Statistical inference in mechanistic models: time warping for improved gradient matching View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-08-09

AUTHORS

Mu Niu, Benn Macdonald, Simon Rogers, Maurizio Filippone, Dirk Husmeier

ABSTRACT

Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios. More... »

PAGES

1091-1123

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00180-017-0753-z

DOI

http://dx.doi.org/10.1007/s00180-017-0753-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1091106421

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/31258254


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/2008/0102", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "School of Mathematics and Statistics, University of Glasgow, Glasgow, UK", 
          "id": "http://www.grid.ac/institutes/grid.8756.c", 
          "name": [
            "School of Mathematics and Statistics, University of Glasgow, Glasgow, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Niu", 
        "givenName": "Mu", 
        "id": "sg:person.01366452107.31", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01366452107.31"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "School of Mathematics and Statistics, University of Glasgow, Glasgow, UK", 
          "id": "http://www.grid.ac/institutes/grid.8756.c", 
          "name": [
            "School of Mathematics and Statistics, University of Glasgow, Glasgow, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Macdonald", 
        "givenName": "Benn", 
        "id": "sg:person.01203321237.78", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01203321237.78"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Computer Science, University of Glasgow, Glasgow, UK", 
          "id": "http://www.grid.ac/institutes/grid.8756.c", 
          "name": [
            "Department of Computer Science, University of Glasgow, Glasgow, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Rogers", 
        "givenName": "Simon", 
        "id": "sg:person.01240064014.24", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01240064014.24"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Data Science Department, Eurecom, Biot, France", 
          "id": "http://www.grid.ac/institutes/grid.28848.3e", 
          "name": [
            "Data Science Department, 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": "School of Mathematics and Statistics, University of Glasgow, Glasgow, UK", 
          "id": "http://www.grid.ac/institutes/grid.8756.c", 
          "name": [
            "School of Mathematics and Statistics, University of Glasgow, Glasgow, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Husmeier", 
        "givenName": "Dirk", 
        "id": "sg:person.0601451763.91", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0601451763.91"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1023/a:1010835316564", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010063057", 
          "https://doi.org/10.1023/a:1010835316564"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/0-306-48389-0_1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004023413", 
          "https://doi.org/10.1007/0-306-48389-0_1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02477753", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000290782", 
          "https://doi.org/10.1007/bf02477753"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2017-08-09", 
    "datePublishedReg": "2017-08-09", 
    "description": "Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s00180-017-0753-z", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.3863303", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1038958", 
        "issn": [
          "0943-4062", 
          "1613-9658"
        ], 
        "name": "Computational Statistics", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "33"
      }
    ], 
    "keywords": [
      "differential equations", 
      "non-linear differential equations", 
      "gradient matching", 
      "parameter estimation accuracy", 
      "parameter adaptation scheme", 
      "periodic limit cycle", 
      "dynamical systems", 
      "computational statistics", 
      "statistical inference", 
      "high computational cost", 
      "intrinsic length scale", 
      "approximate method", 
      "limit cycles", 
      "smoothing scheme", 
      "noisy data", 
      "computational cost", 
      "function interpolation", 
      "estimation accuracy", 
      "soft tissue mechanics", 
      "equations", 
      "manifold learning", 
      "adaptation scheme", 
      "length scales", 
      "scheme", 
      "noise ratio", 
      "inference", 
      "mechanistic model", 
      "challenging problem", 
      "mechanics", 
      "interpolation", 
      "model", 
      "statistics", 
      "biopathways", 
      "wide range", 
      "problem", 
      "matching", 
      "accuracy", 
      "present article", 
      "applications", 
      "approach", 
      "system", 
      "idea", 
      "effectiveness", 
      "signals", 
      "time", 
      "step", 
      "cost", 
      "range", 
      "scale", 
      "data", 
      "significant improvement", 
      "ratio", 
      "comparative evaluation", 
      "learning", 
      "article", 
      "improvement", 
      "evaluation", 
      "cycle", 
      "study", 
      "method", 
      "current computational statistics", 
      "iterative parameter adaptation scheme"
    ], 
    "name": "Statistical inference in mechanistic models: time warping for improved gradient matching", 
    "pagination": "1091-1123", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1091106421"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00180-017-0753-z"
        ]
      }, 
      {
        "name": "pubmed_id", 
        "type": "PropertyValue", 
        "value": [
          "31258254"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00180-017-0753-z", 
      "https://app.dimensions.ai/details/publication/pub.1091106421"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T18:44", 
    "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/article/article_738.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s00180-017-0753-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/s00180-017-0753-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/s00180-017-0753-z'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00180-017-0753-z'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00180-017-0753-z'


 

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

175 TRIPLES      22 PREDICATES      91 URIs      79 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00180-017-0753-z schema:about anzsrc-for:01
2 anzsrc-for:0102
3 anzsrc-for:0104
4 schema:author Naebd3e8a9be748f49efd71461f66906a
5 schema:citation sg:pub.10.1007/0-306-48389-0_1
6 sg:pub.10.1007/bf02477753
7 sg:pub.10.1023/a:1010835316564
8 schema:datePublished 2017-08-09
9 schema:datePublishedReg 2017-08-09
10 schema:description Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios.
11 schema:genre article
12 schema:inLanguage en
13 schema:isAccessibleForFree true
14 schema:isPartOf N6e38ace3326e458a89479fa4ba0b3bad
15 Nf2018831b2a945c98b9a41101ed259f1
16 sg:journal.1038958
17 schema:keywords accuracy
18 adaptation scheme
19 applications
20 approach
21 approximate method
22 article
23 biopathways
24 challenging problem
25 comparative evaluation
26 computational cost
27 computational statistics
28 cost
29 current computational statistics
30 cycle
31 data
32 differential equations
33 dynamical systems
34 effectiveness
35 equations
36 estimation accuracy
37 evaluation
38 function interpolation
39 gradient matching
40 high computational cost
41 idea
42 improvement
43 inference
44 interpolation
45 intrinsic length scale
46 iterative parameter adaptation scheme
47 learning
48 length scales
49 limit cycles
50 manifold learning
51 matching
52 mechanics
53 mechanistic model
54 method
55 model
56 noise ratio
57 noisy data
58 non-linear differential equations
59 parameter adaptation scheme
60 parameter estimation accuracy
61 periodic limit cycle
62 present article
63 problem
64 range
65 ratio
66 scale
67 scheme
68 signals
69 significant improvement
70 smoothing scheme
71 soft tissue mechanics
72 statistical inference
73 statistics
74 step
75 study
76 system
77 time
78 wide range
79 schema:name Statistical inference in mechanistic models: time warping for improved gradient matching
80 schema:pagination 1091-1123
81 schema:productId Na859c8bee4104d09b457f7e3ddc782aa
82 Nb3c1677102d2410c91448ac45200bc39
83 Ncacf65a61de744b29ce7e80670c08d53
84 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091106421
85 https://doi.org/10.1007/s00180-017-0753-z
86 schema:sdDatePublished 2022-01-01T18:44
87 schema:sdLicense https://scigraph.springernature.com/explorer/license/
88 schema:sdPublisher Nbdc63e4fee3a476693dedfe07346b13d
89 schema:url https://doi.org/10.1007/s00180-017-0753-z
90 sgo:license sg:explorer/license/
91 sgo:sdDataset articles
92 rdf:type schema:ScholarlyArticle
93 N21a68692363140019aa63766becb7a91 rdf:first sg:person.01240064014.24
94 rdf:rest N97159821d4f2413dbad4429588b97851
95 N6e38ace3326e458a89479fa4ba0b3bad schema:volumeNumber 33
96 rdf:type schema:PublicationVolume
97 N82909da2d55147dab88a1a8b6db3fca4 rdf:first sg:person.01203321237.78
98 rdf:rest N21a68692363140019aa63766becb7a91
99 N879aa59069b44a88b93b66c860f4798b rdf:first sg:person.0601451763.91
100 rdf:rest rdf:nil
101 N97159821d4f2413dbad4429588b97851 rdf:first sg:person.07706215665.03
102 rdf:rest N879aa59069b44a88b93b66c860f4798b
103 Na859c8bee4104d09b457f7e3ddc782aa schema:name doi
104 schema:value 10.1007/s00180-017-0753-z
105 rdf:type schema:PropertyValue
106 Naebd3e8a9be748f49efd71461f66906a rdf:first sg:person.01366452107.31
107 rdf:rest N82909da2d55147dab88a1a8b6db3fca4
108 Nb3c1677102d2410c91448ac45200bc39 schema:name dimensions_id
109 schema:value pub.1091106421
110 rdf:type schema:PropertyValue
111 Nbdc63e4fee3a476693dedfe07346b13d schema:name Springer Nature - SN SciGraph project
112 rdf:type schema:Organization
113 Ncacf65a61de744b29ce7e80670c08d53 schema:name pubmed_id
114 schema:value 31258254
115 rdf:type schema:PropertyValue
116 Nf2018831b2a945c98b9a41101ed259f1 schema:issueNumber 2
117 rdf:type schema:PublicationIssue
118 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
119 schema:name Mathematical Sciences
120 rdf:type schema:DefinedTerm
121 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
122 schema:name Applied Mathematics
123 rdf:type schema:DefinedTerm
124 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
125 schema:name Statistics
126 rdf:type schema:DefinedTerm
127 sg:grant.3863303 http://pending.schema.org/fundedItem sg:pub.10.1007/s00180-017-0753-z
128 rdf:type schema:MonetaryGrant
129 sg:journal.1038958 schema:issn 0943-4062
130 1613-9658
131 schema:name Computational Statistics
132 schema:publisher Springer Nature
133 rdf:type schema:Periodical
134 sg:person.01203321237.78 schema:affiliation grid-institutes:grid.8756.c
135 schema:familyName Macdonald
136 schema:givenName Benn
137 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01203321237.78
138 rdf:type schema:Person
139 sg:person.01240064014.24 schema:affiliation grid-institutes:grid.8756.c
140 schema:familyName Rogers
141 schema:givenName Simon
142 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01240064014.24
143 rdf:type schema:Person
144 sg:person.01366452107.31 schema:affiliation grid-institutes:grid.8756.c
145 schema:familyName Niu
146 schema:givenName Mu
147 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01366452107.31
148 rdf:type schema:Person
149 sg:person.0601451763.91 schema:affiliation grid-institutes:grid.8756.c
150 schema:familyName Husmeier
151 schema:givenName Dirk
152 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0601451763.91
153 rdf:type schema:Person
154 sg:person.07706215665.03 schema:affiliation grid-institutes:grid.28848.3e
155 schema:familyName Filippone
156 schema:givenName Maurizio
157 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07706215665.03
158 rdf:type schema:Person
159 sg:pub.10.1007/0-306-48389-0_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004023413
160 https://doi.org/10.1007/0-306-48389-0_1
161 rdf:type schema:CreativeWork
162 sg:pub.10.1007/bf02477753 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000290782
163 https://doi.org/10.1007/bf02477753
164 rdf:type schema:CreativeWork
165 sg:pub.10.1023/a:1010835316564 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010063057
166 https://doi.org/10.1023/a:1010835316564
167 rdf:type schema:CreativeWork
168 grid-institutes:grid.28848.3e schema:alternateName Data Science Department, Eurecom, Biot, France
169 schema:name Data Science Department, Eurecom, Biot, France
170 rdf:type schema:Organization
171 grid-institutes:grid.8756.c schema:alternateName Department of Computer Science, University of Glasgow, Glasgow, UK
172 School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
173 schema:name Department of Computer Science, University of Glasgow, Glasgow, UK
174 School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
175 rdf:type schema:Organization
 




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


...