Entropic Trace Estimates for Log Determinants View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2017-12-30

AUTHORS

Jack Fitzsimons , Diego Granziol , Kurt Cutajar , Michael Osborne , Maurizio Filippone , Stephen Roberts

ABSTRACT

The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework of maximum entropy, given information in the form of moment constraints from stochastic trace estimation. The estimates demonstrate a significant improvement on state-of-the-art alternative methods, as shown on a wide variety of matrices from the SparseSuite Matrix Collection. By taking the example of a general Markov random field, we also demonstrate how this approach can significantly accelerate inference in large-scale learning methods involving the log determinant. More... »

PAGES

323-338

Book

TITLE

Machine Learning and Knowledge Discovery in Databases

ISBN

978-3-319-71248-2
978-3-319-71249-9

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-71249-9_20

DOI

http://dx.doi.org/10.1007/978-3-319-71249-9_20

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1100108927


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/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "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"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Engineering, University of Oxford, Oxford, UK", 
          "id": "http://www.grid.ac/institutes/grid.4991.5", 
          "name": [
            "Department of Engineering, University of Oxford, Oxford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Fitzsimons", 
        "givenName": "Jack", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Engineering, University of Oxford, Oxford, UK", 
          "id": "http://www.grid.ac/institutes/grid.4991.5", 
          "name": [
            "Department of Engineering, University of Oxford, Oxford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Granziol", 
        "givenName": "Diego", 
        "id": "sg:person.015405772230.64", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015405772230.64"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Data Science, EURECOM, Biot, France", 
          "id": "http://www.grid.ac/institutes/grid.28848.3e", 
          "name": [
            "Department of Data Science, EURECOM, Biot, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Cutajar", 
        "givenName": "Kurt", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Engineering, University of Oxford, Oxford, UK", 
          "id": "http://www.grid.ac/institutes/grid.4991.5", 
          "name": [
            "Department of Engineering, University of Oxford, Oxford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Osborne", 
        "givenName": "Michael", 
        "id": "sg:person.01157442331.45", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01157442331.45"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Data Science, EURECOM, Biot, France", 
          "id": "http://www.grid.ac/institutes/grid.28848.3e", 
          "name": [
            "Department of Data Science, EURECOM, Biot, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Filippone", 
        "givenName": "Maurizio", 
        "id": "sg:person.07706215665.03", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07706215665.03"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Engineering, University of Oxford, Oxford, UK", 
          "id": "http://www.grid.ac/institutes/grid.4991.5", 
          "name": [
            "Department of Engineering, University of Oxford, Oxford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Roberts", 
        "givenName": "Stephen", 
        "id": "sg:person.01215233070.04", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01215233070.04"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2017-12-30", 
    "datePublishedReg": "2017-12-30", 
    "description": "The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework of maximum entropy, given information in the form of moment constraints from stochastic trace estimation. The estimates demonstrate a significant improvement on state-of-the-art alternative methods, as shown on a wide variety of matrices from the SparseSuite Matrix Collection. By taking the example of a general Markov random field, we also demonstrate how this approach can significantly accelerate inference in large-scale learning methods involving the log determinant.", 
    "editor": [
      {
        "familyName": "Ceci", 
        "givenName": "Michelangelo", 
        "type": "Person"
      }, 
      {
        "familyName": "Hollm\u00e9n", 
        "givenName": "Jaakko", 
        "type": "Person"
      }, 
      {
        "familyName": "Todorovski", 
        "givenName": "Ljup\u010do", 
        "type": "Person"
      }, 
      {
        "familyName": "Vens", 
        "givenName": "Celine", 
        "type": "Person"
      }, 
      {
        "familyName": "D\u017eeroski", 
        "givenName": "Sa\u0161o", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-319-71249-9_20", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isPartOf": {
      "isbn": [
        "978-3-319-71248-2", 
        "978-3-319-71249-9"
      ], 
      "name": "Machine Learning and Knowledge Discovery in Databases", 
      "type": "Book"
    }, 
    "keywords": [
      "log determinant", 
      "Markov random field", 
      "random fields", 
      "general Markov random fields", 
      "art alternative methods", 
      "determinantal point processes", 
      "trace estimates", 
      "scalable calculation", 
      "trace estimation", 
      "moment constraints", 
      "point process", 
      "Gaussian process", 
      "matrix determinant", 
      "matrix collection", 
      "graph model", 
      "learning method", 
      "estimates", 
      "inference", 
      "alternative method", 
      "estimation", 
      "constraints", 
      "matrix", 
      "widespread application", 
      "wide variety", 
      "framework", 
      "model", 
      "field", 
      "approach", 
      "machine", 
      "applications", 
      "bottleneck", 
      "calculations", 
      "form", 
      "process", 
      "work", 
      "state", 
      "information", 
      "significant improvement", 
      "variety", 
      "collection", 
      "improvement", 
      "determinants", 
      "method", 
      "example", 
      "generalised Markov random fields", 
      "stochastic trace estimation", 
      "SparseSuite Matrix Collection", 
      "large-scale learning methods", 
      "Entropic Trace Estimates"
    ], 
    "name": "Entropic Trace Estimates for Log Determinants", 
    "pagination": "323-338", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1100108927"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-319-71249-9_20"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-319-71249-9_20", 
      "https://app.dimensions.ai/details/publication/pub.1100108927"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-01-01T19:12", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/chapter/chapter_221.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-319-71249-9_20"
  }
]
 

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.10.1007/978-3-319-71249-9_20'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-71249-9_20'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-71249-9_20'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-71249-9_20'


 

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

165 TRIPLES      23 PREDICATES      74 URIs      67 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-319-71249-9_20 schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author N2085656d86084fc18a6cd12f8df11a2b
4 schema:datePublished 2017-12-30
5 schema:datePublishedReg 2017-12-30
6 schema:description The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework of maximum entropy, given information in the form of moment constraints from stochastic trace estimation. The estimates demonstrate a significant improvement on state-of-the-art alternative methods, as shown on a wide variety of matrices from the SparseSuite Matrix Collection. By taking the example of a general Markov random field, we also demonstrate how this approach can significantly accelerate inference in large-scale learning methods involving the log determinant.
7 schema:editor Na96d36f7692f496b9ee73e4ee39eb185
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree true
11 schema:isPartOf N9b06bc11a7b441a5b4956935a7683f87
12 schema:keywords Entropic Trace Estimates
13 Gaussian process
14 Markov random field
15 SparseSuite Matrix Collection
16 alternative method
17 applications
18 approach
19 art alternative methods
20 bottleneck
21 calculations
22 collection
23 constraints
24 determinantal point processes
25 determinants
26 estimates
27 estimation
28 example
29 field
30 form
31 framework
32 general Markov random fields
33 generalised Markov random fields
34 graph model
35 improvement
36 inference
37 information
38 large-scale learning methods
39 learning method
40 log determinant
41 machine
42 matrix
43 matrix collection
44 matrix determinant
45 method
46 model
47 moment constraints
48 point process
49 process
50 random fields
51 scalable calculation
52 significant improvement
53 state
54 stochastic trace estimation
55 trace estimates
56 trace estimation
57 variety
58 wide variety
59 widespread application
60 work
61 schema:name Entropic Trace Estimates for Log Determinants
62 schema:pagination 323-338
63 schema:productId N9f8ed0fb6c924962ac779dc0333a30e9
64 Ncad283e9380447dea8035ca7404308c9
65 schema:publisher N5b9cd588d6e14297be2de1cc59691a38
66 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100108927
67 https://doi.org/10.1007/978-3-319-71249-9_20
68 schema:sdDatePublished 2022-01-01T19:12
69 schema:sdLicense https://scigraph.springernature.com/explorer/license/
70 schema:sdPublisher Nff272ee030bc44ecbea5e2d86642c1f3
71 schema:url https://doi.org/10.1007/978-3-319-71249-9_20
72 sgo:license sg:explorer/license/
73 sgo:sdDataset chapters
74 rdf:type schema:Chapter
75 N2085656d86084fc18a6cd12f8df11a2b rdf:first Nd24e70c79dee47f69d27899a4f121328
76 rdf:rest Nf25cffa43fcc497bb9e43b49539dcf2b
77 N21bb6437b81343fda54883c02d514524 rdf:first N571d0a42648b4eeeaa0ecedbc85a770c
78 rdf:rest Nc4633e4fcac54cc9a9763a92e1bbeabf
79 N272de2d281574bbabf5fb4dd9ef0ba46 schema:familyName Todorovski
80 schema:givenName Ljupčo
81 rdf:type schema:Person
82 N28a53518c72c48f09ec3ccd1d46aa479 rdf:first N326fb4c5590c44e1a017a9ed8d0d19dc
83 rdf:rest Nabfd828238f645e2a8898c29aa8cc32d
84 N326fb4c5590c44e1a017a9ed8d0d19dc schema:familyName Hollmén
85 schema:givenName Jaakko
86 rdf:type schema:Person
87 N571d0a42648b4eeeaa0ecedbc85a770c schema:affiliation grid-institutes:grid.28848.3e
88 schema:familyName Cutajar
89 schema:givenName Kurt
90 rdf:type schema:Person
91 N5b9cd588d6e14297be2de1cc59691a38 schema:name Springer Nature
92 rdf:type schema:Organisation
93 N6bc7c2e2492649e9b8ae86af4a2e3d17 rdf:first Nca93dd4d48c14dd89715359f300d4aad
94 rdf:rest rdf:nil
95 N8576a78b5e394d81806eece38e8d8869 rdf:first sg:person.07706215665.03
96 rdf:rest Nc579fa343cab4c818efa09c9093b998b
97 N9b06bc11a7b441a5b4956935a7683f87 schema:isbn 978-3-319-71248-2
98 978-3-319-71249-9
99 schema:name Machine Learning and Knowledge Discovery in Databases
100 rdf:type schema:Book
101 N9b77419abb7f4f39a2a05beb55542f97 schema:familyName Vens
102 schema:givenName Celine
103 rdf:type schema:Person
104 N9f8ed0fb6c924962ac779dc0333a30e9 schema:name dimensions_id
105 schema:value pub.1100108927
106 rdf:type schema:PropertyValue
107 Na96d36f7692f496b9ee73e4ee39eb185 rdf:first Nb534029ab4004a799157734c5da3ca74
108 rdf:rest N28a53518c72c48f09ec3ccd1d46aa479
109 Nabfd828238f645e2a8898c29aa8cc32d rdf:first N272de2d281574bbabf5fb4dd9ef0ba46
110 rdf:rest Ncbe59490fbe74914b3be6ae315ed2c59
111 Nb534029ab4004a799157734c5da3ca74 schema:familyName Ceci
112 schema:givenName Michelangelo
113 rdf:type schema:Person
114 Nc4633e4fcac54cc9a9763a92e1bbeabf rdf:first sg:person.01157442331.45
115 rdf:rest N8576a78b5e394d81806eece38e8d8869
116 Nc579fa343cab4c818efa09c9093b998b rdf:first sg:person.01215233070.04
117 rdf:rest rdf:nil
118 Nca93dd4d48c14dd89715359f300d4aad schema:familyName Džeroski
119 schema:givenName Sašo
120 rdf:type schema:Person
121 Ncad283e9380447dea8035ca7404308c9 schema:name doi
122 schema:value 10.1007/978-3-319-71249-9_20
123 rdf:type schema:PropertyValue
124 Ncbe59490fbe74914b3be6ae315ed2c59 rdf:first N9b77419abb7f4f39a2a05beb55542f97
125 rdf:rest N6bc7c2e2492649e9b8ae86af4a2e3d17
126 Nd24e70c79dee47f69d27899a4f121328 schema:affiliation grid-institutes:grid.4991.5
127 schema:familyName Fitzsimons
128 schema:givenName Jack
129 rdf:type schema:Person
130 Nf25cffa43fcc497bb9e43b49539dcf2b rdf:first sg:person.015405772230.64
131 rdf:rest N21bb6437b81343fda54883c02d514524
132 Nff272ee030bc44ecbea5e2d86642c1f3 schema:name Springer Nature - SN SciGraph project
133 rdf:type schema:Organization
134 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
135 schema:name Mathematical Sciences
136 rdf:type schema:DefinedTerm
137 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
138 schema:name Statistics
139 rdf:type schema:DefinedTerm
140 sg:person.01157442331.45 schema:affiliation grid-institutes:grid.4991.5
141 schema:familyName Osborne
142 schema:givenName Michael
143 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01157442331.45
144 rdf:type schema:Person
145 sg:person.01215233070.04 schema:affiliation grid-institutes:grid.4991.5
146 schema:familyName Roberts
147 schema:givenName Stephen
148 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01215233070.04
149 rdf:type schema:Person
150 sg:person.015405772230.64 schema:affiliation grid-institutes:grid.4991.5
151 schema:familyName Granziol
152 schema:givenName Diego
153 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015405772230.64
154 rdf:type schema:Person
155 sg:person.07706215665.03 schema:affiliation grid-institutes:grid.28848.3e
156 schema:familyName Filippone
157 schema:givenName Maurizio
158 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07706215665.03
159 rdf:type schema:Person
160 grid-institutes:grid.28848.3e schema:alternateName Department of Data Science, EURECOM, Biot, France
161 schema:name Department of Data Science, EURECOM, Biot, France
162 rdf:type schema:Organization
163 grid-institutes:grid.4991.5 schema:alternateName Department of Engineering, University of Oxford, Oxford, UK
164 schema:name Department of Engineering, University of Oxford, Oxford, UK
165 rdf:type schema:Organization
 




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


...