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Overview of ARQMath 2020: CLEF Lab on Answer Retrieval for Questions on Math

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Experimental IR Meets Multilinguality, Multimodality, and Interaction (CLEF 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12260))

Abstract

The ARQMath Lab at CLEF considers finding answers to new mathematical questions among posted answers on a community question answering site (Math Stack Exchange). Queries are question posts held out from the searched collection, each containing both text and at least one formula. This is a challenging task, as both math and text may be needed to find relevant answer posts. ARQMath also includes a formula retrieval sub-task: individual formulas from question posts are used to locate formulae in earlier question and answer posts, with relevance determined considering the context of the post from which a query formula is taken, and the posts in which retrieved formulae appear.

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Notes

  1. 1.

    https://math.stackexchange.com.

  2. 2.

    https://www.cs.rit.edu/~dprl/ARQMath.

  3. 3.

    https://www.w3.org/Math.

  4. 4.

    https://dlmf.nist.gov.

  5. 5.

    https://archive.org/download/stackexchange.

  6. 6.

    https://dlmf.nist.gov/LaTeXML.

  7. 7.

    https://drive.google.com/drive/folders/1ZPKIWDnhMGRaPNVLi1reQxZWTfH2R4u3.

  8. 8.

    https://github.com/ARQMath/ARQMathCode.

  9. 9.

    Note that participating systems did not have access to this information.

  10. 10.

    https://github.com/hltcoe/turkle.

  11. 11.

    H+M binarization corresponds to the definition of relevance usually used in the Text Retrieval Conference (TREC). The TREC definition is “If you were writing a report on the subject of the topic and would use the information contained in the document in the report, then the document is relevant. Only binary judgments (“relevant” or “not relevant”) are made, and a document is judged relevant if any piece of it is relevant (regardless of how small the piece is in relation to the rest of the document).” (source: https://trec.nist.gov/data/reljudge_eng.html).

  12. 12.

    Pooling to at least depth 20 ensures that there are no unjudged posts above rank 10 for any primary or secondary submission, and for four of the five baselines. Note, however, that P@10 can not achieve a value of 1 because some topics have fewer than 10 relevant posts.

  13. 13.

    https://github.com/usnistgov/trec_eval.

  14. 14.

    One team submitted incorrect post id’s for retrieved formulae; those post id’s were not used for pooling.

  15. 15.

    See, for example, MathDeck  [16], in which candidate formulae are suggested to the users during formula editing.

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Acknowledgements

Wei Zhong suggested using Math Stack Exchange for benchmarking, made Approach0 available for participants, and provided helpful feedback. Kenny Davila helped with the Tangent-S formula search results. We also thank our student assessors from RIT: Josh Anglum, Wiley Dole, Kiera Gross, Justin Haverlick, Riley Kieffer, Minyao Li, Ken Shultes, and Gabriella Wolf. This material is based upon work supported by the National Science Foundation (USA) under Grant No. IIS- 1717997 and the Alfred P. Sloan Foundation under Grant No. G-2017-9827.

Author information

Authors and Affiliations

  1. Rochester Institute of Technology, Rochester, NY, USA

    Richard Zanibbi, Anurag Agarwal & Behrooz Mansouri

  2. University of Maryland, College Park, USA

    Douglas W. Oard

Authors
  1. Richard Zanibbi
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Corresponding author

Correspondence to Douglas W. Oard .

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Greece

    Avi Arampatzis

  2. University of Amsterdam, Amsterdam, The Netherlands

    Evangelos Kanoulas

  3. Information Technologies Institute, Centre for Research and Technology Hellas, Thessaloniki, Greece

    Theodora Tsikrika

  4. Information Technologies Institute, Centre for Research and Technology Hellas, Thessaloniki, Greece

    Stefanos Vrochidis

  5. Faculty of Library, Information and Media Science, University of Tsukuba, Ibaraki, Japan

    Hideo Joho

  6. Department of Computer Science, University of Copenhagen, Copenhagen, Denmark

    Christina Lioma

  7. Brown University, Providence, RI, USA

    Carsten Eickhoff

  8. LIMSI-CNRS, Orsay, France

    Aurélie Névéol

  9. Department of Information Engineering, University of Padova, Padua, Italy

    Linda Cappellato

  10. Department of Information Engineering, University of Padova, Padua, Italy

    Nicola Ferro

A Appendix: Evaluation Results

A Appendix: Evaluation Results

Table 4. Task 1 (CQA) results, averaged over 77 topics. P indicates a primary run, M indicates a manual run, and indicates a baseline pooled at the primary run depth. For Precision@10 and MAP, H+M binarization was used. The best baseline results are in parentheses. * indicates that one baseline did not contribute to judgment pools.
Full size table
Table 5. Task 2 (Formula Retrieval) results, averaged over 45 topics and computed over deduplicated ranked lists of visually distinct formulae. P indicates a primary run, and shows the baseline pooled at the primary run depth. For MAP and P@10, relevance was thresholded H+M binarization. All runs were automatic. Baseline results are in parentheses.
Full size table

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Zanibbi, R., Oard, D.W., Agarwal, A., Mansouri, B. (2020). Overview of ARQMath 2020: CLEF Lab on Answer Retrieval for Questions on Math. In: Arampatzis, A., et al. Experimental IR Meets Multilinguality, Multimodality, and Interaction. CLEF 2020. Lecture Notes in Computer Science(), vol 12260. Springer, Cham. https://doi.org/10.1007/978-3-030-58219-7_15

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