Variable selection for functional linear models with strong heredity constraint View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2021-04-28

AUTHORS

Sanying Feng, Menghan Zhang, Tiejun Tong

ABSTRACT

In this paper, we consider the variable selection problem in functional linear regression with interactions. Our goal is to identify relevant main effects and corresponding interactions associated with the response variable. Heredity is a natural assumption in many statistical models involving two-way or higher-order interactions. Inspired by this, we propose an adaptive group Lasso method for the multiple functional linear model that adaptively selects important single functional predictors and pairwise interactions while obeying the strong heredity constraint. The proposed method is based on the functional principal components analysis with two adaptive group penalties, one for main effects and one for interaction effects. With appropriate selection of the tuning parameters, the rates of convergence of the proposed estimators and the consistency of the variable selection procedure are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage. More... »

PAGES

1-19

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10463-021-00798-z

DOI

http://dx.doi.org/10.1007/s10463-021-00798-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1137566710


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": "School of Mathematics and Statistics, Zhengzhou University, 450001, Zhengzhou, China", 
          "id": "http://www.grid.ac/institutes/grid.207374.5", 
          "name": [
            "School of Mathematics and Statistics, Zhengzhou University, 450001, Zhengzhou, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Feng", 
        "givenName": "Sanying", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "School of Mathematics and Statistics, Zhengzhou University, 450001, Zhengzhou, China", 
          "id": "http://www.grid.ac/institutes/grid.207374.5", 
          "name": [
            "School of Mathematics and Statistics, Zhengzhou University, 450001, Zhengzhou, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Zhang", 
        "givenName": "Menghan", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong", 
          "id": "http://www.grid.ac/institutes/grid.221309.b", 
          "name": [
            "Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Tong", 
        "givenName": "Tiejun", 
        "id": "sg:person.01234564122.62", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01234564122.62"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/b98888", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019866592", 
          "https://doi.org/10.1007/b98888"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4614-3655-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037887112", 
          "https://doi.org/10.1007/978-1-4614-3655-3"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2021-04-28", 
    "datePublishedReg": "2021-04-28", 
    "description": "In this paper, we consider the variable selection problem in functional linear regression with interactions. Our goal is to identify relevant main effects and corresponding interactions associated with the response variable. Heredity is a natural assumption in many statistical models involving two-way or higher-order interactions. Inspired by this, we propose an adaptive group Lasso method for the multiple functional linear model that adaptively selects important single functional predictors and pairwise interactions while obeying the strong heredity constraint. The proposed method is based on the functional principal components analysis with two adaptive group penalties, one for main effects and one for interaction effects. With appropriate selection of the tuning parameters, the rates of convergence of the proposed estimators and the consistency of the variable selection procedure are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s10463-021-00798-z", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1041657", 
        "issn": [
          "0020-3157", 
          "1572-9052"
        ], 
        "name": "Annals of the Institute of Statistical Mathematics", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }
    ], 
    "keywords": [
      "functional linear model", 
      "heredity constraint", 
      "functional linear regression", 
      "variable selection problem", 
      "rate of convergence", 
      "group lasso method", 
      "linear model", 
      "variable selection procedure", 
      "functional principal component analysis", 
      "group penalty", 
      "natural assumptions", 
      "statistical model", 
      "functional predictors", 
      "variable selection", 
      "tuning parameters", 
      "higher-order interactions", 
      "LASSO method", 
      "simulation study", 
      "real example", 
      "selection problem", 
      "pairwise interactions", 
      "selection procedure", 
      "constraints", 
      "estimator", 
      "practical usage", 
      "convergence", 
      "model", 
      "corresponding interactions", 
      "linear regression", 
      "appropriate selection", 
      "problem", 
      "assumption", 
      "parameters", 
      "two-way", 
      "principal component analysis", 
      "component analysis", 
      "procedure", 
      "penalty", 
      "interaction", 
      "selection", 
      "interaction effects", 
      "performance", 
      "main effect", 
      "consistency", 
      "regression", 
      "effect", 
      "analysis", 
      "goal", 
      "usage", 
      "rate", 
      "study", 
      "response", 
      "heredity", 
      "predictors", 
      "method", 
      "example", 
      "paper", 
      "relevant main effects", 
      "adaptive group Lasso method", 
      "multiple functional linear model", 
      "important single functional predictors", 
      "single functional predictors", 
      "strong heredity constraint", 
      "adaptive group penalties"
    ], 
    "name": "Variable selection for functional linear models with strong heredity constraint", 
    "pagination": "1-19", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1137566710"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10463-021-00798-z"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10463-021-00798-z", 
      "https://app.dimensions.ai/details/publication/pub.1137566710"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T18:56", 
    "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_876.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s10463-021-00798-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/s10463-021-00798-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/s10463-021-00798-z'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10463-021-00798-z'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10463-021-00798-z'


 

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

139 TRIPLES      22 PREDICATES      89 URIs      79 LITERALS      4 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10463-021-00798-z schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author Nc6b23c6197e24b479ba94a2d3e74b282
4 schema:citation sg:pub.10.1007/978-1-4614-3655-3
5 sg:pub.10.1007/b98888
6 schema:datePublished 2021-04-28
7 schema:datePublishedReg 2021-04-28
8 schema:description In this paper, we consider the variable selection problem in functional linear regression with interactions. Our goal is to identify relevant main effects and corresponding interactions associated with the response variable. Heredity is a natural assumption in many statistical models involving two-way or higher-order interactions. Inspired by this, we propose an adaptive group Lasso method for the multiple functional linear model that adaptively selects important single functional predictors and pairwise interactions while obeying the strong heredity constraint. The proposed method is based on the functional principal components analysis with two adaptive group penalties, one for main effects and one for interaction effects. With appropriate selection of the tuning parameters, the rates of convergence of the proposed estimators and the consistency of the variable selection procedure are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.
9 schema:genre article
10 schema:inLanguage en
11 schema:isAccessibleForFree false
12 schema:isPartOf sg:journal.1041657
13 schema:keywords LASSO method
14 adaptive group Lasso method
15 adaptive group penalties
16 analysis
17 appropriate selection
18 assumption
19 component analysis
20 consistency
21 constraints
22 convergence
23 corresponding interactions
24 effect
25 estimator
26 example
27 functional linear model
28 functional linear regression
29 functional predictors
30 functional principal component analysis
31 goal
32 group lasso method
33 group penalty
34 heredity
35 heredity constraint
36 higher-order interactions
37 important single functional predictors
38 interaction
39 interaction effects
40 linear model
41 linear regression
42 main effect
43 method
44 model
45 multiple functional linear model
46 natural assumptions
47 pairwise interactions
48 paper
49 parameters
50 penalty
51 performance
52 practical usage
53 predictors
54 principal component analysis
55 problem
56 procedure
57 rate
58 rate of convergence
59 real example
60 regression
61 relevant main effects
62 response
63 selection
64 selection problem
65 selection procedure
66 simulation study
67 single functional predictors
68 statistical model
69 strong heredity constraint
70 study
71 tuning parameters
72 two-way
73 usage
74 variable selection
75 variable selection problem
76 variable selection procedure
77 schema:name Variable selection for functional linear models with strong heredity constraint
78 schema:pagination 1-19
79 schema:productId N4b98085cbf444bb49433bd69179de772
80 Na90665ee9f874febb44c84db4cd59587
81 schema:sameAs https://app.dimensions.ai/details/publication/pub.1137566710
82 https://doi.org/10.1007/s10463-021-00798-z
83 schema:sdDatePublished 2022-01-01T18:56
84 schema:sdLicense https://scigraph.springernature.com/explorer/license/
85 schema:sdPublisher Naaeb270011214a01b5185b08e4444764
86 schema:url https://doi.org/10.1007/s10463-021-00798-z
87 sgo:license sg:explorer/license/
88 sgo:sdDataset articles
89 rdf:type schema:ScholarlyArticle
90 N01c55ffd270a42c6b160a575339b1c13 schema:affiliation grid-institutes:grid.207374.5
91 schema:familyName Feng
92 schema:givenName Sanying
93 rdf:type schema:Person
94 N38c27642f1cc43ab850ac760242cdb59 rdf:first Nbe71ba5a96a44d319c36100c791a644e
95 rdf:rest Nf69c75b3fb46471b958286cb560d84f5
96 N4b98085cbf444bb49433bd69179de772 schema:name doi
97 schema:value 10.1007/s10463-021-00798-z
98 rdf:type schema:PropertyValue
99 Na90665ee9f874febb44c84db4cd59587 schema:name dimensions_id
100 schema:value pub.1137566710
101 rdf:type schema:PropertyValue
102 Naaeb270011214a01b5185b08e4444764 schema:name Springer Nature - SN SciGraph project
103 rdf:type schema:Organization
104 Nbe71ba5a96a44d319c36100c791a644e schema:affiliation grid-institutes:grid.207374.5
105 schema:familyName Zhang
106 schema:givenName Menghan
107 rdf:type schema:Person
108 Nc6b23c6197e24b479ba94a2d3e74b282 rdf:first N01c55ffd270a42c6b160a575339b1c13
109 rdf:rest N38c27642f1cc43ab850ac760242cdb59
110 Nf69c75b3fb46471b958286cb560d84f5 rdf:first sg:person.01234564122.62
111 rdf:rest rdf:nil
112 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
113 schema:name Mathematical Sciences
114 rdf:type schema:DefinedTerm
115 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
116 schema:name Statistics
117 rdf:type schema:DefinedTerm
118 sg:journal.1041657 schema:issn 0020-3157
119 1572-9052
120 schema:name Annals of the Institute of Statistical Mathematics
121 schema:publisher Springer Nature
122 rdf:type schema:Periodical
123 sg:person.01234564122.62 schema:affiliation grid-institutes:grid.221309.b
124 schema:familyName Tong
125 schema:givenName Tiejun
126 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01234564122.62
127 rdf:type schema:Person
128 sg:pub.10.1007/978-1-4614-3655-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037887112
129 https://doi.org/10.1007/978-1-4614-3655-3
130 rdf:type schema:CreativeWork
131 sg:pub.10.1007/b98888 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019866592
132 https://doi.org/10.1007/b98888
133 rdf:type schema:CreativeWork
134 grid-institutes:grid.207374.5 schema:alternateName School of Mathematics and Statistics, Zhengzhou University, 450001, Zhengzhou, China
135 schema:name School of Mathematics and Statistics, Zhengzhou University, 450001, Zhengzhou, China
136 rdf:type schema:Organization
137 grid-institutes:grid.221309.b schema:alternateName Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong
138 schema:name Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong
139 rdf:type schema:Organization
 




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


...