# SAT Analogy Questions (State of the art)

• SAT = Scholastic Aptitude Test
• 374 multiple-choice analogy questions; 5 choices per question
• SAT questions collected by Michael Littman, available from Peter Turney
• introduced in Turney et al. (2003) as a way of evaluating algorithms for measuring relational similarity

## Sample question

 Stem: Choices: Solution: mason:stone (a) teacher:chalk (b) carpenter:wood (c) soldier:gun (d) photograph:camera (e) book:word (b) carpenter:wood

## Table of results

Algorithm Reference for algorithm Reference for experiment Type Correct 95% confidence
Random Random guessing 1 / 5 = 20.0% Random 20.0% 16.1-24.5%
JC Jiang and Conrath (1997) Turney (2006b) Hybrid 27.3% 23.1-32.4%
LIN Lin (1998) Turney (2006b) Hybrid 27.3% 23.1-32.4%
LC Leacock and Chodrow (1998) Turney (2006b) Lexicon-based 31.3% 26.9-36.5%
HSO Hirst and St.-Onge (1998) Turney (2006b) Lexicon-based 32.1% 27.6-37.4%
RES Resnik (1995) Turney (2006b) Hybrid 33.2% 28.7-38.5%
PMI-IR Turney (2001) Turney (2006b) Corpus-based 35.0% 30.2-40.1%
LSA+Predication Mangalath et al. (2004) Mangalath et al. (2004) Corpus-based 42.0% 37.2-47.4%
KNOW-BEST Veale (2004) Veale (2004) Lexicon-based 43.0% 38.0-48.2%
k-means Bicici and Yuret (2006) Bicici and Yuret (2006) Corpus-based 44.0% 39.0-49.3%
BagPack Herdağdelen and Baroni (2009) Herdağdelen and Baroni (2009) Corpus-based 44.1% (not stated in paper)
VSM Turney and Littman (2005) Turney and Littman (2005) Corpus-based 47.1% 42.2-52.5%
BMI Bollegala et al. (2009) Bollegala et al. (2009) Corpus-based 51.1% (not stated in paper)
PairClass Turney (2008) Turney (2008) Corpus-based 52.1% 46.9-57.3%
PERT Turney (2006a) Turney (2006a) Corpus-based 53.5% 48.5-58.9%
LRA Turney (2006b) Turney (2006b) Corpus-based 56.1% 51.0–61.2%
Human Average US college applicant Turney and Littman (2005) Human 57.0% 52.0-62.3%

## Explanation of table

• Algorithm = name of algorithm
• Reference for algorithm = where to find out more about given algorithm
• Reference for experiment = where to find out more about evaluation of given algorithm with SAT questions
• Type = general type of algorithm: corpus-based, lexicon-based, hybrid
• Correct = percent of 374 questions that given algorithm answered correctly
• 95% confidence = confidence interval calculated using Binomial Exact Test
• table rows sorted in order of increasing percent correct
• several WordNet-based similarity measures are implemented in Ted Pedersen's WordNet::Similarity package
• KNOW-BEST = KNOWledge-Based Entertainment and Scholastic Testing
• VSM = Vector Space Model
• LRA = Latent Relational Analysis
• PERT = Pertinence
• PMI-IR = Pointwise Mutual Information - Information Retrieval
• LSA+Predication = Latent Semantic Analysis + Predication
• BagPack = Bag of words representation of Paired concept knowledge

## References

Bicici, E., and Yuret, D. (2006). Clustering word pairs to answer analogy questions. Proceedings of the Fifteenth Turkish Symposium on Artificial Intelligence and Neural Networks (TAINN 2006).

Herdağdelen A. and Baroni M. BagPack: A general framework to repre- sent semantic relations. Proceedings of the EACL 2009 Geometrical Models for Natural Language Semantics (GEMS) Workshop, East Stroudsburg PA: ACL, 33-40.

Hirst, G., and St-Onge, D. (1998). Lexical chains as representation of context for the detection and correction of malapropisms. In C. Fellbaum (ed.), WordNet: An Electronic Lexical Database. Cambridge: MIT Press, 305-332.

Jiang, J.J., and Conrath, D.W. (1997). Semantic similarity based on corpus statistics and lexical taxonomy. Proceedings of the International Conference on Research in Computational Linguistics, Taiwan.

Leacock, C., and Chodorow, M. (1998). Combining local context and WordNet similarity for word sense identification. In C. Fellbaum (ed.), WordNet: An Electronic Lexical Database. Cambridge: MIT Press, pp. 265-283.

Lin, D. (1998). An information-theoretic definition of similarity. Proceedings of the 15th International Conference on Machine Learning (ICML-98), Madison, WI, pp. 296-304.

Mangalath, P., Quesada, J., and Kintsch, W. (2004). Analogy-making as predication using relational information and LSA vectors. In K.D. Forbus, D. Gentner & T. Regier (Eds.), Proceedings of the 26th Annual Meeting of the Cognitive Science Society. Chicago: Lawrence Erlbaum Associates.

Resnik, P. (1995). Using information content to evaluate semantic similarity. Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI-95), Montreal, pp. 448-453.

Turney, P.D., Littman, M.L., Bigham, J., and Shnayder, V. (2003). Combining independent modules to solve multiple-choice synonym and analogy problems. Proceedings of the International Conference on Recent Advances in Natural Language Processing (RANLP-03), Borovets, Bulgaria, pp. 482-489.

Turney, P.D., and Littman, M.L. (2005). Corpus-based learning of analogies and semantic relations. Machine Learning, 60 (1-3), 251-278.

Turney, P.D. (2001). Mining the Web for synonyms: PMI-IR versus LSA on TOEFL. Proceedings of the Twelfth European Conference on Machine Learning (ECML-2001), Freiburg, Germany, pp. 491-502.

Turney, P.D. (2006a). Expressing implicit semantic relations without supervision. Proceedings of the 21st International Conference on Computational Linguistics and 44th Annual Meeting of the Association for Computational Linguistics (Coling/ACL-06), Sydney, Australia, pp. 313-320.

Turney, P.D. (2006b). Similarity of semantic relations. Computational Linguistics, 32 (3), 379-416.

Turney, P.D. (2008). A uniform approach to analogies, synonyms, antonyms, and associations. Proceedings of the 22nd International Conference on Computational Linguistics (Coling 2008), Manchester, UK, pp. 905-912.

Veale, T. (2004). WordNet sits the SAT: A knowledge-based approach to lexical analogy. Proceedings of the 16th European Conference on Artificial Intelligence (ECAI 2004), pp. 606–612, Valencia, Spain.