Learning Bayesian networks: The combination of knowledge and statistical data View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1995-09

AUTHORS

David Heckerman, Dan Geiger, David M. Chickering

ABSTRACT

We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption oflikelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen—aprior network—and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highest-scoring network structures in the special case where every node has at mostk=1 parent. For the general case (k>1), which is NP-hard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesian-network learning algorithms, and apply this approach to a comparison of various approaches. More... »

PAGES

197-243

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00994016

DOI

http://dx.doi.org/10.1007/bf00994016

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1035524560


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": "Microsoft (United States)", 
          "id": "https://www.grid.ac/institutes/grid.419815.0", 
          "name": [
            "Microsoft Research, 9S, 98052-6399, Redmond, WA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Heckerman", 
        "givenName": "David", 
        "id": "sg:person.01134362461.98", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01134362461.98"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Microsoft (United States)", 
          "id": "https://www.grid.ac/institutes/grid.419815.0", 
          "name": [
            "Microsoft Research, 9S, 98052-6399, Redmond, WA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Geiger", 
        "givenName": "Dan", 
        "id": "sg:person.0653041745.45", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0653041745.45"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Microsoft (United States)", 
          "id": "https://www.grid.ac/institutes/grid.419815.0", 
          "name": [
            "Microsoft Research, 9S, 98052-6399, Redmond, WA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Chickering", 
        "givenName": "David M.", 
        "id": "sg:person.011240332636.47", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011240332636.47"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1004816646", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-2748-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004816646", 
          "https://doi.org/10.1007/978-1-4612-2748-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-2748-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004816646", 
          "https://doi.org/10.1007/978-1-4612-2748-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/b978-1-4832-1451-1.50005-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008675702"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1111/j.1539-6924.1988.tb01156.x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012078361"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/b978-1-4832-1451-1.50034-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012131640"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-93437-7_28", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012429812", 
          "https://doi.org/10.1007/978-3-642-93437-7_28"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/b978-1-55860-332-5.50035-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013517653"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/b978-1-55860-332-5.50042-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016450454"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/b978-1-4832-1451-1.50024-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020892954"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0004-3702(93)90045-d", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025341727"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0004-3702(93)90045-d", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025341727"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aoms/1177729694", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026070931"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0010-4809(92)90035-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031375708"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0010-4809(92)90035-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031375708"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/b978-1-55860-203-8.50010-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1034203065"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/net.3230070103", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038102583"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/net.3230010305", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044610968"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/net.3230200507", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045466199"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00994110", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046316965", 
          "https://doi.org/10.1007/bf00994110"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-011-5430-7_7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046982324", 
          "https://doi.org/10.1007/978-94-011-5430-7_7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-011-5430-7_7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046982324", 
          "https://doi.org/10.1007/978-94-011-5430-7_7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1145/168304.168314", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049465492"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/net.3230100202", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049552581"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/b978-1-4832-1451-1.50037-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052870567"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1699114", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057769646"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1967.10500894", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058300184"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1994.10476894", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058304758"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tit.1968.1054142", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061646459"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aos/1176349260", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064408817"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/ss/1177010888", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064409646"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/sfcs.1984.715935", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1086163608"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/2347231", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1101982136"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/2347231", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1101982136"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1995-09", 
    "datePublishedReg": "1995-09-01", 
    "description": "We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption oflikelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen\u2014aprior network\u2014and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highest-scoring network structures in the special case where every node has at mostk=1 parent. For the general case (k>1), which is NP-hard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesian-network learning algorithms, and apply this approach to a comparison of various approaches.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf00994016", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1125588", 
        "issn": [
          "0885-6125", 
          "1573-0565"
        ], 
        "name": "Machine Learning", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "20"
      }
    ], 
    "name": "Learning Bayesian networks: The combination of knowledge and statistical data", 
    "pagination": "197-243", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "a9393fabec1f0309f78dd95501dd2a4d481f2a245f3b2b381241957e8fe5fa04"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf00994016"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1035524560"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf00994016", 
      "https://app.dimensions.ai/details/publication/pub.1035524560"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T21:33", 
    "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_8687_00000496.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/BF00994016"
  }
]
 

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/bf00994016'

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/bf00994016'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00994016'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00994016'


 

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

165 TRIPLES      21 PREDICATES      56 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf00994016 schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author N653edfe9152144be990ac3e2cd03eeb3
4 schema:citation sg:pub.10.1007/978-1-4612-2748-9
5 sg:pub.10.1007/978-3-642-93437-7_28
6 sg:pub.10.1007/978-94-011-5430-7_7
7 sg:pub.10.1007/bf00994110
8 https://app.dimensions.ai/details/publication/pub.1004816646
9 https://doi.org/10.1002/net.3230010305
10 https://doi.org/10.1002/net.3230070103
11 https://doi.org/10.1002/net.3230100202
12 https://doi.org/10.1002/net.3230200507
13 https://doi.org/10.1016/0004-3702(93)90045-d
14 https://doi.org/10.1016/0010-4809(92)90035-9
15 https://doi.org/10.1016/b978-1-4832-1451-1.50005-6
16 https://doi.org/10.1016/b978-1-4832-1451-1.50024-x
17 https://doi.org/10.1016/b978-1-4832-1451-1.50034-2
18 https://doi.org/10.1016/b978-1-4832-1451-1.50037-8
19 https://doi.org/10.1016/b978-1-55860-203-8.50010-3
20 https://doi.org/10.1016/b978-1-55860-332-5.50035-3
21 https://doi.org/10.1016/b978-1-55860-332-5.50042-0
22 https://doi.org/10.1063/1.1699114
23 https://doi.org/10.1080/01621459.1967.10500894
24 https://doi.org/10.1080/01621459.1994.10476894
25 https://doi.org/10.1109/sfcs.1984.715935
26 https://doi.org/10.1109/tit.1968.1054142
27 https://doi.org/10.1111/j.1539-6924.1988.tb01156.x
28 https://doi.org/10.1145/168304.168314
29 https://doi.org/10.1214/aoms/1177729694
30 https://doi.org/10.1214/aos/1176349260
31 https://doi.org/10.1214/ss/1177010888
32 https://doi.org/10.2307/2347231
33 schema:datePublished 1995-09
34 schema:datePublishedReg 1995-09-01
35 schema:description We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption oflikelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen—aprior network—and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highest-scoring network structures in the special case where every node has at mostk=1 parent. For the general case (k>1), which is NP-hard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesian-network learning algorithms, and apply this approach to a comparison of various approaches.
36 schema:genre research_article
37 schema:inLanguage en
38 schema:isAccessibleForFree true
39 schema:isPartOf N7323abe86fb741a585183edd0de4c27a
40 N906bb9254316488397e42f0b8c93128b
41 sg:journal.1125588
42 schema:name Learning Bayesian networks: The combination of knowledge and statistical data
43 schema:pagination 197-243
44 schema:productId N79bcc5a79d2247c3b095cbfc82a14f35
45 Na9a03b88f8314ee1bfed82abab0e0f59
46 Nbad0005508c74d4ea1d7670437cd826c
47 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035524560
48 https://doi.org/10.1007/bf00994016
49 schema:sdDatePublished 2019-04-10T21:33
50 schema:sdLicense https://scigraph.springernature.com/explorer/license/
51 schema:sdPublisher N4507f205ca254433b0a862afc3c884aa
52 schema:url http://link.springer.com/10.1007/BF00994016
53 sgo:license sg:explorer/license/
54 sgo:sdDataset articles
55 rdf:type schema:ScholarlyArticle
56 N2bf45a2bbadd4c21afdaa7e5f5431ebc rdf:first sg:person.0653041745.45
57 rdf:rest Nddc62dd4bceb470ea5ffe7897f7cdcca
58 N4507f205ca254433b0a862afc3c884aa schema:name Springer Nature - SN SciGraph project
59 rdf:type schema:Organization
60 N653edfe9152144be990ac3e2cd03eeb3 rdf:first sg:person.01134362461.98
61 rdf:rest N2bf45a2bbadd4c21afdaa7e5f5431ebc
62 N7323abe86fb741a585183edd0de4c27a schema:issueNumber 3
63 rdf:type schema:PublicationIssue
64 N79bcc5a79d2247c3b095cbfc82a14f35 schema:name dimensions_id
65 schema:value pub.1035524560
66 rdf:type schema:PropertyValue
67 N906bb9254316488397e42f0b8c93128b schema:volumeNumber 20
68 rdf:type schema:PublicationVolume
69 Na9a03b88f8314ee1bfed82abab0e0f59 schema:name doi
70 schema:value 10.1007/bf00994016
71 rdf:type schema:PropertyValue
72 Nbad0005508c74d4ea1d7670437cd826c schema:name readcube_id
73 schema:value a9393fabec1f0309f78dd95501dd2a4d481f2a245f3b2b381241957e8fe5fa04
74 rdf:type schema:PropertyValue
75 Nddc62dd4bceb470ea5ffe7897f7cdcca rdf:first sg:person.011240332636.47
76 rdf:rest rdf:nil
77 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
78 schema:name Mathematical Sciences
79 rdf:type schema:DefinedTerm
80 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
81 schema:name Statistics
82 rdf:type schema:DefinedTerm
83 sg:journal.1125588 schema:issn 0885-6125
84 1573-0565
85 schema:name Machine Learning
86 rdf:type schema:Periodical
87 sg:person.011240332636.47 schema:affiliation https://www.grid.ac/institutes/grid.419815.0
88 schema:familyName Chickering
89 schema:givenName David M.
90 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011240332636.47
91 rdf:type schema:Person
92 sg:person.01134362461.98 schema:affiliation https://www.grid.ac/institutes/grid.419815.0
93 schema:familyName Heckerman
94 schema:givenName David
95 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01134362461.98
96 rdf:type schema:Person
97 sg:person.0653041745.45 schema:affiliation https://www.grid.ac/institutes/grid.419815.0
98 schema:familyName Geiger
99 schema:givenName Dan
100 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0653041745.45
101 rdf:type schema:Person
102 sg:pub.10.1007/978-1-4612-2748-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004816646
103 https://doi.org/10.1007/978-1-4612-2748-9
104 rdf:type schema:CreativeWork
105 sg:pub.10.1007/978-3-642-93437-7_28 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012429812
106 https://doi.org/10.1007/978-3-642-93437-7_28
107 rdf:type schema:CreativeWork
108 sg:pub.10.1007/978-94-011-5430-7_7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046982324
109 https://doi.org/10.1007/978-94-011-5430-7_7
110 rdf:type schema:CreativeWork
111 sg:pub.10.1007/bf00994110 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046316965
112 https://doi.org/10.1007/bf00994110
113 rdf:type schema:CreativeWork
114 https://app.dimensions.ai/details/publication/pub.1004816646 schema:CreativeWork
115 https://doi.org/10.1002/net.3230010305 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044610968
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1002/net.3230070103 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038102583
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1002/net.3230100202 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049552581
120 rdf:type schema:CreativeWork
121 https://doi.org/10.1002/net.3230200507 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045466199
122 rdf:type schema:CreativeWork
123 https://doi.org/10.1016/0004-3702(93)90045-d schema:sameAs https://app.dimensions.ai/details/publication/pub.1025341727
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1016/0010-4809(92)90035-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031375708
126 rdf:type schema:CreativeWork
127 https://doi.org/10.1016/b978-1-4832-1451-1.50005-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008675702
128 rdf:type schema:CreativeWork
129 https://doi.org/10.1016/b978-1-4832-1451-1.50024-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1020892954
130 rdf:type schema:CreativeWork
131 https://doi.org/10.1016/b978-1-4832-1451-1.50034-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012131640
132 rdf:type schema:CreativeWork
133 https://doi.org/10.1016/b978-1-4832-1451-1.50037-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052870567
134 rdf:type schema:CreativeWork
135 https://doi.org/10.1016/b978-1-55860-203-8.50010-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034203065
136 rdf:type schema:CreativeWork
137 https://doi.org/10.1016/b978-1-55860-332-5.50035-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013517653
138 rdf:type schema:CreativeWork
139 https://doi.org/10.1016/b978-1-55860-332-5.50042-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016450454
140 rdf:type schema:CreativeWork
141 https://doi.org/10.1063/1.1699114 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057769646
142 rdf:type schema:CreativeWork
143 https://doi.org/10.1080/01621459.1967.10500894 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058300184
144 rdf:type schema:CreativeWork
145 https://doi.org/10.1080/01621459.1994.10476894 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058304758
146 rdf:type schema:CreativeWork
147 https://doi.org/10.1109/sfcs.1984.715935 schema:sameAs https://app.dimensions.ai/details/publication/pub.1086163608
148 rdf:type schema:CreativeWork
149 https://doi.org/10.1109/tit.1968.1054142 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061646459
150 rdf:type schema:CreativeWork
151 https://doi.org/10.1111/j.1539-6924.1988.tb01156.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1012078361
152 rdf:type schema:CreativeWork
153 https://doi.org/10.1145/168304.168314 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049465492
154 rdf:type schema:CreativeWork
155 https://doi.org/10.1214/aoms/1177729694 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026070931
156 rdf:type schema:CreativeWork
157 https://doi.org/10.1214/aos/1176349260 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064408817
158 rdf:type schema:CreativeWork
159 https://doi.org/10.1214/ss/1177010888 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064409646
160 rdf:type schema:CreativeWork
161 https://doi.org/10.2307/2347231 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101982136
162 rdf:type schema:CreativeWork
163 https://www.grid.ac/institutes/grid.419815.0 schema:alternateName Microsoft (United States)
164 schema:name Microsoft Research, 9S, 98052-6399, Redmond, WA
165 rdf:type schema:Organization
 




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


...