature - SN SciGraph project
44 rdf:type schema:Organization
45 N9252156fb2fc4e4b9d78172dd825bcbb schema:familyName Barbaresco
46 schema:givenName Frédéric
47 rdf:type schema:Person
48 Nc629aa8628f34379bfa694bb5f8406ce schema:familyName Nielsen
49 schema:givenName Frank
50 rdf:type schema:Person
51 Ndfbb84a73a5d4da0b8f75c226071bacb schema:location Cham
52 schema:name Springer International Publishing
53 rdf:type schema:Organisation
54 Ne566b309e4eb4a26b4c740924c6e7c8a schema:name dimensions_id
55 schema:value pub.1092381058
56 rdf:type schema:PropertyValue
57 Nf09977c2be284ed790ef99e05855d3b5 schema:name readcube_id
58 schema:value 9db0074d7c1742438d83e3834a0054a4c5bb3232f11c95b19d168c87299c2d12
59 rdf:type schema:PropertyValue
60 Nfe2560e15acf4df7952ed5a18b9710e2 schema:isbn 978-3-319-68444-4
61 978-3-319-68445-1
62 schema:name Geometric Science of Information
63 rdf:type schema:Book
64 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
65 schema:name Mathematical Sciences
66 rdf:type schema:DefinedTerm
67 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
68 schema:name Statistics
69 rdf:type schema:DefinedTerm
70 sg:person.010636166221.26 schema:affiliation https://www.grid.ac/institutes/grid.412041.2
71 schema:familyName Berthoumieu
72 schema:givenName Yannick
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010636166221.26
74 rdf:type schema:Person
75 sg:person.016161076243.21 schema:affiliation https://www.grid.ac/institutes/grid.412041.2
76 schema:familyName Said
77 schema:givenName Salem
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016161076243.21
79 rdf:type schema:Person
80 sg:pub.10.1007/978-1-4757-2201-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1109705737
81 https://doi.org/10.1007/978-1-4757-2201-7
82 rdf:type schema:CreativeWork
83 sg:pub.10.1007/978-3-642-18855-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032041249
84 https://doi.org/10.1007/978-3-642-18855-8
85 rdf:type schema:CreativeWork
86 https://app.dimensions.ai/details/publication/pub.1032041249 schema:CreativeWork
87 https://doi.org/10.1109/tit.2017.2653803 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084206540
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1109/tit.2017.2713829 schema:sameAs https://app.dimensions.ai/details/publication/pub.1085953112
90 rdf:type schema:CreativeWork
91 https://www.grid.ac/institutes/grid.412041.2 schema:alternateName University of Bordeaux
92 schema:name Laboratoire IMS (CNRS - UMR 5218), Université de Bordeaux, Bordeaux, France
93 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...