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Volumn 13, Issue 7, 2011, Pages 1229-1266

On accuracy of PDF divergence estimators and their applicability to representative data sampling

Author keywords

Cross validation; Divergence estimation; Generalisation error estimation; Kullback Leibler divergence; Sampling

Indexed keywords


EID: 80051601039     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e13071229     Document Type: Article
Times cited : (28)

References (49)
  • 1
    • 79959476267 scopus 로고    scopus 로고
    • Correntropy-based density-preserving data sampling as an alternative to standard cross-validation
    • IJCNN 2010, part of the IEEE World Congress on Computational Intelligence, WCCI, 2010, Barcelona, Spain, 18-23 July
    • Budka, M.; Gabrys, B. Correntropy-based density-preserving data sampling as an alternative to standard cross-validation. In Proceedings of the International Joint Conference on Neural Networks, IJCNN 2010, part of the IEEE World Congress on Computational Intelligence, WCCI 2010, Barcelona, Spain, 18-23 July 2010; pp. 1437-1444.
    • (2010) Proceedings of the International Joint Conference on Neural Networks , pp. 1437-1444
    • Budka, M.1    Gabrys, B.2
  • 2
    • 80051601886 scopus 로고    scopus 로고
    • Density Preserving Sampling (DPS) for error estimation and model selection
    • submitted for publication
    • Budka, M.; Gabrys, B. Density Preserving Sampling (DPS) for error estimation and model selection. IEEE Trans. Pattern Anal. Mach. Intell. submitted for publication, 2011.
    • (2011) IEEE Trans. Pattern Anal. Mach. Intell.
    • Budka, M.1    Gabrys, B.2
  • 3
    • 85164392958 scopus 로고
    • A study of cross-validation and bootstrap for accuracy estimation and model selection
    • Montreal, Canada, 20-25 August 1995, Morgan Kaufmann: San Francisco, CA, USA
    • Kohavi, R. A study of cross-validation and bootstrap for accuracy estimation and model selection. In Proceedings of the 14th International Joint Conference on Artificial Intelligence, Montreal, Canada, 20-25 August 1995; Morgan Kaufmann: San Francisco, CA, USA, 1995; Volume 2, pp. 1137-1145.
    • (1995) Proceedings of the 14th International Joint Conference on Artificial Intelligence , vol.2 , pp. 1137-1145
    • Kohavi, R.1
  • 5
    • 0001473437 scopus 로고
    • On estimation of a probability density function and mode
    • Parzen, E. On estimation of a probability density function and mode. Ann. Math. Stat. 1962, 33, 1065-1076.
    • (1962) Ann. Math. Stat. , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 7
    • 0016355478 scopus 로고
    • A new look at the statistical model identification
    • Akaike, H. A new look at the statistical model identification. IEEE Trans. Automat. Contr. 1974, 19, 716-723.
    • (1974) IEEE Trans. Automat. Contr. , vol.19 , pp. 716-723
    • Akaike, H.1
  • 8
    • 9744257850 scopus 로고    scopus 로고
    • A small sample model selection criterion based on Kullback's symmetric divergence
    • Seghouane, A.; Bekara, M. A small sample model selection criterion based on Kullback's symmetric divergence. IEEE Trans. Signal Process. 2004, 52, 3314-3323.
    • (2004) IEEE Trans. Signal Process. , vol.52 , pp. 3314-3323
    • Seghouane, A.1    Bekara, M.2
  • 9
    • 0000859675 scopus 로고
    • An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion
    • Stone, M. An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. J. Roy. Stat. Soc. B 1977, 39, 44-47.
    • (1977) J. Roy. Stat. Soc. B , vol.39 , pp. 44-47
    • Stone, M.1
  • 10
    • 77958588617 scopus 로고    scopus 로고
    • Estimating divergence functionals and the likelihood ratio by convex risk minimization
    • Nguyen, X.; Wainwright, M.; Jordan, M. Estimating divergence functionals and the likelihood ratio by convex risk minimization. IEEE Trans. Inform. Theor. 2010, 56, 5847-5861.
    • (2010) IEEE Trans. Inform. Theor. , vol.56 , pp. 5847-5861
    • Nguyen, X.1    Wainwright, M.2    Jordan, M.3
  • 11
    • 33750503776 scopus 로고    scopus 로고
    • The Cauchy-Schwarz divergence and Parzen windowing: Connections to graph theory and Mercer kernels
    • Jenssen, R.; Principe, J.; Erdogmus, D.; Eltoft, T. The Cauchy-Schwarz divergence and Parzen windowing: Connections to graph theory and Mercer kernels. J. Franklin Inst. 2006, 343, 614-629.
    • (2006) J. Franklin Inst. , vol.343 , pp. 614-629
    • Jenssen, R.1    Principe, J.2    Erdogmus, D.3    Eltoft, T.4
  • 12
    • 68849117465 scopus 로고
    • Bandwidth selection in kernel density estimation: A review
    • Turlach, B. Bandwidth selection in kernel density estimation: A review. CORE and Institut de Statistique 1993, 23-493.
    • (1993) CORE and Institut de Statistique , pp. 23-493
    • Turlach, B.1
  • 13
    • 0017017305 scopus 로고
    • On the choice of smoothing parameters for Parzen estimators of probability density functions
    • Duin, R. On the choice of smoothing parameters for Parzen estimators of probability density functions. IEEE Trans. Comput. 1976, 100, 1175-1179.
    • (1976) IEEE Trans. Comput. , vol.100 , pp. 1175-1179
    • Duin, R.1
  • 15
    • 0001268552 scopus 로고
    • A Reliable Data-Based Bandwidth SelectionMethod for Kernel Density Estimation
    • Sheather, S.J.; Jones,M.C. A Reliable Data-Based Bandwidth SelectionMethod for Kernel Density Estimation. J. Roy. Stat. Soc. B 1991, 53, 683-690.
    • (1991) J. Roy. Stat. Soc. B , vol.53 , pp. 683-690
    • Sheather, S.J.1    Jones, M.C.2
  • 16
    • 0001050272 scopus 로고    scopus 로고
    • A Brief Survey of Bandwidth Selection for Density Estimation
    • Jones, M.C.; Marron, J.S.; Sheather, S.J. A Brief Survey of Bandwidth Selection for Density Estimation. J. Am. Stat. Assoc. 1996, 91, 401-407.
    • (1996) J. Am. Stat. Assoc. , vol.91 , pp. 401-407
    • Jones, M.C.1    Marron, J.S.2    Sheather, S.J.3
  • 17
    • 33745476564 scopus 로고    scopus 로고
    • Fast optimal bandwidth selection for kernel density estimation
    • Bethesda, Maryland, USA, 20-22 April 2006, Ghosh, J., Lambert, D., Skillicorn, D., Srivastava, J., Eds.; SIAM: Philadelphia, PA, USA
    • Raykar, V.C.; Duraiswami, R. Fast optimal bandwidth selection for kernel density estimation. In Proceedings of the 6th SIAM International Conference on Data Mining, Bethesda, Maryland, USA, 20-22 April 2006; Ghosh, J., Lambert, D., Skillicorn, D., Srivastava, J., Eds.; SIAM: Philadelphia, PA, USA, 2006; pp. 524-528.
    • (2006) Proceedings of the 6th SIAM International Conference on Data Mining , pp. 524-528
    • Raykar, V.C.1    Duraiswami, R.2
  • 18
  • 19
    • 77956416620 scopus 로고    scopus 로고
    • Families of Alpha-Beta-and Gamma-Divergences: Flexible and Robust Measures of Similarities
    • Cichocki, A.; Amari, S. Families of Alpha-Beta-and Gamma-Divergences: Flexible and Robust Measures of Similarities. Entropy 2010, 12, 1532-1568.
    • (2010) Entropy , vol.12 , pp. 1532-1568
    • Cichocki, A.1    Amari, S.2
  • 21
    • 0001927585 scopus 로고
    • On information and sufficiency
    • Kullback, S.; Leibler, R. On information and sufficiency. Ann. Math. Stat. 1951, 22, 79-86.
    • (1951) Ann. Math. Stat. , vol.22 , pp. 79-86
    • Kullback, S.1    Leibler, R.2
  • 24
    • 0031122399 scopus 로고    scopus 로고
    • Infomax and maximum likelihood for blind source separation
    • Cardoso, J. Infomax and maximum likelihood for blind source separation. IEEE Signal Process. Lett. 1997, 4, 112-114.
    • (1997) IEEE Signal Process. Lett. , vol.4 , pp. 112-114
    • Cardoso, J.1
  • 25
    • 0032187518 scopus 로고    scopus 로고
    • Blind signal separation: statistical principles
    • Cardoso, J. Blind signal separation: statistical principles. Proc. IEEE 1998, 86, 2009-2025.
    • (1998) Proc. IEEE , vol.86 , pp. 2009-2025
    • Cardoso, J.1
  • 26
    • 0029669420 scopus 로고    scopus 로고
    • A comparative study of texture measures with classification based on featured distributions
    • Ojala, T.; Pietik̈ainen, M.; Harwood, D. A comparative study of texture measures with classification based on featured distributions. Pattern Recogn. 1996, 29, 51-59.
    • (1996) Pattern Recogn , vol.29 , pp. 51-59
    • Ojala, T.1    Pietik̈ainen, M.2    Harwood, D.3
  • 27
    • 0032355984 scopus 로고    scopus 로고
    • Classification by pairwise coupling
    • Hastie, T.; Tibshirani, R. Classification by pairwise coupling. Ann. Stat. 1998, 26, 451-471.
    • (1998) Ann. Stat. , vol.26 , pp. 451-471
    • Hastie, T.1    Tibshirani, R.2
  • 28
    • 0033338289 scopus 로고    scopus 로고
    • Image compression via joint statistical characterization in the wavelet domain
    • Buccigrossi, R.; Simoncelli, E. Image compression via joint statistical characterization in the wavelet domain. IEEE Trans. Image Process. 1999, 8, 1688-1701.
    • (1999) IEEE Trans. Image Process. , vol.8 , pp. 1688-1701
    • Buccigrossi, R.1    Simoncelli, E.2
  • 29
    • 84899001695 scopus 로고    scopus 로고
    • A Kullback-Leibler divergence based kernel for SVM classification inmultimedia applications
    • Moreno, P.; Ho, P.; Vasconcelos, N. A Kullback-Leibler divergence based kernel for SVM classification inmultimedia applications. Adv. Neural Inform. Process. Syst. 2004, 16, 1385-1392.
    • (2004) Adv. Neural Inform. Process. Syst. , vol.16 , pp. 1385-1392
    • Moreno, P.1    Ho, P.2    Vasconcelos, N.3
  • 31
  • 32
    • 34547516258 scopus 로고    scopus 로고
    • Approximating the Kullback-Leibler divergence between Gaussian mixture models
    • Speech and Signal Processing, Honolulu, Hawaii, 15-20 April
    • Hershey, J.; Olsen, P. Approximating the Kullback-Leibler divergence between Gaussian mixture models. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Honolulu, Hawaii, 15-20 April 2007; Volume 4, pp. 317-320.
    • (2007) Proceedings of the IEEE International Conference on Acoustics , vol.4 , pp. 317-320
    • Hershey, J.1    Olsen, P.2
  • 33
    • 33846036765 scopus 로고    scopus 로고
    • The AIC criterion and symmetrizing the Kullback-Leibler divergence
    • Seghouane, A.; Amari, S. The AIC criterion and symmetrizing the Kullback-Leibler divergence. IEEE Trans. Neural Network 2007, 18, 97-106.
    • (2007) IEEE Trans. Neural Network , vol.18 , pp. 97-106
    • Seghouane, A.1    Amari, S.2
  • 34
    • 84873751778 scopus 로고
    • An invariant form for the prior probability in estimation problems
    • Jeffreys, H. An invariant form for the prior probability in estimation problems. Proc. Roy. Soc. Lond. Math. Phys. Sci. A 1946, 186, pp. 453-461.
    • (1946) Proc. Roy. Soc. Lond. Math. Phys. Sci. A , vol.186 , pp. 453-461
    • Jeffreys, H.1
  • 35
    • 0025952277 scopus 로고
    • Divergence measures based on the Shannon entropy
    • Lin, J. Divergence measures based on the Shannon entropy. IEEE Trans. Inform. Theor. 1991, 37, 145-151.
    • (1991) IEEE Trans. Inform. Theor. , vol.37 , pp. 145-151
    • Lin, J.1
  • 36
    • 2942723846 scopus 로고    scopus 로고
    • A divisive information theoretic feature clustering algorithm for text classification
    • Dhillon, I.; Mallela, S.; Kumar, R. A divisive information theoretic feature clustering algorithm for text classification. J.Mach. Learn. Res. 2003, 3, 1265-1287.
    • (2003) J. Mach. Learn. Res. , vol.3 , pp. 1265-1287
    • Dhillon, I.1    Mallela, S.2    Kumar, R.3
  • 39
    • 0000986833 scopus 로고    scopus 로고
    • Information theoretic learning
    • Haykin, S., Ed.; John Wiley & Sons: Toronto, Canada
    • Principe, J.; Xu, D.; Fisher, J. Information theoretic learning. In Unsupervised Adaptive Filtering; Haykin, S., Ed.; John Wiley & Sons: Toronto, Canada, 2000; pp. 265-319.
    • (2000) Unsupervised Adaptive Filtering , pp. 265-319
    • Principe, J.1    Xu, D.2    Fisher, J.3
  • 41
    • 33646557981 scopus 로고    scopus 로고
    • Optimizing the Cauchy-Schwarz PDF distance for information theoretic, non-parametric clustering
    • Rangarajan, A., Vemurl, B., Yuille, A., Eds.; Springer, Berlin, Germany; Lect. Notes Comput. Sci
    • Jenssen, R.; Erdogmus, D.; Hild, K.; Principe, J.; Eltoft, T. Optimizing the Cauchy-Schwarz PDF distance for information theoretic, non-parametric clustering. In Energy Minimization Methods in Computer Vision and Pattern Recognition; Rangarajan, A., Vemurl, B., Yuille, A., Eds.; Springer, Berlin, Germany; Lect. Notes Comput. Sci., 2005, 3257, 34-45.
    • (2005) Energy Minimization Methods in Computer Vision and Pattern Recognition , vol.3257 , pp. 34-45
    • Jenssen, R.1    Erdogmus, D.2    Hild, K.3    Principe, J.4    Eltoft, T.5
  • 43
    • 84864853600 scopus 로고    scopus 로고
    • Kullback-Leibler distance between two Gaussian densities in reproducing kernel Hilbert space
    • Chicago, IL, USA, 27 June-2 July
    • Zhou, S.; Chellappa, R. Kullback-Leibler distance between two Gaussian densities in reproducing kernel Hilbert space. In Proceedings of the IEEE International Symposium on Information Theory, Chicago, IL, USA, 27 June-2 July 2004.
    • (2004) Proceedings of the IEEE International Symposium on Information Theory
    • Zhou, S.1    Chellappa, R.2
  • 46
    • 65549165901 scopus 로고    scopus 로고
    • A framework for machine learning based on dynamic physical fields
    • Ruta, D.; Gabrys, B. A framework for machine learning based on dynamic physical fields. Nat. Comput. 2009, 8, 219-237.
    • (2009) Nat. Comput. , vol.8 , pp. 219-237
    • Ruta, D.1    Gabrys, B.2
  • 48
    • 0041877169 scopus 로고    scopus 로고
    • Estimation of entropy and mutual information
    • Paninski, L. Estimation of entropy and mutual information. Neural Comput. 2003, 15, 1191-1253.
    • (2003) Neural Comput , vol.15 , pp. 1191-1253
    • Paninski, L.1
  • 49
    • 0345414074 scopus 로고    scopus 로고
    • An efficient image similarity measure based on approximations of KL-divergence between two Gaussian mixtures
    • Nice, France, 13-16 October
    • Goldberger, J.; Gordon, S.; Greenspan, H. An efficient image similarity measure based on approximations of KL-divergence between two Gaussian mixtures. In Proceedings of the 9th IEEE International Conference on Computer Vision, Nice, France, 13-16 October 2003; Volume 1, pp. 487-493.
    • (2003) Proceedings of the 9th IEEE International Conference on Computer Vision , vol.1 , pp. 487-493
    • Goldberger, J.1    Gordon, S.2    Greenspan, H.3


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