November 20, 2022 Dataset Open Access

Bartlett, Deaglan J.; Desmond, Harry; Ferreira, Pedro G.

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  <identifier identifierType="DOI">10.5281/zenodo.7339113</identifier>
  <creators>
    <creator>
      <creatorName>Bartlett, Deaglan J.</creatorName>
      <givenName>Deaglan J.</givenName>
      <familyName>Bartlett</familyName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0001-9426-7723</nameIdentifier>
      <affiliation>CNRS &amp; Sorbonne Université, Institut d'Astrophysique de Paris and Astrophysics, University of Oxford</affiliation>
    </creator>
    <creator>
      <creatorName>Desmond, Harry</creatorName>
      <givenName>Harry</givenName>
      <familyName>Desmond</familyName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0003-0685-9791</nameIdentifier>
      <affiliation>Institute of Cosmology &amp; Gravitation, University of Portsmouth</affiliation>
    </creator>
    <creator>
      <creatorName>Ferreira, Pedro G.</creatorName>
      <givenName>Pedro G.</givenName>
      <familyName>Ferreira</familyName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-3021-2851</nameIdentifier>
      <affiliation>Astrophysics, University of Oxford</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Exhaustive Symbolic Regression Function Sets</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2022</publicationYear>
  <subjects>
    <subject>Symbolic Regression</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2022-11-20</date>
  </dates>
  <resourceType resourceTypeGeneral="Dataset"/>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/7339113</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.7339112</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;ESR (Exhaustive Symbolic Regression) is a symbolic regression algorithm which efficiently and systematically finds all possible equations at fixed complexity (defined to be the number of nodes in its tree representation) given a set of basis functions.&amp;nbsp;This is achieved by identifying the unique equations, so that one minimises the number of equations which one would have to fit to data.&lt;/p&gt;

&lt;p&gt;Here we provide the functions generated, the unique equations, and the mappings between all equations and unique ones&amp;nbsp;using different sets of basis functions. These are:&lt;/p&gt;

&lt;ul&gt;
	&lt;li&gt;&amp;quot;core_maths&amp;quot;:&amp;nbsp;&lt;span class="math-tex"&gt;\(\{x, a, {\rm inv}, +, -, \times, \div, {\rm pow} \}\)&lt;/span&gt;&lt;/li&gt;
	&lt;li&gt;&amp;quot;ext_maths&amp;quot;:&amp;nbsp;&lt;span class="math-tex"&gt;\(\{x, a, {\rm inv}, \sqrt{\cdot}, {\rm square}, \exp, +, -, \times, \div, {\rm pow} \}\)&lt;/span&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;where &lt;span class="math-tex"&gt;\(x\)&lt;/span&gt;&amp;nbsp;is the input variable and &lt;span class="math-tex"&gt;\(a\)&lt;/span&gt;&amp;nbsp;denotes a constant.&lt;/p&gt;

&lt;p&gt;One can fit these functions to a data set of interest by using the &lt;a href="https://esr.readthedocs.io"&gt;ESR package&lt;/a&gt;.&lt;/p&gt;</description>
    <description descriptionType="Other">DJB is supported by the Simons Collaboration on ``Learning the Universe'' and was supported by STFC and Oriel College, Oxford. HD is supported by a Royal Society University Research Fellowship (grant no. 211046). PGF acknowledges support from European Research Council Grant No: 693024 and the Beecroft Trust.</description>
  </descriptions>
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