D-MORPH regression: Application to modeling with unknown parameters more than observation data

Journal of Mathematical Chemistry

Volumn 48, Issue 4, 2010, Pages 1010-1035

  Li, Genyuan ^a   Rabitz, Herschel ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

D MORPH; Least squares regression; Orthonormal polynomial; Regularization; Ridge regression; Smoothing splines

Indexed keywords

EID: 77957373559     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-010-9722-2     Document Type: Article

References (31)

1. Peters D. C., Korosec F. R., Grist T. M., Block W. F., Holden J. E., Vigen K. K., Mistretta C. A.: Magn. Reson. Med. 43, 91-101 (2000).
2. Daniel B. L., Yen Y. F., Glover G. H. et al.: Radiology 209, 499-509 (1998).
3. E. J. Candés, J. Romberg, in Proceedings of SPIE International Symposium on Electro. Imaging 1, 76-86 (2005), San Jose.
4. Spira A., Beane J., Shah V., Liu G., Schembri F., Yang X., Palma J., Brosy J. S.: Effects of cigarette smoke on the human airway epithelial cell transcriptome. Proc. Nat. Acad. Sci. USA 101(27), 10143-10148 (2004).
5. Li J., Zhao Z. W., Kazakov A., Dryer F. L.: Int. J. Chem. Kinet. 36, 566-575 (2004).
6. J. Kettenring, B. Lindsay, D. Siegmud (eds). Statistics: Challenges and opportunities for the twenty-first century. NSF report. Available at www. pnl. gov/scales/docs/nsf_report. pdf.
7. Cades E., Tao T.: Ann. Statist. 35, 2313 (2007).
8. Carvalho C. M., Chang J. C., Lucas J. E., Nevins J. R., Wang Q., West M.: Am. Stat. Assoc. 103, 1438 (2008).
9. Hastie T., Tibshirani R., Friedman J.: The elements of statistical learning: data mining, inference, and prediction. Springer, New York (2001).
10. Bishop C. M.: Pattern recognition and machine learning. Springer, New York (2007).
11. Tikhonov A. N.: Dokl. Akad. Nauk. SSSR 39, 195-198 (1943).
12. A. N. Tikhonov, Soviet Math. Dokl. 4, 1035-1038(1963). English translation of Dokl. Akad. Nauk. SSSR 151, 501-504 (1963).
13. Tikhonov A. N., Arsenin V. A.: Solution of Ill-posed Problems. Winston & Sons, Washington (1977) ISBN 0-470-99124-0.
14. P. C. Hansen, Rank-deficient and Discrete ill-posed problems. (1998), SIAM.
15. Hoerl A. E.: Chem. Eng. Prog. 58, 54-59 (1962).
16. Hoerl A. E., Kennard R.: Technometrics 12, 55-67 (1970).
17. Wahba G.: Spline models for observational data. SIAM, Philadelphia (1990).
18. Wahba G.: Ann. Stat. 13, 1378-1402 (1985).
19. Wahba G., Wang Y. D., Gu C., Klein R., Klein B.: Ann. Stat. 23, 1865-1895 (1995).
20. http://en. wikipedia. org/wiki/Tikhonov_regularization, Categories: Linear algebra, Estimation theory Views.
21. Rothman A., Ho T.-S., Rabitz H.: Phys. Rev. A 72, 023416 (2005).
22. Rothman A., Ho T.-S., Rabitz H.: J. Chem. Phys. 123, 134104 (2005).
23. Rothman A., Ho T.-S., Rabitz H.: Phys. Rev. A 73, 053401 (2006).
24. N. Danielson, V. Beltrani, J. Dominy, H. Rabitz, (manuscript in preparation).
25. Rao C. R., Mitra S. K.: Generalized inverse of matrix and its applications. Willey, New York (1971).
26. Matlab [7. 0R14], 2004. MathWorks, Inc.
27. Bellman R.: Introduction to matrix analysis. 2nd edn, pp. 118. McGraw-hill, New York (1970).
28. Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P.: Numerical recipes in FORTRAN-The art of science computing. 2nd edn, pp. 51. Cambridge university press, New York (1992).
29. Alis O. F., Rabitz H.: J. Math. Chem. 25, 197-233 (1999).
30. Li G., Wang S. W., Rabitz H.: J. Phys. Chem. A 106, 8721-8733 (2002).
31. Li G., Hu J. S., Wang S. W., Georgopoulos P. G., Schoendorf J., Rabitz H.: J. Phys. Chem. A 110, 2474-2485 (2006).