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<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Cell Dev. Biol.</journal-id>
<journal-title>Frontiers in Cell and Developmental Biology</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Cell Dev. Biol.</abbrev-journal-title>
<issn pub-type="epub">2296-634X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fcell.2021.700355</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Cell and Developmental Biology</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Prediction of Genetic Factors of Hyperthyroidism Based on Gene Interaction Network</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Shen</surname> <given-names>Fei</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="author-notes" rid="fn002"><sup>&#x2020;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1147054/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Cai</surname> <given-names>Wensong</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="author-notes" rid="fn002"><sup>&#x2020;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1208670/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Gan</surname> <given-names>Xiaoxiong</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1208768/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Feng</surname> <given-names>Jianhua</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1208671/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Chen</surname> <given-names>Zhen</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1208764/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Guo</surname> <given-names>Mengli</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1187985/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Wei</surname> <given-names>Fang</given-names></name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Cao</surname> <given-names>Jie</given-names></name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x002A;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1327231/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Xu</surname> <given-names>Bo</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="corresp" rid="c002"><sup>&#x002A;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1176499/overview"/>
</contrib>
</contrib-group>
<aff id="aff1"><sup>1</sup><institution>Department of Thyroid Surgery, School of Medicine, Guangzhou First People&#x2019;s Hospital, South China University of Technology</institution>, <addr-line>Guangzhou</addr-line>, <country>China</country></aff>
<aff id="aff2"><sup>2</sup><institution>Department of Thyroid Surgery, Guangzhou First People&#x2019;s Hospital, Guangzhou Medical University</institution>, <addr-line>Guangzhou</addr-line>, <country>China</country></aff>
<aff id="aff3"><sup>3</sup><institution>Department of General Surgery, School of Medicine, Guangzhou First People&#x2019;s Hospital, South China University of Technology</institution>, <addr-line>Guangzhou</addr-line>, <country>China</country></aff>
<author-notes>
<fn fn-type="edited-by"><p>Edited by: Lei Deng, Central South University, China</p></fn>
<fn fn-type="edited-by"><p>Reviewed by: Haixiu Yang, Harbin Medical University, China; Lingling Zhao, Harbin Institute of Technology, China</p></fn>
<corresp id="c001">&#x002A;Correspondence: Jie Cao, <email>eycaojie@scut.edu.cn</email></corresp>
<corresp id="c002">Bo Xu, <email>eyboxu@scut.edu.cn</email></corresp>
<fn fn-type="other" id="fn002"><p><sup>&#x2020;</sup>These authors have contributed equally to this work</p></fn>
<fn fn-type="other" id="fn004"><p>This article was submitted to Molecular and Cellular Pathology, a section of the journal Frontiers in Cell and Developmental Biology</p></fn>
</author-notes>
<pub-date pub-type="epub">
<day>02</day>
<month>08</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="collection">
<year>2021</year>
</pub-date>
<volume>9</volume>
<elocation-id>700355</elocation-id>
<history>
<date date-type="received">
<day>26</day>
<month>04</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>02</day>
<month>06</month>
<year>2021</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x00A9; 2021 Shen, Cai, Gan, Feng, Chen, Guo, Wei, Cao and Xu.</copyright-statement>
<copyright-year>2021</copyright-year>
<copyright-holder>Shen, Cai, Gan, Feng, Chen, Guo, Wei, Cao and Xu</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/"><p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p></license>
</permissions>
<abstract>
<p>The number of hyperthyroidism patients is increasing these years. As a disease that can lead to cardiovascular disease, it brings great potential health risks to humans. Since hyperthyroidism can induce the occurrence of many diseases, studying its genetic factors will promote the early diagnosis and treatment of hyperthyroidism and its related diseases. Previous studies have used genome-wide association analysis (GWAS) to identify genes related to hyperthyroidism. However, these studies only identify significant sites related to the disease from a statistical point of view and ignore the complex regulation relationship between genes. In addition, mutation is not the only genetic factor of causing hyperthyroidism. Identifying hyperthyroidism-related genes from gene interactions would help researchers discover the disease mechanism. In this paper, we purposed a novel machine learning method for identifying hyperthyroidism-related genes based on gene interaction network. The method, which is called &#x201C;RW-RVM,&#x201D; is a combination of Random Walk (RW) and Relevance Vector Machines (RVM). RW was implemented to encode the gene interaction network. The features of genes were the regulation relationship between genes and non-coding RNAs. Finally, multiple RVMs were applied to identify hyperthyroidism-related genes. The result of 10-cross validation shows that the area under the receiver operating characteristic curve (AUC) of our method reached 0.9, and area under the precision-recall curve (AUPR) was 0.87. Seventy-eight novel genes were found to be related to hyperthyroidism. We investigated two genes of these novel genes with existing literature, which proved the accuracy of our result and method.</p>
</abstract>
<kwd-group>
<kwd>hyperthyroidism</kwd>
<kwd>gene interaction network</kwd>
<kwd>random walk</kwd>
<kwd>a novel machine learning method</kwd>
<kwd>multiple Relevance Vector Machines</kwd>
</kwd-group>
<counts>
<fig-count count="4"/>
<table-count count="3"/>
<equation-count count="13"/>
<ref-count count="32"/>
<page-count count="7"/>
<word-count count="0"/>
</counts>
</article-meta>
</front>
<body>
<sec id="S1">
<title>Introduction</title>
<p>Hyperthyroidism refers to a type of common endocrinology disease in which the level of thyroid hormone in the body is abnormally increased (<xref ref-type="bibr" rid="B21">Ross, 2011</xref>). The main manifestations of patients are palpitations, sweating, increased eating but weight loss, etc., which are harmful to the cardiovascular system (<xref ref-type="bibr" rid="B4">Ertek and Cicero, 2013</xref>), digestive system (<xref ref-type="bibr" rid="B7">Journy et al., 2017</xref>), nervous system (<xref ref-type="bibr" rid="B8">Ku et al., 2005</xref>), etc. Hyperthyroidism will cause a certain degree of damage, which will seriously affect the quality of life of patients. Hyperthyroidism occurs mostly in the elderly and pregnant women. Hyperthyroidism has significant adverse effects on the heart, bones, and cognitive functions. Standardized management is of great significance for improving the clinical diagnosis and treatment of thyroid diseases in the elderly and protecting the health of the elderly (<xref ref-type="bibr" rid="B11">Martin and Deam, 1996</xref>). The thyroid hormone is very important for the health of pregnant women and the growth and development of the fetus. During pregnancy, thyroid function will undergo a series of physiological changes (<xref ref-type="bibr" rid="B13">Moleti et al., 2019</xref>). Hyperthyroidism during pregnancy can cause adverse pregnancy outcomes and maternal and infant complications.</p>
<p>The common causes of hyperthyroidism in the elderly include Graves&#x2019; disease (GD) (<xref ref-type="bibr" rid="B17">Okosieme et al., 2019</xref>), toxic multinodular goiter (TMNG) (<xref ref-type="bibr" rid="B2">Azizi et al., 2019</xref>), and toxic adenomas (TA) (<xref ref-type="bibr" rid="B22">Sharma and Abraham, 2020</xref>). Other rare causes include pituitary thyroid-stimulating hormone (TSH) tumors, nourishment cell layer tumors, and metastatic differentiated thyroid cancer. The etiology spectrum of elderly hyperthyroidism is not completely consistent with that of non-elderly patients: GD is mainly observed in iodine-sufficient areas (<xref ref-type="bibr" rid="B10">Liu et al., 2017</xref>), and it decreases with age after the age of 40 years; in iodine-deficient areas, TMNG is the main source, and the proportion of people over 60 years old with hyperthyroidism is 28&#x2013;65%, while that of people under 40 years old with hyperthyroidism is only 5&#x2013;10%. In pregnant women the blood TSH drops by 30&#x2013;50% in the first trimester and gradually rises in the second trimester (<xref ref-type="bibr" rid="B24">Smaniotto et al., 2017</xref>). However, it is worth noting that the TSH of some pregnant women cannot return to the non-pregnancy level during the third trimester. The magnitude of this physiological change of TSH is also different in different races. These physiological changes leading to the diagnosis of abnormal thyroid function during pregnancy must use the pregnancy-specific reference range. Compared with the reference range of TSH for non-pregnant women (<xref ref-type="bibr" rid="B14">Moon et al., 2015</xref>), the lower limit of the TSH reference range for pregnant women is reduced by about 0.1&#x2013;0.2 mU/L, and the upper limit of TSH is reduced by about 0.5&#x2013;1.0 mU/L. And, the decrease in TSH is more obvious than in the middle and late pregnancy (<xref ref-type="bibr" rid="B1">Asik et al., 2014</xref>). Women with twin and multiple pregnancies have higher hCG concentrations in their bodies, and their TSH also decreases more significantly than women with single pregnancies.</p>
<p>Although several clinical studies have researched the causal reason of hyperthyroidism, the genetic factors of hyperthyroidism are still unclear. GD is caused by genetic and environmental factors, and 79% susceptibility can be attributed to genetic factors (<xref ref-type="bibr" rid="B9">Ku&#x015B; et al., 2015</xref>). Through candidate gene analysis, genome-wide association study, and some functional studies, researchers had identified several susceptible genes of GD, such as HLA, CTLA4, PTPN22, FCRL3, RNASET2, and TSHR (<xref ref-type="bibr" rid="B3">Chu et al., 2011</xref>; <xref ref-type="bibr" rid="B23">Simmonds, 2013</xref>). GD can occur at any age, but the cutoff age of early onset GD has not been clearly defined (most researchers chose patients younger than or 30 years old as early onset GD). Research about the unique loci of early onset GD were reported several years ago, but considering their insufficient sample size and deficient analysis methods, these loci should be verified in more studies. A study did genotyping of 196,524 polymorphisms in 106 early onset patients (onset at age &#x003C; 30 years) and 855 healthy subjects through Illumina Infinium Immunochip and performed case&#x2013;control association analyses, which finally found 30 specific single-nucleotide polymorphisms (SNPs) in early onset patients (these SNPs were located in the genes of HLA-I, HLA-II, BTNL2, NOTCH4, TNFAIP3, and CXCR4). Another study had reported that FOXP3 in the X chromosome was a unique gene of early onset patients (onset at age &#x2264; 30 years).</p>
<p>Although genome-wide association analysis (GWAS) can reveal susceptible genes of hyperthyroidism, this method does not take gene interaction into account. However, the regulation relationship between genes plays a vital role in the occurrence and development of diseases (<xref ref-type="bibr" rid="B12">Maurano et al., 2012</xref>; <xref ref-type="bibr" rid="B30">Zhao et al., 2020b</xref>). Previous studies have proven the effectiveness of biological network in identifying diseases-related molecules (<xref ref-type="bibr" rid="B18">Peng and Zhao, 2020</xref>). Multiple computational methods have been developed to process the biological network, which achieved drug&#x2013;target interaction prediction (<xref ref-type="bibr" rid="B26">Tianyi et al., 2020</xref>), regulatory relationship prediction (<xref ref-type="bibr" rid="B31">Zhao et al., 2021a</xref>), diseases-related metabolites (<xref ref-type="bibr" rid="B29">Zhao et al., 2020a</xref>), etc. Random Walk (RW) is a common method to deal with biological networks. Researchers have applied this method to identify miRNAs (<xref ref-type="bibr" rid="B16">Niu et al., 2019</xref>), proteins (<xref ref-type="bibr" rid="B20">Rathore and de Pablo, 2002</xref>), gene expression (<xref ref-type="bibr" rid="B32">Zhao et al., 2021b</xref>), and multiple diseases-related molecules. In addition, Relevance Vector Machines (RVM) has been also widely used in disease-related research. <xref ref-type="bibr" rid="B27">Veeramani and Muthusamy (2016)</xref> used RVM-classified lung image to identify lung cancer. <xref ref-type="bibr" rid="B28">Wang et al. (2013)</xref> implemented early diagnosis of Parkinson&#x2019;s disease by RVM. In this paper, we propose a novel method called &#x201C;RW-RVM&#x201D; to predict hyperthyroidism. Using RW-RVM, we extracted the topological relations of gene interaction network and fused them with regulation relationship of non-coding RNAs. Multiple RVM models were implemented to predict hyperthyroidism-related genes by weight voting.</p>
</sec>
<sec id="S2" sec-type="materials|methods">
<title>Materials and Methods</title>
<sec id="S2.SS1">
<title>Construction of Gene Network</title>
<p>First, we obtained hyperthyroidism-related known genes from DisGeNET (<xref ref-type="bibr" rid="B19">Pi&#x00F1;ero et al., 2020</xref>). Two hundred sixty-nine have been reported to be related to hyperthyroidism. These genes were input into the String database (<xref ref-type="bibr" rid="B25">Szklarczyk et al., 2016</xref>), and the gene interaction network was constructed as shown in <xref ref-type="fig" rid="F1">Figure 1</xref>.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption><p>Two hundred sixty-nine hyperthyroidism-related genes network.</p></caption>
<graphic xlink:href="fcell-09-700355-g001.tif"/>
</fig>
<p>As we can see in <xref ref-type="fig" rid="F1">Figure 1</xref>, most of these genes have close interactions with each other, which supports our hypothesis: Disease-related genes are related to gene interactions. Therefore, the genes that can interact with these 269 genes are potential genes related to hyperthyroidism. Our aim is to determine the possibility that these genes are associated with hyperthyroidism.</p>
<p>From HumanNet database (<xref ref-type="bibr" rid="B6">Hwang et al., 2019</xref>), we obtained 1,517 genes that can interact with these 269 genes. Using these 1,786 genes, we constructed a gene interaction network. The nodes in this network are genes, and the edges are interactions between genes.</p>
</sec>
<sec id="S2.SS2">
<title>Random Walk</title>
<p>The edges of the gene network have different weights. Based on the edges and known 269 genes, we implemented RW to traverse this network to reach steady state. Because the gene interaction network we constructed is a two-dimensional graph, when we travel in the form of probability according to the interaction scores and we know the current gene node information, the historical gene node traversal information has nothing to do with the future gene node traversal path. Therefore, we can regard the method of mining disease-related genes based on RW as a Markov chain. In each step of the Markov chain, the probability distribution of hyperthyroidism-related genes can change from one state to another or maintain the current state. The change of state is called transition, and the probability associated with different states is called transition probability.</p>
<p>If <italic>A</italic> is the adjacency matrix of the gene interaction network, we can normalize <italic>A</italic> to:</p>
<disp-formula id="S2.E1"><label>(1)</label><mml:math id="M1" display="block"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>&#x2062;</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:mrow></mml:math></disp-formula>
<p><italic>D</italic> is a diagonal matrix, which is the degree matrix of the gene interaction network, and its diagonal element is <italic>D</italic>(<italic>i</italic>,<italic>i</italic>) = &#x2211;<italic>A</italic>(<italic>i</italic>,<italic>j</italic>). Here, <italic>P</italic> is a RW matrix, and the sum of transition probability of each node is 1, which is the probability matrix of hyperthyroidism associated with all genes.</p>
<p>A RW matrix corresponds to a Markov chain, and the probability distribution of hyperthyroidism-related genes changes with the change of state in the Markov chain. The probability from any state to the next state is as follows:</p>
<disp-formula id="S2.E2"><label>(2)</label><mml:math id="M2" display="block"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>&#x2062;</mml:mo><mml:mi>P</mml:mi></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>This process continues, and the relationship between hyperthyroidism and genes is also changing. After a period of time, it reaches equilibrium. The equilibrium state, also known as steady state, means that the probability distribution of the association between hyperthyroidism and genes does not change. The calculation method of the steady state is as follows:</p>
<disp-formula id="S2.E3"><label>(3)</label><mml:math id="M3" display="block"><mml:mrow><mml:mi mathvariant="normal">&#x03C0;</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mi>D</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:munder><mml:mo largeop="true" movablelimits="false" symmetric="true">&#x2211;</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:mrow><mml:munder><mml:mo largeop="true" movablelimits="false" symmetric="true">&#x2211;</mml:mo><mml:mi>j</mml:mi></mml:munder><mml:mrow><mml:mi>A</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>When &#x03C0;<italic>P</italic> = &#x03C0;, the whole system reaches steady state. This steady state is the final calculated correlation between hyperthyroidism and genes. The workflow of encoding the gene interaction network is shown in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap position="float" id="T1">
<label>TABLE 1</label>
<caption><p>Encoding gene interaction network based on random walk.</p></caption>
<table cellspacing="5" cellpadding="5" frame="hsides" rules="groups">
<tbody>
<tr>
<td valign="top" align="left">INPUT:Probability matrix of initial hyperthyroidism-related genes <sub><italic>P0</italic></sub>, parameter &#x03B3;,control accuracy is <sub>&#x2113;</sub>, iteration times is <sub><italic>N</italic></sub>, gene interaction network G(V, E, W)</td>
</tr>
<tr>
<td valign="top" align="left">OUTPUT:Probability matrix of hyperthyroidism-related genes</td>
</tr>
<tr>
<td><hr/></td>
</tr>
<tr>
<td valign="top" align="left">1.FOR <italic>i</italic> = 0 to <sub><italic>N</italic></sub>{</td>
</tr>
<tr>
<td valign="top" align="left">2. Update the probability matrix of hyperthyroidism-related genes <sub><italic>P<sub>t+1</sub> =(1&#x2013;&#x03B3;)AP<sub>t +&#x03B3;</sub>P<sub>0</sub></italic></sub> ;</td>
</tr>
<tr>
<td valign="top" align="left">3. IF ||<italic>P</italic><sub><italic>t</italic> + 1</sub>&#x2212;<italic>P</italic><sub><italic>t</italic></sub>|| &#x003E; &#x2113;{</td>
</tr>
<tr>
<td valign="top" align="left">4. <sub><italic>P<sub>t+1</sub> =(1&#x2013;&#x03B3;)AP<sub>t +&#x03B3;</sub>P<sub>0</sub></italic></sub> ;</td>
</tr>
<tr>
<td valign="top" align="left">5. }</td>
</tr>
<tr>
<td valign="top" align="left">6. ELSE {</td>
</tr>
<tr>
<td valign="top" align="left">7. RETURN Probability matrix <sub><italic>P<sub>t+1</sub></italic></sub> ;</td>
</tr>
<tr>
<td valign="top" align="left">8. }</td>
</tr>
<tr>
<td valign="top" align="left">9. }</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="S2.SS3">
<title>Extracting Gene Feature</title>
<p>Since the relationship between genes and diseases is related to the gene regulation, we extract the regulatory relationship between non-coding RNAs and genes as a feature of genes. The features of each gene could be represented as follows:</p>
<disp-formula id="S2.E4"><label>(4)</label><mml:math id="M4" display="block"><mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>e</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>n</mml:mi><mml:mo>&#x2062;</mml:mo><mml:msub><mml:mi>e</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mtable displaystyle="true" rowspacing="0pt"><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">&#x2026;</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">&#x2026;</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math></disp-formula>
<p><italic>l</italic><sub>1</sub> represents the regulatory relationship between lncRNA1 and <italic>g</italic><italic>e</italic><italic>n</italic><italic>e</italic><sub><italic>t</italic></sub>, and <italic>m</italic><sub>1</sub> represents the regulatory relationship between miRNA1 and <italic>g</italic><italic>e</italic><italic>n</italic><italic>e</italic><sub><italic>t</italic></sub>. If lncRNA1 can interact with <italic>g</italic><italic>e</italic><italic>n</italic><italic>e</italic><sub><italic>t</italic></sub>, <italic>l</italic><sub>1</sub> = 1; otherwise, <italic>l</italic><sub>1</sub> = 0</p>
<p>After obtaining all features of the genes, the final features of genes are the following:</p>
<disp-formula id="S2.E5"><label>(5)</label><mml:math id="M5" display="block"><mml:mrow><mml:mrow><mml:mi>F</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>e</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>a</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>t</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>u</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>r</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>e</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2022;</mml:mo><mml:mi>g</mml:mi></mml:mrow><mml:mo>&#x2062;</mml:mo><mml:mi>e</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>n</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>e</mml:mi></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>Therefore, the final features not only contain the regulatory relationship between non-coding RNAs and genes but also the topological characteristics of the gene interaction network. In the next step, these features could be input into RVM models to obtain the probability of genes associated with hyperthyroidism.</p>
</sec>
<sec id="S2.SS4">
<title>Construction of RVM Model</title>
<p>The kernel function of the RVM is not limited by Mercer conditions; it is more sparse and has less super-parameters so it reduces the computational burden of kernel functions.</p>
<p>For a given dataset {<italic>x</italic><sub><italic>i</italic></sub>,<italic>t</italic><sub><italic>i</italic></sub>}<italic>i</italic> = 1<sup><italic>N</italic></sup>, <italic>x</italic><sub><italic>i</italic></sub> &#x2208; R<sup><italic>d</italic></sup>, the non-linear model is:</p>
<disp-formula id="S2.E6"><label>(6)</label><mml:math id="M6" display="block"><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mi>y</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">&#x03B5;</mml:mi></mml:mrow></mml:mrow></mml:math></disp-formula>
<p><italic>N</italic> is the sample number, <italic>y</italic> is the non-linear function, &#x03B5; is the noise, <inline-formula><mml:math id="INEQ13"><mml:mrow><mml:mi mathvariant="normal">&#x03B5;</mml:mi><mml:mo>&#x223C;</mml:mo><mml:mi>N</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mpadded width="+3.3pt"><mml:mi mathvariant="normal">&#x03C3;</mml:mi></mml:mpadded><mml:mmultiscripts><mml:mo stretchy="false">)</mml:mo><mml:mprescripts/><mml:none/><mml:mn>2</mml:mn></mml:mmultiscripts></mml:mrow></mml:mrow></mml:math></inline-formula>.</p>
<p>The final function of RVM is:</p>
<disp-formula id="S2.E7"><label>(7)</label><mml:math id="M7" display="block"><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03A6;</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi mathvariant="normal">&#x03C9;</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">&#x03B5;</mml:mi></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>&#x03C9; = (&#x03C9;<sub>0</sub>,&#x22EF;,&#x03C9;<sub><italic>N</italic></sub>)<sup>T</sup> is the weight, and &#x03A6; is the matrix of the kernel function. <italic>K</italic>() is the kernel function. &#x03D5;<sub><italic>i</italic></sub>(<italic>x</italic><sub><italic>i</italic></sub>) = [1,<italic>K</italic>(<italic>x</italic><sub><italic>i</italic></sub>,<italic>x</italic><sub>1</sub>),&#x22EF;,<italic>K</italic>(<italic>x</italic><sub><italic>i</italic></sub>,<italic>x</italic><sub><italic>N</italic></sub>)],<italic>i</italic> = 1,2,&#x22EF;,<italic>N</italic>.</p>
<p>The distribution of <italic>p</italic>(<italic>t</italic>|<italic>x</italic>) obeys <italic>N</italic>(<italic>t</italic>|<italic>y</italic>(<italic>x</italic>),&#x03C3;<sup>2</sup>). The likelihood estimation of data is:</p>
<disp-formula id="S2.E8"><label>(8)</label><mml:math id="M8" display="block"><mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo lspace="2.5pt" rspace="2.5pt" stretchy="false">|</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03C9;</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mo>&#x2062;</mml:mo><mml:mi>&#x03C0;</mml:mi><mml:mo>&#x2062;</mml:mo><mml:msup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mrow></mml:msup><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mi>exp</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo stretchy="false">{</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mo fence="true">||</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>-</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03A6;</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi mathvariant="normal">&#x03C9;</mml:mi></mml:mrow></mml:mrow><mml:mo fence="true">||</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mo>&#x2062;</mml:mo><mml:msup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo stretchy="false">}</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>Tipping defines a zero mean Gauss-type prior distribution on &#x03C9; :</p>
<disp-formula id="S2.E9"><label>(9)</label><mml:math id="M9" display="block"><mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03C9;</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">&#x03B1;</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:munderover><mml:mo largeop="true" movablelimits="false" symmetric="true">&#x220F;</mml:mo><mml:mn>0</mml:mn><mml:mi>N</mml:mi></mml:munderover><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03C9;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo lspace="2.5pt" rspace="2.5pt" stretchy="false">|</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:munderover><mml:mo largeop="true" movablelimits="false" symmetric="true">&#x220F;</mml:mo><mml:mn>0</mml:mn><mml:mi>N</mml:mi></mml:munderover><mml:mrow><mml:mfrac><mml:msub><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msqrt><mml:mrow><mml:mn>2</mml:mn><mml:mo>&#x2062;</mml:mo><mml:mi mathvariant="normal">&#x03C0;</mml:mi></mml:mrow></mml:msqrt></mml:mfrac><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mi>exp</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">&#x03C9;</mml:mi><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>&#x2062;</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:mfrac><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>&#x03B1; is the super-parameter; it has a one-to-one correspondence with the weight.</p>
<p>&#x03B1; and the variance of noise &#x03C3;<sup>2</sup> meet the Gamma distribution.</p>
<disp-formula id="S2.E10"><label>(10)</label><mml:math id="M10" display="block"><mml:mtable displaystyle="true" rowspacing="0pt"><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mo largeop="true" symmetric="true">&#x220F;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:msubsup></mml:mstyle><mml:mrow><mml:mtext>Gamma</mml:mtext><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo lspace="2.5pt" rspace="2.5pt" stretchy="false">|</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mo largeop="true" symmetric="true">&#x220F;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:msubsup></mml:mstyle><mml:mrow><mml:mtext>Gamma</mml:mtext><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03B2;</mml:mi><mml:mo lspace="2.5pt" rspace="2.5pt" stretchy="false">|</mml:mo><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>The prediction based on the sparse Bayesian learning framework can be expressed as follows:</p>
<disp-formula id="S2.E11"><label>(11)</label><mml:math id="M11" display="block"><mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo lspace="2.5pt" rspace="2.5pt" stretchy="false">|</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo largeop="true" symmetric="true">&#x222B;</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo lspace="2.5pt" rspace="2.5pt" stretchy="false">|</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03C9;</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2062;</mml:mo><mml:mi>p</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="normal">&#x03C9;</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mo>,</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo lspace="2.5pt" rspace="2.5pt" stretchy="false">|</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo mathvariant="italic" rspace="0pt">d</mml:mo><mml:mi mathvariant="normal">&#x03C9;</mml:mi></mml:mrow><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo mathvariant="italic" rspace="0pt">d</mml:mo><mml:mi mathvariant="normal">&#x03B1;</mml:mi></mml:mrow><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo mathvariant="italic" rspace="0pt">d</mml:mo><mml:msup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>
<p><italic>t</italic><sub><italic>N</italic> + 1</sub> is the target value of the new observation <italic>x</italic><sub><italic>N</italic> + 1</sub>.</p>
<p>For a new set of inputs x<sub>&#x002A;</sub>, the output t<sub>&#x002A;</sub> should meet the distribution p(t<sub>&#x002A;</sub> &#x2014;t)&#x223C; N(&#x03BC;<sup>T</sup> &#x03A6; (x<sup>&#x2217;</sup>),<inline-formula><mml:math id="INEQ21"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mo>&#x002A;</mml:mo><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
<disp-formula id="S2.E12"><label>(12)</label><mml:math id="M12" display="block"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:msup><mml:mi/><mml:mo>&#x002A;</mml:mo></mml:msup></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant="normal">&#x03BC;</mml:mi><mml:mrow><mml:mtext>T</mml:mtext></mml:mrow></mml:msup><mml:mo>&#x2062;</mml:mo><mml:mi mathvariant="normal">&#x03A6;</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:msup><mml:mi/><mml:mo>&#x002A;</mml:mo></mml:msup></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>
<disp-formula id="S2.E13"><label>(13)</label><mml:math id="M13" display="block"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:msup><mml:mi/><mml:mo>&#x002A;</mml:mo></mml:msup><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>P</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03A6;</mml:mi><mml:mo>&#x2062;</mml:mo><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:msup><mml:mi/><mml:mo>&#x002A;</mml:mo></mml:msup></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mtext>T</mml:mtext></mml:mrow></mml:msup><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo largeop="true" movablelimits="false" symmetric="true">&#x2211;</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03A6;</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:msup><mml:mi/><mml:mo>&#x002A;</mml:mo></mml:msup></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>
<p><inline-formula><mml:math id="INEQ22"><mml:msubsup><mml:mi mathvariant="normal">&#x03C3;</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mo>&#x2062;</mml:mo><mml:mi>P</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:math></inline-formula> is the final variance of noise.</p>
<p>To accomplish the construction of the RVM model, we also need to set the various parameters in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<table-wrap position="float" id="T2">
<label>TABLE 2</label>
<caption><p>Parameters and functions of RVM.</p></caption>
<table cellspacing="5" cellpadding="5" frame="hsides" rules="groups">
<thead>
<tr>
<td valign="top" align="left"><bold>Setting items</bold></td>
<td valign="top" align="center"><bold>The value set</bold></td>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Max iterations</td>
<td valign="top" align="center">100</td>
</tr>
<tr>
<td valign="top" align="left">Kernel function</td>
<td valign="top" align="center">Gauss</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Since the output of the RW is not stable, we constructed three RVM models to obtain the final prediction. These three models have equal weights, so the average of the predictions is the final probability of genes associated with hyperthyroidism.</p>
<p>The workflow of the RVM is shown in <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption><p>Workflow of constructing RVM models.</p></caption>
<graphic xlink:href="fcell-09-700355-g002.tif"/>
</fig>
<p>As we can see from <xref ref-type="fig" rid="F2">Figure 2</xref>, we generated three kinds of features from three RW times. Then, the features of the genes were input into the kernel function, and likelihood estimation was done. After obtaining the prior distribution, three RVM models could be built. Finally, we could obtain the final prediction by averaging the three predicted values.</p>
</sec>
</sec>
<sec id="S3">
<title>Results</title>
<sec id="S3.SS1">
<title>Results of 10-Cross Validation</title>
<p>Since we only know the genes which are reported to be related to hyperthyroidism, we cannot define whether other genes are related to hyperthyroidism. Therefore, we randomly select negative samples from 1,517 genes. As we have 269 positive samples, we randomly select 269 negative samples each time and repeat 10 times. For each negative dataset, we combined it with the positive samples as a whole dataset and implemented 10-cross validation. Therefore, we did 10-cross validation a total of 10 times.</p>
<p>The process of 10-cross validation is as follows: (1) Randomly group negative dataset and positive dataset into 10 groups. (2) Select nine negative groups and nine positive groups to build the RW-RVM model. (3) Input the other negative group and positive group to test the RW-RVM model. (4) Repeat steps 2 and 3 10 times.</p>
<p>The results of performing 10-cross validation 10 times are shown in <xref ref-type="table" rid="T3">Table 3</xref>.</p>
<table-wrap position="float" id="T3">
<label>TABLE 3</label>
<caption><p>The AUC and AUPR of 10-cross validation.</p></caption>
<table cellspacing="5" cellpadding="5" frame="hsides" rules="groups">
<thead>
<tr>
<td valign="top" align="left"><bold>Experiment</bold></td>
<td valign="top" align="center"><bold>AUC</bold></td>
<td valign="top" align="center"><bold>AUPR</bold></td>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">1</td>
<td valign="top" align="center">0.89 &#x00B1; 0.010</td>
<td valign="top" align="center">0.84 &#x00B1; 0.012</td>
</tr>
<tr>
<td valign="top" align="left">2</td>
<td valign="top" align="center">0.92 &#x00B1; 0.008</td>
<td valign="top" align="center">0.87 &#x00B1; 0.013</td>
</tr>
<tr>
<td valign="top" align="left">3</td>
<td valign="top" align="center">0.89 &#x00B1; 0.009</td>
<td valign="top" align="center">0.85 &#x00B1; 0.011</td>
</tr>
<tr>
<td valign="top" align="left">4</td>
<td valign="top" align="center">0.88 &#x00B1; 0.011</td>
<td valign="top" align="center">0.85 &#x00B1; 0.012</td>
</tr>
<tr>
<td valign="top" align="left">5</td>
<td valign="top" align="center">0.90 &#x00B1; 0.008</td>
<td valign="top" align="center">0.86 &#x00B1; 0.013</td>
</tr>
<tr>
<td valign="top" align="left">6</td>
<td valign="top" align="center">0.91 &#x00B1; 0.008</td>
<td valign="top" align="center">0.88 &#x00B1; 0.012</td>
</tr>
<tr>
<td valign="top" align="left">7</td>
<td valign="top" align="center">0.91 &#x00B1; 0.009</td>
<td valign="top" align="center">0.89 &#x00B1; 0.017</td>
</tr>
<tr>
<td valign="top" align="left">8</td>
<td valign="top" align="center">0.89 &#x00B1; 0.008</td>
<td valign="top" align="center">0.87 &#x00B1; 0.011</td>
</tr>
<tr>
<td valign="top" align="left">9</td>
<td valign="top" align="center">0.90 &#x00B1; 0.010</td>
<td valign="top" align="center">0.86 &#x00B1; 0.009</td>
</tr>
<tr>
<td valign="top" align="left">10</td>
<td valign="top" align="center">0.90 &#x00B1; 0.009</td>
<td valign="top" align="center">0.87 &#x00B1; 0.011</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>As we can see from <xref ref-type="table" rid="T3">Table 3</xref>, the performance of the RW-RVM model is stable. The average area under the receiver operating characteristic curve (AUC) is 0.90, and the AUPR is 0.87.</p>
</sec>
<sec id="S3.SS2">
<title>Compare With Other Methods</title>
<p>We compared RW-RVM with several other methods, such as random forest (RF), na&#x00EF;ve Bayes (NB), and artificial neural network (ANN). The AUC and AUPR curves of these methods are shown in <xref ref-type="fig" rid="F3">Figures 3</xref>, <xref ref-type="fig" rid="F4">4</xref>.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption><p>AUC curves of four methods.</p></caption>
<graphic xlink:href="fcell-09-700355-g003.tif"/>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption><p>AUPR curves of four methods.</p></caption>
<graphic xlink:href="fcell-09-700355-g004.tif"/>
</fig>
<p>As shown in <xref ref-type="fig" rid="F3">Figures 3</xref>, <xref ref-type="fig" rid="F4">4</xref>, RW-RVM performed best among these methods, and RF ranked second. Due to the small sample set, ANN cannot be fully trained, so the AUC and AUPR of the ANN are not satisfactory. The theory of RVM is similar to support vector machine (SVM), which is very suitable for small-sample modeling. Therefore, the performance of the RVM is the best.</p>
</sec>
</sec>
<sec id="S4">
<title>Discussion</title>
<p>Biological experiments have found that hundreds of genes are associated with hyperthyroidism. However, as the cost of sequencing continues to decrease and the amount of data continues to grow, computing methods have already dug out knowledge on a large scale from massive amounts of data. Gene regulation information could help researchers reveal pathogenic mechanisms. Therefore, in this paper, we proposed a novel method, &#x201C;RW-RVM,&#x201D; to identify hyperthyroidism-related genes. We constructed a gene interaction network based on the known gene interactions and used RW to encode this network to obtain the network topology relationship. In addition, we considered the regulation relationship between genes and non-coding RNAs. After fusing network topology relationship with regulation relationship, we built RVM models to identify hyperthyroidism-related genes. We performed 10-cross validation 10 times to verify the effectiveness of our method. We compared our method with several other methods and found our method performed best in both AUC and AUPR. Seventy-eight novel genes were found to be related to hyperthyroidism (<xref ref-type="supplementary-material" rid="TS1">Supplementary Table 1</xref>).</p>
<p>To verify the accuracy of our results, we did case studies. We found CD34 and MBL2 were associated with hyperthyroidism. <xref ref-type="bibr" rid="B15">Nagura et al. (2001)</xref> found that endothelial cells showing CD34 positivity were frequently observed in GD tissue. <xref ref-type="bibr" rid="B5">Filho et al. (2012)</xref> reported that MBL2 gene exon 1 variants are related to thyroid disease by sequencing 163 Brazilian patients and 214 healthy controls.</p>
<p>Overall, RW-RVM is a useful tool for discovering hyperthyroidism-related genes in large scale.</p>
</sec>
<sec id="S5">
<title>Data Availability Statement</title>
<p>The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/<xref ref-type="supplementary-material" rid="S9">Supplementary Material</xref>.</p>
</sec>
<sec id="S6">
<title>Ethics Statement</title>
<p>Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements. Written informed consent was not obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.</p>
</sec>
<sec id="S7">
<title>Author Contributions</title>
<p>FS, WC, JC, and BX participated in designing the study. FS, WC, XG, JF, ZC, MG, and FW analyzed the data. FS and WC wrote the manuscript. All authors read and approved the final manuscript.</p>
</sec>
<sec sec-type="COI-statement" id="conf1">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="pudiscl1">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
</body>
<back>
<fn-group>
<fn fn-type="financial-disclosure">
<p><bold>Funding.</bold> This work was supported by the Guangzhou Medicine and Health Care Technology Projects (20211A011010) and the Guangzhou Science and Technology Plan Project (202102080170).</p>
</fn>
</fn-group>
<sec id="S9" sec-type="supplementary-material">
<title>Supplementary Material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fcell.2021.700355/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fcell.2021.700355/full#supplementary-material</ext-link></p>
<supplementary-material xlink:href="Table_1.xls" id="TS1" mimetype="application/vnd.ms-excel" xmlns:xlink="http://www.w3.org/1999/xlink"/>
</sec>
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