Partition-based conditional density estimation

ESAIM - Probability and Statistics

Volumn 17, Issue , 2013, Pages 672-697

  Cohen, S X ^a   le Pennec, E ^b  

^a IPANEMA   (France)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

Conditional density estimation; Gaussian mixture model; Partition; Penalized likelihood; Piecewise polynomial density

Indexed keywords

EID: 84996135386     PISSN: 12928100     EISSN: 12623318     Source Type: Journal    
DOI: 10.1051/ps/2012017     Document Type: Article

References (43)

1. N. Akakpo, Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection. Math. Meth. Stat. 21 (2012) 1-28.
2. N. Akakpo and C. Lacour, Inhomogeneous and anisotropic conditional density estimation from dependent data. Electon. J. Statist. 5 (2011) 1618-1653.
3. A. Antoniadis, J. Bigot and R. von Sachs, A multiscale approach for statistical characterization of functional images. J. Comput. Graph. Stat. 18 (2008) 216-237.
4. A. Barron, C. Huang, J. Li and X. Luo, MDL Principle, Penalized Likelihood, and Statistical Risk, in Festschrift in Honor of Jorma Rissanen on the Occasion of his 75th Birthday. Tampere University Press (2008).
5. D. Bashtannyk and R. Hyndman, Bandwidth selection for kernel conditional density estimation. Comput. Stat. Data Anal. 36 (2001) 279-298.
6. L. Bertrand, M.-A. Languille, S.X. Cohen, L. Robinet, C. Gervais, S. Leroy, D. Bernard, E. Le Pennec, W. Josse, J. Doucet and S. Schoder, European research platform IPANEMA at the SOLEIL synchrotron for ancient and historical materials. J. Synchrotron Radiat. 18 (2011) 765-772.
7. Ch. Biernacki, G. Celeux, G. Govaert and F. Langrognet, Model-based cluster and discriminant analysis with the MIXMOD software. Comput. Stat. Data Anal. 51 (2006) 587-600.
8. L. Birge and P. Massart, Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli 4 (1998) 329-375.
9. L. Birge and P. Massart, Minimal penalties for gaussian model selection. Probab. Theory Related Fields 138 (2007) 33-73.
10. G. Blanchard, C. Schafer, Y. Rozenholc and K.R. Miiller, Optimal dyadic decision trees. Mach. Learn. 66 (2007) 209-241.
11. E. Brunel, F. Comte and C. Lacour, Adaptive estimation of the conditional density in presence of censoring. Sankhya 69 (2007) 734-763.
12. S.X. Cohen and E. Le Pennec, Conditional density estimation by penalized likelihood model selection and applications. Technical report, RR-7596. INRIA (2011). arXiv:1103.2021.
13. S.X. Cohen and E. Le Pennec, Conditional density estimation by penalized likelihood model selection. Submitted (2012).
14. S.X. Cohen and E. Le Pennec, Unsupervised segmentation of hyperspectral images with spatialized Gaussian mixture model and model selection. Submitted (2012).
15. J. de Gooijer and D. Zerom, On conditional density estimation. Stat. Neerlandica 57 (2003) 159-176.
16. D. Donoho, CART and best-ortho-basis: a connection. Ann. Stat. 25 (1997) 1870-1911.
17. S. Efromovich, Conditional density estimation in a regression setting. Ann. Stat. 35 (2007) 2504-2535.
18. S. Efromovich, Oracle inequality for conditional density estimation and an actuarial example. Ann. Inst. Stat. Math. 62 (2010) 249-275.
19. J. Fan, Q. Yao and H. Tong, Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. Biometrika 83 (1996) 189-206.
20. Ch. Genovese and L. Wasserman, Rates of convergence for the Gaussian mixture sieve. Ann. Stat. 28 (2000) 1105-1127.
21. L. Gyorfi and M. Kohler, Nonparametric estimation of conditional distributions. IEEE Trans. Inform. Theory 53 (2007) 1872-1879.
22. P. Hall, R. Wolff and Q. Yao, Methods for estimating a conditional distribution function. J. Amer. Stat. Assoc. 94 (1999) 154-163.
23. T. Hofmann, Probabilistic latent semantic analysis, in Proc. Of Uncertainty in Artificial Intelligence (1999).
24. Y. Huang, I. Pollak, M. Do and C. Bouman, Fast search for best representations in multitree dictionaries. IEEE Trans. Image Process. 15 (2006) 1779-1793.
25. R. Hyndman and Q. Yao, Nonparametric estimation and symmetry tests for conditional density functions. J. Nonparam. Stat. 14 (2002) 259-278.
26. R. Hyndman, D. Bashtannyk and G. Grunwald, Estimating and visualizing conditional densities. J. Comput. Graphical Stat. 5 (1996) 315-336.
27. B. Karaivanov and P. Petrushev, Nonlinear piecewise polynomial approximation beyond besov spaces. Appl. Comput. Harmonic Anal. 15 (2003) 177-223.
28. E. Kolaczyk and R. Nowak, Multiscale generalised linear models for nonparametric function estimation. Biometrika 92 (2005) 119-133.
29. E. Kolaczyk, J. Ju and S. Gopal, Multiscale, multigranular statistical image segmentation. J. Amer. Stat. Assoc. 100 (2005) 1358-1369.
30. Q. Li and J. Racine, Nonparametric Econometrics: Theory and Practice. Princeton University Press (2007).
31. J. Lin, Divergence measures based on the Shannon entropy. IEEE Trans. Inform. Theory 37 (1991) 145-151.
32. P. Massart, Concentration inequalities and model selection, vol. 1896 of Lecture Notes in Mathematics (2007). Lectures from the 33rd Summer School on Probability Theory held in Saint-Flour (2003), With a foreword by Jean Picard.
33. C. Maugis and B. Michel, A non asymptotic penalized criterion for Gaussian mixture model selection. ESAIM: PS 15 (2012) 41-68.
34. C. Maugis and B. Michel, Data-driven penalty calibration: a case study for Gaussian mixture model selection. ESAIM: PS 15 (2012) 320-339.
35. M. Rosenblatt, Conditional probability density and regression estimators, in Multivariate Analysis II, Proc. Of Second Internat. Sympos., Dayton, Ohio, 1968. Academic Press (1969) 25-31.
36. L. Si and R. Jin, Adjusting mixture weights of gaussian mixture model via regularized probabilistic latent semantic analysis, in Advances in Knowledge Discovery and Data Mining (2005) 218-252.
37. Ch. Stone, The use of polynomial splines and their tensor products in multivariate function estimation. Ann. Stat. 22 (1994) 118-171.
38. S. Szarek, Metric entropy of homogeneous spaces, in Quantum Probability (Gdansk 1997) (1998) 395-410.
39. S. van de Geer, The method of sieves and minimum contrast estimators. Math. Methods Stat. 4 (1995) 20-38.
40. A. van der Vaart and J. Wellner, Weak Convergence. Springer (1996).
41. I. van Keilegom and N. Veraverbeke, Density and hazard estimation in censored regression models. Bernoulli 8 (2002) 607-625.
42. R. Willett and R. Nowak, Multiscale poisson intensity and density estimation. IEEE Trans. Inform. Theory 53 (2007) 3171-3187.
43. D. Young and D. Hunter, Mixtures of regressions with predictor-dependent mixing proportions. Comput. Stat. Data Anal. 54 (2010) 2253-2266.