Direct density-ratio estimation with dimensionality reduction via least-squares hetero-distributional subspace search

Neural Networks

Volumn 24, Issue 2, 2011, Pages 183-198

  Sugiyama, Masashi ^a,b   Yamada, Makoto ^a   von Bünau, Paul ^c   Suzuki, Taiji ^d   Kanamori, Takafumi ^e   Kawanabe, Motoaki ^f  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^c TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^d UNIVERSITY OF TOKYO   (Japan)

^e NAGOYA UNIVERSITY   (Japan)

^f FRAUNHOFER FIRST   (Germany)

Author keywords

Density ratio estimation; Dimensionality reduction; Unconstrained least squares importance fitting

Indexed keywords

DATA HANDLING; PROBABILITY DENSITY FUNCTION;

BASELINE METHODS; DENSITY-RATIO ESTIMATIONS; DIMENSIONALITY REDUCTION; LEAST SQUARE; LOW-DIMENSIONAL SUBSPACE; NON-STATIONARITIES; OUTLIER DETECTION;

LEAST SQUARES APPROXIMATIONS;

ACCURACY; AREA UNDER THE CURVE; ARTICLE; DENSITY FUNCTIONAL THEORY; INFORMATION PROCESSING; MACHINE LEARNING; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; PROBABILITY; RECEIVER OPERATING CHARACTERISTIC; REGRESSION ANALYSIS;

EID: 79251612332     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2010.10.005     Document Type: Article

References (78)

1. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control 1974, AC-19:716-723.
2. Akiyama T., Hachiya H., Sugiyama M. Efficient exploration through active learning for value function approximation in reinforcement learning. Neural Networks 2010, 23:639-648.
3. Ali S.M., Silvey S.D. A general class of coefficients of divergence of one distribution from another. Journal of the Royal Statistical Society, Series B 1966, 28:131-142.
4. Amari S. Natural gradient works efficiently in learning. Neural Computation 1998, 10:251-276.
5. Aronszajn N. Theory of reproducing kernels. Transactions of the American Mathematical Society 1950, 68:337-404.
6. Asuncion, A., & Newman, D. (2007). UCI machine learning repository.
7. Bensaid N., Fabre J.P. Optimal asymptotic quadratic error of kernel estimators of Radon-Nikodym derivatives for strong mixing data. Journal of Nonparametric Statistics 2007, 19:77-88.
8. Bickel, S., Bogojeska, J., Lengauer, T., & Scheffer, T. (2008). Multi-task learning for HIV therapy screening. In Proceedings of 25th annual international conference on machine learning. ICML2008 (pp. 56-63).
9. Bickel, S., Brückner, M., & Scheffer, T. (2007). Discriminative learning for differing training and test distributions. In Proceedings of the 24th international conference on machine learning. ICML2007 (pp. 81-88).
10. Bishop C.M. Pattern recognition and machine learning 2006, Springer, New York, NY, USA.
11. Boyd S., Vandenberghe L. Convex optimization 2004, Cambridge University Press, Cambridge, UK.
12. Bradley A.P. The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recognition 1997, 30:1145-1159.
13. Chen S.-M., Hsu Y.-S., Liaw J.-T. On kernel estimators of density ratio. Statistics 2009, 43:463-479.
14. Cheng K.F., Chu C.K. Semiparametric density estimation under a two-sample density ratio model. Bernoulli 2004, 10:583-604.
15. Cover T.M., Thomas J.A. Elements of information theory 2006, John Wiley & Sons, Inc., Hoboken, NJ, USA. 2nd ed.
16. Csiszár I. Information-type measures of difference of probability distributions and indirect observation. Studia Scientiarum Mathematicarum Hungarica 1967, 2:229-318.
17. Ćwik J., Mielniczuk J. Estimating density ratio with application to discriminant analysis. Communications in Statistics: Theory and Methods 1989, 18:3057-3069.
18. Fishman G.S. Monte Carlo: concepts, algorithms, and applications 1996, Springer-Verlag, Berlin, Germany.
19. Gijbels I., Mielniczuk J. Asymptotic properties of kernel estimators of the Radon-Nikodym derivative with applications to discriminant analysis. Statistica Sinica 1995, 5:261-278.
20. Golub G.H., Loan C.F.V. Matrix computations 1996, Johns Hopkins University Press, Baltimore, MD, USA.
21. Hachiya H., Akiyama T., Sugiyama M., Peters J. Adaptive importance sampling for value function approximation in off-policy reinforcement learning. Neural Networks 2009, 22:1399-1410.
22. Hachiya H., Peters J., Sugiyama M. Efficient sample reuse in EM-based policy search. Machine learning and knowledge discovery in databases 2009, 469-484. Springer, Berlin.
23. Härdle W., Müller M., Sperlich S., Werwatz A. Nonparametric and semiparametric models 2004, Springer, Berlin, Germany.
24. Henkel R.E. Tests of significance 1979, SAGE Publication, Beverly Hills, CA, USA.
25. Hido, S., Tsuboi, Y., Kashima, H., Sugiyama, M., & Kanamori, T. (2008). Inlier-based outlier detection via direct density ratio estimation. In Proceedings of IEEE international conference on data mining. ICDM2008 (pp. 223-232).
26. Hido, S., Tsuboi, Y., Kashima, H., Sugiyama, M., & Kanamori, T. (2010). Statistical outlier detection using direct density ratio estimation. Knowledge and Information Systems (in press).
27. Huang J., Smola A., Gretton A., Borgwardt K.M., Schölkopf B. Correcting sample selection bias by unlabeled data. Advances in neural information processing systems 2007, vol. 19:601-608. MIT Press, Cambridge, MA, USA.
28. Hulle M.M.V. Edgeworth approximation of multivariate differential entropy. Neural Computation 2005, 17:1903-1910.
29. Jacob P., Oliveira P.E. Kernel estimators of general Radon-Nikodym derivatives. Statistics 1997, 30:25-46.
30. Kanamori T., Shimodaira H. Active learning algorithm using the maximum weighted log-likelihood estimator. Journal of Statistical Planning and Inference 2003, 116:149-162.
31. Kanamori T., Hido S., Sugiyama M. A least-squares approach to direct importance estimation. Journal of Machine Learning Research 2009, 10:1391-1445.
32. Kanamori, T., Suzuki, T., & Sugiyama, M. (2009). Condition number analysis of kernel-based density ratio estimation. Technical report. arXiv.
33. Kawahara, Y., & Sugiyama, M. (2009). Change-point detection in time-series data by direct density-ratio estimation. In Proceedings of 2009 SIAM international conference on data mining. SDM2009 (pp. 389-400).
34. Kraskov A., Stögbauer H., Grassberger P. Estimating mutual information. Physical Review E 2004, 69:066138.
35. Kullback S., Leibler R.A. On information and sufficiency. Annals of Mathematical Statistics 1951, 22:79-86.
36. Nguyen, X., Wainwright, M. J., & Jordan, M. I. (2010). Estimating divergence functionals and the likelihood ratio by convex risk minimization. IEEE Transactions on Information Theory (in press).
37. Nishimori Y., Akaho S. Learning algorithms utilizing quasi-geodesic flows on the Stiefel manifold. Neurocomputing 2005, 67:106-135.
38. Patriksson M. Nonlinear programming and variational inequality problems 1999, Kluwer Academic, Dordrecht, The Netherlands.
39. Petersen, K. B., & Pedersen, M. S. (2008). The matrix cookbook. Technical report. Technical University of Denmark.
40. Plumbley M.D. Geometrical methods for non-negative ICA: manifolds, Lie groups and toral subalgebras. Neurocomputing 2005, 67:161-197.
41. Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T. Numerical recipes in C 1992, Cambridge University Press, Cambridge, UK. 2nd ed.
42. Qin J. Inferences for case-control and semiparametric two-sample density ratio models. Biometrika 1998, 85:619-639.
43. Dataset shift in machine learning 2009, MIT Press, Cambridge, Massachusetts, USA. J. Quiñonero-Candela, M. Sugiyama, A. Schwaighofer, N. Lawrence (Eds.).
44. Shimodaira H. Improving predictive inference under covariate shift by weighting the log-likelihood function. Journal of Statistical Planning and Inference 2000, 90:227-244.
45. Silverman B.W. Density ratios, empirical likelihood and cot death. Journal of the Royal Statistical Society, Series C 1978, 27:26-33.
46. Silverman B.W. Density estimation for statistics and data analysis 1986, Chapman and Hall, London, UK.
47. Smola, A., Song, L., & Teo, C. H. (2009). Relative novelty detection. In Proceedings of twelfth international conference on artificial intelligence and statistics. AISTATS2009. Clearwater Beach, FL, USA (pp. 536-543).
48. Steinwart I. On the influence of the kernel on the consistency of support vector machines. Journal of Machine Learning Research 2001, 2:67-93.
49. Stone M. Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, Series B 1974, 36:111-147.
50. Storkey A., Sugiyama M. Mixture regression for covariate shift. Advances in neural information processing systems 2007, vol. 19:1337-1344. MIT Press, Cambridge, Massachusetts, USA.
51. Sugiyama M. Active learning in approximately linear regression based on conditional expectation of generalization error. Journal of Machine Learning Research 2006, 7:141-166.
52. Sugiyama M. Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. Journal of Machine Learning Research 2007, 8:1027-1061.
53. Sugiyama M. Superfast-trainable multi-class probabilistic classifier by least-squares posterior fitting. IEICE Transactions on Information and Systems 2010, E93-D:2690-2701.
54. Sugiyama M., Kanamori T., Suzuki T., Hido S., Sese J., Takeuchi I., et al. A density-ratio framework for statistical data processing. IPSJ Transactions on Computer Vision and Applications 2009, 1:183-208.
55. Sugiyama, M., & Kawanabe, M. (2010). Covariate shift adaptation: towards machine learning in non-stationary environment. Cambridge, MA, USA. MIT Press (in press).
56. Sugiyama M., Kawanabe M., Chui P.L. Dimensionality reduction for density ratio estimation in high-dimensional spaces. Neural Networks 2010, 23:44-59.
57. Sugiyama M., Krauledat M., Müller K.-R. Covariate shift adaptation by importance weighted cross validation. Journal of Machine Learning Research 2007, 8:985-1005.
58. Sugiyama M., Müller K.-R. Input-dependent estimation of generalization error under covariate shift. Statistics & Decisions 2005, 23:249-279.
59. Sugiyama M., Nakajima S. Pool-based active learning in approximate linear regression. Machine Learning 2009, 75:249-274.
60. Sugiyama M., Suzuki T., Kanamori T. Density ratio estimation: a comprehensive review. RIMS Kokyuroku 2010, 10-31.
61. Sugiyama M., Suzuki T., Kanamori T. Density ratio estimation in machine learning: a versatile tool for statistical data processing 2011, Cambridge University Press, Cambridge, UK.
62. Sugiyama M., Suzuki T., Nakajima S., Kashima H., von Bünau P., Kawanabe M. Direct importance estimation for covariate shift adaptation. Annals of the Institute of Statistical Mathematics 2008, 60:699-746.
63. Sugiyama M., Takeuchi I., Suzuki T., Kanamori T., Hachiya H., Okanohara D. Least-squares conditional density estimation. IEICE Transactions on Information and Systems 2010, E93-D:583-594.
64. Sun J., Woodroofe M. Semi-parametric estimates under biased sampling. Statistica Sinica 1997, 7:545-575.
65. Suzuki T., Sugiyama M. Estimating squared-loss mutual information for independent component analysis. Independent component analysis and signal separation 2009, 130-137. Springer, Berlin, Germany.
66. Suzuki, T., & Sugiyama, M. (2010). Sufficient dimension reduction via squared-loss mutual information estimation. In Proceedings of the thirteenth international conference on artificial intelligence and statistics. AISTATS2010 (pp. 804-811).
67. Suzuki T., Sugiyama M., Kanamori T., Sese J. Mutual information estimation reveals global associations between stimuli and biological processes. BMC Bioinformatics 2009, 10:S52.
68. Suzuki, T., Sugiyama, M., Sese, J., & Kanamori, T. (2008). Approximating mutual information by maximum likelihood density ratio estimation. In Proceedings of ECML-PKDD2008 workshop on new challenges for feature selection in data mining and knowledge discovery 2008. FSDM2008 (pp. 5-20).
69. Suzuki, T., Sugiyama, M., & Tanaka, T. (2009). Mutual information approximation via maximum likelihood estimation of density ratio. In Proceedings of 2009 IEEE international symposium on information theory. ISIT2009 (pp. 463-467).
70. Takeuchi I., Nomura K., Kanamori T. Nonparametric conditional density estimation using piecewise-linear solution path of kernel quantile regression. Neural Computation 2009, 21:533-559.
71. Tsuboi Y., Kashima H., Hido S., Bickel S., Sugiyama M. Direct density ratio estimation for large-scale covariate shift adaptation. Journal of Information Processing 2009, 17:138-155.
72. Ueki, K., Sugiyama, M., & Ihara, Y. (2010). Perceived age estimation under lighting condition change by covariate shift adaptation. In 20th international conference on pattern recognition. ICPR2010 (pp. 3400-3403).
73. Vapnik V.N. Statistical learning theory 1998, Wiley, New York, NY, USA.
74. Wahba G. Spline models for observational data 1990, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.
75. Wiens D.P. Robust weights and designs for biased regression models: least squares and generalized M-estimation. Journal of Statistical Planning and Inference 2000, 83:395-412.
76. Yamada M., Sugiyama M. Dependence minimizing regression with model selection for non-linear causal inference under non-Gaussian noise. Proceedings of the twenty-fourth AAAI conference on artificial intelligence 2010, 643-648. The AAAI Press, Atlanta, Georgia, USA.
77. Yamada M., Sugiyama M., Matsui T. Semi-supervised speaker identification under covariate shift. Signal Processing 2010, 90:2353-2361.
78. Zadrozny B. Learning and evaluating classifiers under sample selection bias. Proceedings of the twenty-first international conference on machine learning 2004, 903-910. ACM Press, New York, NY, USA.