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This algorithm is based on a generalization of the H-criterion as the objective function and the growth transformations as the optimization method. For the development of the discriminative estimation algorithm, the <jats:italic>N<\/jats:italic>-best interpretations provided by the 2D-PCFG have been considered. Experimental results are reported on two available datasets: <jats:italic>Im2Latex<\/jats:italic> and <jats:italic>IBEM<\/jats:italic>. The first experiment compares the proposed discriminative estimation method with the classic Viterbi-based estimation method. The second one studies the performance of the estimated models depending on the length of the mathematical expressions and the number of admissible errors in the metric used.<\/jats:p>","DOI":"10.1007\/s10044-023-01158-8","type":"journal-article","created":{"date-parts":[[2023,4,18]],"date-time":"2023-04-18T11:10:21Z","timestamp":1681816221000},"page":"1571-1584","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Discriminative estimation of probabilistic context-free grammars for mathematical expression recognition and retrieval"],"prefix":"10.1007","volume":"26","author":[{"given":"Ernesto","family":"Noya","sequence":"first","affiliation":[]},{"given":"Jos\u00e9 Miguel","family":"Bened\u00ed","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0423-2020","authenticated-orcid":false,"given":"Joan Andreu","family":"S\u00e1nchez","sequence":"additional","affiliation":[]},{"given":"Dan","family":"Anitei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,18]]},"reference":[{"issue":"2","key":"1158_CR1","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1109\/TPAMI.1983.4767370","volume":"5","author":"LR Bahl","year":"1983","unstructured":"Bahl LR, Jelinek F, Mercer RL (1983) A maximum likelihood approach to continuous speech recognition. 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