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Control Variates for Similarity Search

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Pattern Recognition and Computer Vision (PRCV 2021)

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Abstract

We present an alternative technique for similarity estimation under locality sensitive hashing (LSH) schemes with discrete output. By utilising control variates and extra information, we are able to achieve better theoretical variance reductions compared to maximum likelihood estimation with extra information. We show that our method obtains equivalent results, but slight modifications can provide better empirical results and stability at lower dimensions. Finally, we compare the various methods’ performances on the MNIST and Gisette dataset, and show that our model achieves better accuracy and stability.

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References

  1. Achlioptas, D.: Database-friendly random projections: Johnson-Lindenstrauss with binary coins. J. Comput. Syst. Sci. 66(4), 671–687 (2003)

    Article  MathSciNet  Google Scholar 

  2. Broder, A.Z.: On the resemblance and containment of documents. In: Compression and Complexity of Sequences 1997, Proceedings, pp. 21–29. IEEE (1997)

    Google Scholar 

  3. Charikar, M.S.: Similarity estimation techniques from rounding algorithms. In: Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, pp. 380–388. ACM (2002)

    Google Scholar 

  4. Glynn, P.W., Szechtman, R.: Some new perspectives on the method of control variates. In: Fang, K.T., Niederreiter, H., Hickernell, F.J. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 27–49. Springer, Heidelberg (2002). https://doi.org/10.1007/978-3-642-56046-0_3

  5. Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM (JACM) 42(6), 1115–1145 (1995)

    Article  MathSciNet  Google Scholar 

  6. Guyon, I., Gunn, S., Ben-Hur, A., Dror, G.: Result analysis of the NIPS 2003 feature selection challenge. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems 17, pp. 545–552. MIT Press (2005)

    Google Scholar 

  7. Guyon, I., Gunn, S.R., Ben-Hur, A., Dror, G.: Result analysis of the NIPS 2003 feature selection challenge. In: NIPS, vol. 4, pp. 545–552 (2004)

    Google Scholar 

  8. Indyk, P., Motwani, R.: Approximate nearest neighbors: towards removing the curse of dimensionality. In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, STOC 1998, pp. 604–613. ACM, New York (1998). https://doi.org/10.1145/276698.276876, http://doi.acm.org/10.1145/276698.276876

  9. Kang, K.: Using the multivariate normal to improve random projections. In: Yin, H., et al. (eds.) IDEAL 2017. LNCS, vol. 10585, pp. 397–405. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68935-7_43

    Chapter  Google Scholar 

  10. Kang, K.: Correlations between random projections and the bivariate normal. Data Min. Knowl. Disc. 35(4), 1622–1653 (2021). https://doi.org/10.1007/s10618-021-00764-6

    Article  MathSciNet  Google Scholar 

  11. Kang, K., Wong, W.P.: Improving sign random projections with additional information. In: International Conference on Machine Learning, pp. 2479–2487. PMLR (2018)

    Google Scholar 

  12. LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)

    Article  Google Scholar 

  13. Li, P., Hastie, T.J., Church, K.W.: Improving random projections using marginal information. In: Lugosi, G., Simon, H.U. (eds.) COLT 2006. LNCS (LNAI), vol. 4005, pp. 635–649. Springer, Heidelberg (2006). https://doi.org/10.1007/11776420_46

    Chapter  Google Scholar 

  14. Lichman, M.: UCI Machine Learning Repository (2013). http://archive.ics.uci.edu/ml

  15. Rubinstein, R.Y., Marcus, R.: Efficiency of multivariate control variates in Monte Carlo simulation. Oper. Res. 33(3), 661–677 (1985)

    Article  MathSciNet  Google Scholar 

  16. Slaney, M., Casey, M.: Locality-sensitive hashing for finding nearest neighbors [lecture notes]. IEEE Signal Process. Mag. 25(2), 128–131 (2008)

    Article  Google Scholar 

  17. Szechtman, R., Glynn, P.W.: Constrained Monte Carlo and the method of control variates. In: Proceeding of the 2001 Winter Simulation Conference (Cat. No. 01CH37304), vol. 1, pp. 394–400. IEEE (2001)

    Google Scholar 

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Acknowledgements

This work is funded by the Singapore Ministry of Education Academic Research Fund Tier 2 Grant MOE2018-T2-2-013, as well as with the support of the Singapore University of Technology and Design’s Undergraduate Research Opportunities Programme.

The authors also thank the anonymous reviewers for their comments and suggestions for improvement, which has helped to enhance the quality of the paper.

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Correspondence to Jeremy Chew .

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Chew, J., Kang, K. (2021). Control Variates for Similarity Search. In: Ma, H., et al. Pattern Recognition and Computer Vision. PRCV 2021. Lecture Notes in Computer Science(), vol 13019. Springer, Cham. https://doi.org/10.1007/978-3-030-88004-0_38

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  • DOI: https://doi.org/10.1007/978-3-030-88004-0_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-88003-3

  • Online ISBN: 978-3-030-88004-0

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