Convexification for data fitting View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2009-03-31

AUTHORS

James Ting-Ho Lo

ABSTRACT

The main results reported in this paper are two theorems concerning the use of a newtype of risk-averting error criterion for data fitting. The first states that the convexity region of the risk-averting error criterion expands monotonically as its risk-sensitivity index increases. The risk-averting error criterion is easily seen to converge to the mean squared error criterion as its risk-sensitivity index goes to zero. Therefore, the risk-averting error criterion can be used to convexify the mean squared error criterion to avoid local minima. The second main theorem shows that as the risk-sensitivity index increases to infinity, the risk-averting error criterion approaches the minimax error criterion, which is widely used for robustifying system controllers and filters. More... »

PAGES

307-315

References to SciGraph publications

  • 1993-12. A remark on the GOP algorithm for global optimization in JOURNAL OF GLOBAL OPTIMIZATION
  • 2005-07. On the Liu–Floudas Convexification of Smooth Programs in JOURNAL OF GLOBAL OPTIMIZATION
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10898-009-9417-z

    DOI

    http://dx.doi.org/10.1007/s10898-009-9417-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1045872816


    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/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Applied Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "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/2008/0802", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Computation Theory and Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Mathematics and Statistics, University of Maryland Baltimore County, 21250, Baltimore, MD, USA", 
              "id": "http://www.grid.ac/institutes/grid.266673.0", 
              "name": [
                "Department of Mathematics and Statistics, University of Maryland Baltimore County, 21250, Baltimore, MD, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Lo", 
            "givenName": "James Ting-Ho", 
            "id": "sg:person.013512526631.81", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013512526631.81"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s10898-004-3134-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005121424", 
              "https://doi.org/10.1007/s10898-004-3134-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01096418", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043978923", 
              "https://doi.org/10.1007/bf01096418"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2009-03-31", 
        "datePublishedReg": "2009-03-31", 
        "description": "The main results reported in this paper are two theorems concerning the use of a newtype of risk-averting error criterion for data fitting. The first states that the convexity region of the risk-averting error criterion expands monotonically as its risk-sensitivity index increases. The risk-averting error criterion is easily seen to converge to the mean squared error criterion as its risk-sensitivity index goes to zero. Therefore, the risk-averting error criterion can be used to convexify the mean squared error criterion to avoid local minima. The second main theorem shows that as the risk-sensitivity index increases to infinity, the risk-averting error criterion approaches the minimax error criterion, which is widely used for robustifying system controllers and filters.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s10898-009-9417-z", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1050312", 
            "issn": [
              "0925-5001", 
              "1573-2916"
            ], 
            "name": "Journal of Global Optimization", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "46"
          }
        ], 
        "keywords": [
          "error criterion", 
          "mean squared error criterion", 
          "squared error criterion", 
          "risk-averting error criterion", 
          "second main theorem", 
          "main theorem", 
          "minimax error criterion", 
          "main results", 
          "theorem", 
          "data fitting", 
          "convexity region", 
          "local minima", 
          "infinity", 
          "system controller", 
          "controller", 
          "convexification", 
          "criteria", 
          "fitting", 
          "index increases", 
          "filter", 
          "first state", 
          "state", 
          "minimum", 
          "results", 
          "newtype", 
          "region", 
          "data", 
          "use", 
          "increase", 
          "index", 
          "paper", 
          "risk-sensitivity index"
        ], 
        "name": "Convexification for data fitting", 
        "pagination": "307-315", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1045872816"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10898-009-9417-z"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10898-009-9417-z", 
          "https://app.dimensions.ai/details/publication/pub.1045872816"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-09-02T15:53", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220902/entities/gbq_results/article/article_481.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s10898-009-9417-z"
      }
    ]
     

    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/s10898-009-9417-z'

    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/s10898-009-9417-z'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10898-009-9417-z'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10898-009-9417-z'


     

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

    109 TRIPLES      21 PREDICATES      61 URIs      48 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10898-009-9417-z schema:about anzsrc-for:01
    2 anzsrc-for:0102
    3 anzsrc-for:0103
    4 anzsrc-for:08
    5 anzsrc-for:0802
    6 schema:author N46be54e83c7d424aaeda3508d9af166f
    7 schema:citation sg:pub.10.1007/bf01096418
    8 sg:pub.10.1007/s10898-004-3134-4
    9 schema:datePublished 2009-03-31
    10 schema:datePublishedReg 2009-03-31
    11 schema:description The main results reported in this paper are two theorems concerning the use of a newtype of risk-averting error criterion for data fitting. The first states that the convexity region of the risk-averting error criterion expands monotonically as its risk-sensitivity index increases. The risk-averting error criterion is easily seen to converge to the mean squared error criterion as its risk-sensitivity index goes to zero. Therefore, the risk-averting error criterion can be used to convexify the mean squared error criterion to avoid local minima. The second main theorem shows that as the risk-sensitivity index increases to infinity, the risk-averting error criterion approaches the minimax error criterion, which is widely used for robustifying system controllers and filters.
    12 schema:genre article
    13 schema:isAccessibleForFree true
    14 schema:isPartOf Na38cb45301e74b0bae265ee8fbc2956b
    15 Nd9eb15de515f49a09824a494cc3f688a
    16 sg:journal.1050312
    17 schema:keywords controller
    18 convexification
    19 convexity region
    20 criteria
    21 data
    22 data fitting
    23 error criterion
    24 filter
    25 first state
    26 fitting
    27 increase
    28 index
    29 index increases
    30 infinity
    31 local minima
    32 main results
    33 main theorem
    34 mean squared error criterion
    35 minimax error criterion
    36 minimum
    37 newtype
    38 paper
    39 region
    40 results
    41 risk-averting error criterion
    42 risk-sensitivity index
    43 second main theorem
    44 squared error criterion
    45 state
    46 system controller
    47 theorem
    48 use
    49 schema:name Convexification for data fitting
    50 schema:pagination 307-315
    51 schema:productId Nabec2dcc406c442c9dc876c15f6cbbc9
    52 Nbd2ea461c02f4e2eb1da81fe32b752eb
    53 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045872816
    54 https://doi.org/10.1007/s10898-009-9417-z
    55 schema:sdDatePublished 2022-09-02T15:53
    56 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    57 schema:sdPublisher N56ff10b398c94ce1b9d05dab91d35bb8
    58 schema:url https://doi.org/10.1007/s10898-009-9417-z
    59 sgo:license sg:explorer/license/
    60 sgo:sdDataset articles
    61 rdf:type schema:ScholarlyArticle
    62 N46be54e83c7d424aaeda3508d9af166f rdf:first sg:person.013512526631.81
    63 rdf:rest rdf:nil
    64 N56ff10b398c94ce1b9d05dab91d35bb8 schema:name Springer Nature - SN SciGraph project
    65 rdf:type schema:Organization
    66 Na38cb45301e74b0bae265ee8fbc2956b schema:issueNumber 2
    67 rdf:type schema:PublicationIssue
    68 Nabec2dcc406c442c9dc876c15f6cbbc9 schema:name dimensions_id
    69 schema:value pub.1045872816
    70 rdf:type schema:PropertyValue
    71 Nbd2ea461c02f4e2eb1da81fe32b752eb schema:name doi
    72 schema:value 10.1007/s10898-009-9417-z
    73 rdf:type schema:PropertyValue
    74 Nd9eb15de515f49a09824a494cc3f688a schema:volumeNumber 46
    75 rdf:type schema:PublicationVolume
    76 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    77 schema:name Mathematical Sciences
    78 rdf:type schema:DefinedTerm
    79 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
    80 schema:name Applied Mathematics
    81 rdf:type schema:DefinedTerm
    82 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
    83 schema:name Numerical and Computational Mathematics
    84 rdf:type schema:DefinedTerm
    85 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    86 schema:name Information and Computing Sciences
    87 rdf:type schema:DefinedTerm
    88 anzsrc-for:0802 schema:inDefinedTermSet anzsrc-for:
    89 schema:name Computation Theory and Mathematics
    90 rdf:type schema:DefinedTerm
    91 sg:journal.1050312 schema:issn 0925-5001
    92 1573-2916
    93 schema:name Journal of Global Optimization
    94 schema:publisher Springer Nature
    95 rdf:type schema:Periodical
    96 sg:person.013512526631.81 schema:affiliation grid-institutes:grid.266673.0
    97 schema:familyName Lo
    98 schema:givenName James Ting-Ho
    99 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013512526631.81
    100 rdf:type schema:Person
    101 sg:pub.10.1007/bf01096418 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043978923
    102 https://doi.org/10.1007/bf01096418
    103 rdf:type schema:CreativeWork
    104 sg:pub.10.1007/s10898-004-3134-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005121424
    105 https://doi.org/10.1007/s10898-004-3134-4
    106 rdf:type schema:CreativeWork
    107 grid-institutes:grid.266673.0 schema:alternateName Department of Mathematics and Statistics, University of Maryland Baltimore County, 21250, Baltimore, MD, USA
    108 schema:name Department of Mathematics and Statistics, University of Maryland Baltimore County, 21250, Baltimore, MD, USA
    109 rdf:type schema:Organization
     




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


    ...