Advertisement

On the Hardness of Domain Adaptation and the Utility of Unlabeled Target Samples

  • Shai Ben-David
  • Ruth Urner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7568)

Abstract

The Domain Adaptation problem in machine learning occurs when the test and training data generating distributions differ. We consider the covariate shift setting, where the labeling function is the same in both domains. Many works have proposed algorithms for Domain Adaptation in this setting. However, there are only very few generalization guarantees for these algorithms. We show that, without strong prior knowledge about the training task, such guarantees are actually unachievable (unless the training samples are prohibitively large). The contributions of this paper are two-fold: On the one hand we show that Domain Adaptation in this setup is hard. Even under very strong assumptions about the relationship between source and target distribution and, on top of that, a realizability assumption for the target task with respect to a small class, the required total sample sizes grow unboundedly with the domain size. On the other hand, we present settings where we achieve almost matching upper bounds on the sum of the sizes of the two samples. Moreover, the (necessarily large) samples can be mostly unlabeled (target) samples, which are often much cheaper to obtain than labels. The size of the labeled (source) sample shrinks back to standard dependence on the VC-dimension of the concept class. This implies that unlabeled target-generated data is provably beneficial for DA learning.

Keywords

Statistical Learning Theory Domain Adaptation Sample Complexity Unlabeled Data 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mansour, Y., Mohri, M., Rostamizadeh, A.: Domain adaptation: Learning bounds and algorithms. In: COLT (2009)Google Scholar
  2. 2.
    Cortes, C., Mansour, Y., Mohri, M.: Learning bounds for importance weighting. In: Lafferty, J., Williams, C.K.I., Shawe-Taylor, J., Zemel, R., Culotta, A. (eds.) Advances in Neural Information Processing Systems 23, pp. 442–450 (2010)Google Scholar
  3. 3.
    Sugiyama, M., Krauledat, M., Müller, K.R.: Covariate shift adaptation by importance weighted cross validation. Journal of Machine Learning Research 8, 985–1005 (2007)zbMATHGoogle Scholar
  4. 4.
    Tsuboi, Y., Kashima, H., Hido, S., Bickel, S., Sugiyama, M.: Direct density ratio estimation for large-scale covariate shift adaptation. Journal of Information Processing 17, 138–155 (2009)CrossRefGoogle Scholar
  5. 5.
    Ben-David, S., Blitzer, J., Crammer, K., Kulesza, A., Pereira, F., Vaughan, J.W.: A theory of learning from different domains. Machine Learning 79(1-2), 151–175 (2010)CrossRefGoogle Scholar
  6. 6.
    Ben-David, S., Shalev-Shwartz, S., Urner, R.: Domain adaptation–can quantity compensate for quality? In: ISAIM (2012)Google Scholar
  7. 7.
    Huang, J., Gretton, A., Schölkopf, B., Smola, A.J., Borgwardt, K.M.: Correcting sample selection bias by unlabeled data. In: NIPS. MIT Press (2007)Google Scholar
  8. 8.
    Sugiyama, M., Müller, K.: Generalization error estimation under covariate shift. In: Workshop on Information-Based Induction Sciences (2005)Google Scholar
  9. 9.
    Cortes, C., Mohri, M., Riley, M., Rostamizadeh, A.: Sample Selection Bias Correction Theory. In: Freund, Y., Györfi, L., Turán, G., Zeugmann, T. (eds.) ALT 2008. LNCS (LNAI), vol. 5254, pp. 38–53. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Kifer, D., Ben-David, S., Gehrke, J.: Detecting change in data streams. In: VLDB, pp. 180–191 (2004)Google Scholar
  11. 11.
    Cortes, C., Mohri, M.: Domain Adaptation in Regression. In: Kivinen, J., Szepesvári, C., Ukkonen, E., Zeugmann, T. (eds.) ALT 2011. LNCS, vol. 6925, pp. 308–323. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Ben-David, S., Lu, T., Luu, T., Pál, D.: Impossibility theorems for domain adaptation. In: AISTATS, vol. 9, pp. 129–136 (2010)Google Scholar
  13. 13.
    Kelly, B.G., Tularak, T., Wagner, A.B., Viswanath, P.: Universal hypothesis testing in the learning-limited regime. In: IEEE International Symposium on Information Theory (ISIT) (2010)Google Scholar
  14. 14.
    Batu, T., Fortnow, L., Rubinfeld, R., Smith, W.D., White, P.: Testing closeness of discrete distributions. CoRR abs/1009.5397 (2010)Google Scholar
  15. 15.
    Haussler, D., Welzl, E.: Epsilon-nets and simplex range queries. In: Proceedings of the Second Annual Symposium on Computational Geometry, SCG 1986, pp. 61–71. ACM, New York (1986)CrossRefGoogle Scholar
  16. 16.
    Ben-David, S., Litman, A.: Combinatorial variability of vapnik-chervonenkis classes with applications to sample compression schemes. Discrete Applied Mathematics 86(1), 3–25 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Ben-David, S.: Private communication (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shai Ben-David
    • 1
  • Ruth Urner
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations