A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

1998

AUTHORS

Radford M. Neal , Geoffrey E. Hinton

ABSTRACT

The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the distribution over the unobserved variables. From this perspective, it is easy to justify an incremental variant of the EM algorithm in which the distribution for only one of the unobserved variables is recalculated in each E step. This variant is shown empirically to give faster convergence in a mixture estimation problem. A variant of the algorithm that exploits sparse conditional distributions is also described, and a wide range of other variant algorithms are also seen to be possible. More... »

PAGES

355-368

Book

TITLE

Learning in Graphical Models

ISBN

978-94-010-6104-9
978-94-011-5014-9

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-94-011-5014-9_12

DOI

http://dx.doi.org/10.1007/978-94-011-5014-9_12

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009494930


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/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational Mathematics", 
        "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 Toronto", 
          "id": "https://www.grid.ac/institutes/grid.17063.33", 
          "name": [
            "Dept. of Statistics and Dept. of Computer Science, University of Toronto, Toronto, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Neal", 
        "givenName": "Radford M.", 
        "id": "sg:person.07677172755.27", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07677172755.27"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Toronto", 
          "id": "https://www.grid.ac/institutes/grid.17063.33", 
          "name": [
            "Department of Computer Science, University of Toronto, Toronto, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hinton", 
        "givenName": "Geoffrey E.", 
        "id": "sg:person.0615147542.17", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0615147542.17"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/0167-7152(86)90016-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016253042"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0167-7152(86)90016-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016253042"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1111/1467-9868.00082", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021869359"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1998", 
    "datePublishedReg": "1998-01-01", 
    "description": "The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the distribution over the unobserved variables. From this perspective, it is easy to justify an incremental variant of the EM algorithm in which the distribution for only one of the unobserved variables is recalculated in each E step. This variant is shown empirically to give faster convergence in a mixture estimation problem. A variant of the algorithm that exploits sparse conditional distributions is also described, and a wide range of other variant algorithms are also seen to be possible.", 
    "editor": [
      {
        "familyName": "Jordan", 
        "givenName": "Michael I.", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-94-011-5014-9_12", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": {
      "isbn": [
        "978-94-010-6104-9", 
        "978-94-011-5014-9"
      ], 
      "name": "Learning in Graphical Models", 
      "type": "Book"
    }, 
    "name": "A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants", 
    "pagination": "355-368", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-94-011-5014-9_12"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "2d3abc1f5dad12b0910bcec46e23443c19b1f7e08be428998e4ba18d9c5a2b89"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1009494930"
        ]
      }
    ], 
    "publisher": {
      "location": "Dordrecht", 
      "name": "Springer Netherlands", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-94-011-5014-9_12", 
      "https://app.dimensions.ai/details/publication/pub.1009494930"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T17:47", 
    "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/v90/0000000001_0000000264/records_8678_00000553.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-94-011-5014-9_12"
  }
]
 

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.10.1007/978-94-011-5014-9_12'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-5014-9_12'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-5014-9_12'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-5014-9_12'


 

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

79 TRIPLES      23 PREDICATES      29 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-94-011-5014-9_12 schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author N3ac3af1bd47d4c729668773fbc825d43
4 schema:citation https://doi.org/10.1016/0167-7152(86)90016-7
5 https://doi.org/10.1111/1467-9868.00082
6 schema:datePublished 1998
7 schema:datePublishedReg 1998-01-01
8 schema:description The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the distribution over the unobserved variables. From this perspective, it is easy to justify an incremental variant of the EM algorithm in which the distribution for only one of the unobserved variables is recalculated in each E step. This variant is shown empirically to give faster convergence in a mixture estimation problem. A variant of the algorithm that exploits sparse conditional distributions is also described, and a wide range of other variant algorithms are also seen to be possible.
9 schema:editor N3cac5c32eead4351a8e56dbc05643c1a
10 schema:genre chapter
11 schema:inLanguage en
12 schema:isAccessibleForFree true
13 schema:isPartOf Nbfce5d32468d41ecab2d3dfdee72d012
14 schema:name A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants
15 schema:pagination 355-368
16 schema:productId N0928a3fa1cd44a52a29cd5e11ecd95c2
17 N2101d07837534c0a844c8d615bef0a3e
18 N900a7f6af5824722b245ef5aa1ab3bdf
19 schema:publisher Ne1d267f11fdb463d94b699275cab4ae4
20 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009494930
21 https://doi.org/10.1007/978-94-011-5014-9_12
22 schema:sdDatePublished 2019-04-15T17:47
23 schema:sdLicense https://scigraph.springernature.com/explorer/license/
24 schema:sdPublisher N8f3ebb9b2da64b499e9013412e00566a
25 schema:url http://link.springer.com/10.1007/978-94-011-5014-9_12
26 sgo:license sg:explorer/license/
27 sgo:sdDataset chapters
28 rdf:type schema:Chapter
29 N0928a3fa1cd44a52a29cd5e11ecd95c2 schema:name dimensions_id
30 schema:value pub.1009494930
31 rdf:type schema:PropertyValue
32 N2101d07837534c0a844c8d615bef0a3e schema:name readcube_id
33 schema:value 2d3abc1f5dad12b0910bcec46e23443c19b1f7e08be428998e4ba18d9c5a2b89
34 rdf:type schema:PropertyValue
35 N3ac3af1bd47d4c729668773fbc825d43 rdf:first sg:person.07677172755.27
36 rdf:rest Nbf28743400814d08aef2308b2b94ab7a
37 N3cac5c32eead4351a8e56dbc05643c1a rdf:first N774bf82ae97f49ec8cd682dc231c1b45
38 rdf:rest rdf:nil
39 N774bf82ae97f49ec8cd682dc231c1b45 schema:familyName Jordan
40 schema:givenName Michael I.
41 rdf:type schema:Person
42 N8f3ebb9b2da64b499e9013412e00566a schema:name Springer Nature - SN SciGraph project
43 rdf:type schema:Organization
44 N900a7f6af5824722b245ef5aa1ab3bdf schema:name doi
45 schema:value 10.1007/978-94-011-5014-9_12
46 rdf:type schema:PropertyValue
47 Nbf28743400814d08aef2308b2b94ab7a rdf:first sg:person.0615147542.17
48 rdf:rest rdf:nil
49 Nbfce5d32468d41ecab2d3dfdee72d012 schema:isbn 978-94-010-6104-9
50 978-94-011-5014-9
51 schema:name Learning in Graphical Models
52 rdf:type schema:Book
53 Ne1d267f11fdb463d94b699275cab4ae4 schema:location Dordrecht
54 schema:name Springer Netherlands
55 rdf:type schema:Organisation
56 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
57 schema:name Mathematical Sciences
58 rdf:type schema:DefinedTerm
59 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
60 schema:name Numerical and Computational Mathematics
61 rdf:type schema:DefinedTerm
62 sg:person.0615147542.17 schema:affiliation https://www.grid.ac/institutes/grid.17063.33
63 schema:familyName Hinton
64 schema:givenName Geoffrey E.
65 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0615147542.17
66 rdf:type schema:Person
67 sg:person.07677172755.27 schema:affiliation https://www.grid.ac/institutes/grid.17063.33
68 schema:familyName Neal
69 schema:givenName Radford M.
70 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07677172755.27
71 rdf:type schema:Person
72 https://doi.org/10.1016/0167-7152(86)90016-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016253042
73 rdf:type schema:CreativeWork
74 https://doi.org/10.1111/1467-9868.00082 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021869359
75 rdf:type schema:CreativeWork
76 https://www.grid.ac/institutes/grid.17063.33 schema:alternateName University of Toronto
77 schema:name Department of Computer Science, University of Toronto, Toronto, Ontario, Canada
78 Dept. of Statistics and Dept. of Computer Science, University of Toronto, Toronto, Ontario, Canada
79 rdf:type schema:Organization
 




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


...