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Analysis of co-evolutionary events among residues has been proved effective in inferring inter-residue contacts. The Markov random field (MRF) technique, although being widely used for contact prediction, suffers from the following dilemma: the actual likelihood function of MRF is accurate but time-consuming to calculate; in contrast, approximations to the actual likelihood, say pseudo-likelihood, are efficient to calculate but inaccurate. Thus, how to achieve both accuracy and efficiency simultaneously remains a challenge.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>In this study, we present such an approach (called clmDCA) for contact prediction. Unlike plmDCA using pseudo-likelihood, i.e., the product of conditional probability of individual residues, our approach uses composite-likelihood, i.e., the product of conditional probability of all residue pairs. Composite likelihood has been theoretically proved as a better approximation to the actual likelihood function than pseudo-likelihood. Meanwhile, composite likelihood is still efficient to maximize, thus ensuring the efficiency of clmDCA. We present comprehensive experiments on popular benchmark datasets, including PSICOV dataset and CASP-11 dataset, to show that:<jats:italic>i<\/jats:italic>) clmDCA alone outperforms the existing MRF-based approaches in prediction accuracy.<jats:italic>i<\/jats:italic><jats:italic>i<\/jats:italic>) When equipped with deep learning technique for refinement, the prediction accuracy of clmDCA was further significantly improved, suggesting the suitability of clmDCA for subsequent refinement procedure. We further present a successful application of the predicted contacts to accurately build tertiary structures for proteins in the PSICOV dataset.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>Composite likelihood maximization algorithm can efficiently estimate the parameters of Markov Random Fields and can improve the prediction accuracy of protein inter-residue contacts.<\/jats:p><\/jats:sec>","DOI":"10.1186\/s12859-019-3051-7","type":"journal-article","created":{"date-parts":[[2019,10,30]],"date-time":"2019-10-30T20:44:43Z","timestamp":1572468283000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Predicting protein inter-residue contacts using composite likelihood maximization and deep learning"],"prefix":"10.1186","volume":"20","author":[{"given":"Haicang","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fusong","family":"Ju","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianwei","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yujuan","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ziwei","family":"Xie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minghua","family":"Deng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shiwei","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei-Mou","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4119-4238","authenticated-orcid":false,"given":"Dongbo","family":"Bu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,10,29]]},"reference":[{"issue":"4096","key":"3051_CR1","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1126\/science.181.4096.223","volume":"181","author":"C. 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