Weighted isotonic regression under the L 1 norm

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2006, Pages 783-791

  Angelov, Stanislav ^a   Harb, Boulos ^a   Kannan, Sampath ^a   Wang, Li San ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ISOTONIC REGRESSION; MICROARRAY ANALYSIS; ORDERING CONSTRAINTS; PARTIAL ORDERING;

DATA REDUCTION; ERROR ANALYSIS; PROBLEM SOLVING;

REGRESSION ANALYSIS;

EID: 33244469312     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1109557.1109643     Document Type: Conference Paper

References (35)

1. Ravindra K. Ahuja and James B. Orlin, A fast scaling algorithm for minimizing separable convex functions subject to chain constraints, Oper. Res. 49 (2001), no. 5, 784-789.
2. D. Avis, A survey of heuristics for the weighted matching problem, Networks 13 (1983), 475-493.
3. M. B. Ayer, H.D. Brunk, G. M. Ewing, W.T. Reid, and E. Silverman, An empirical distribution function for sampling with incomplete information, Annals of Mathematical Statistics 26 (1955), 641-647.
4. R. E. Barlow and V. A. Ubhaya, Isotonic approximation, In Optimizing Methods in Statistics (1971), 77-86.
5. Amir Ben-Dor, Benny Chor, Richard M. Karp, and Zohar Yakhini, Discovering local structure in gene expression data: The order-preserving submatrix problem, Journal of Computational Biology 10 (2003), no. 3/4, 373-384.
6. ∞ norms, Journal of Discrete Algorithms, in press (2005).
7. 1 isotonic optimization on a partially ordered set, Ph.D. thesis, ISU Math. Dept., Ames, Iowa, 1987.
8. 1 isotonic optimization with weights on a partially ordered set, Bulletin of the Korean Mathematical Society 28 (1991), no. 2, 243-254.
9. Don Coppersmith and Shmuel Winograd, Matrix multiplication via arithmetic progressions, J. Symb. Comput. 9 (1990), no. 3, 251-280.
10. T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Introduction to algorithms, MIT Press, 2003.
11. Hirsch I. Dilleen M., Heimann G., Non-parametric estimators of a monotonic dose-response curve and bootstrap confidence intervals, Stat Med. 22 (2003), no. 6, 869-882.
12. Doratha E. Drake and Stefan Hougardy, Improved linear time approximation algorithms for weighted matchings, RANDOM-APPROX, 2003, pp. 14-23.
13. Jack Edmonds and Richard M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems, J. ACM 19 (1972), no. 2, 248-264.
14. J. Ernst, G. Nau, and Z. Bar-Joseph, Clustering short time series gene expression data bioinformatics, Bioinformatics 21 (2005), no. 1, 159-168.
15. M. Frisén, Unimodal regression, The Statistician 35 (1980), 304-307.
16. Z. Geng and N.-Z. Shi, Isotonic regression for umbrella orderings, Appl. Statist. 39 (1990), 397-424.
17. Debashis Ghosh, Moulinath Banerjee, and Pinaki Biswas, Binary isotonic regression procedures, with application to cancer biomarkers, Working Paper, Department of Biostatistics, University of Michigan, 2004.
18. A. Ivanova arid K. Wang, A non-parametric approach to the design and analysis of two-dimensional dose-finding trials, Stat Med 23 (2004), no. 12, 1861-1870.
19. W.S. Jewell, Isotonic optimization in tariff construction, ASTIN Bulletin 8 2 (1975), 175-203.
20. K. Leuraud and J. Benichou, A comparison of several methods to test for the existence of a monotonic dose-response relationship in clinical and epidemiological studies, Stat. Med 20 (2001), no. 22, 3335-3351.
21. J.Y. Mancuso, H. Ahn H., and J.J. Chen, Order-restricted dose-related trend tests, Stat Med 20 (2001), no. 15, 2305-18.
22. William L. Maxwell and John A. Muckstadt, Establishing consistent and realistic reorder intervals in production-distribution systems, Operations Research 33 (1985), no. 6, 1316-1341.
23. T. Morton-Jones, P. Diggle, L. Parker, H.O. Dickinson, and K. Binks, Additive isotonic regression models in epidemiology, Stat Med 19 (2000), no. 6, 849-59.
24. R.A. Mureika, T.R. Turner, and P.C. Wollan, An algorithm for unimodal isotonic regression, with application to locating a maximum, Univ. New Brunswichk Dept. Math, and Stat. Tech. Report 92-4, 1992.
25. P. M. Pardalos, G.L. Xue, and L. Yong, Efficient computation of an isotonic median regression, Appl. Math. Lett 8 (1995), no. 2, 67-70.
26. Panos M. Pardalos and Guoliang Xue, Algorithms for a class of isotonic regression problems, Algorithmica 23 (1999), no. 3, 211-222.
27. Shyamal D. Peddada, Edward K. Lobenhofer, Leping Li, Cynthia A. Afshari, Clarice R. Weinberg, and David M. Umbach, Gene selection and clustering for time-course and dose-response microarray experiments using order-restricted inference, Bioinformatics 19 (2003), no. 7, 834-841.
28. N-G. Pehrsson and M. Frisén, The UREGR procedure, Gothenburg Computer Central, 1983.
29. T. Robertson and P. Waltman, On estimating monotone parameters, Ann. Math. Stat. (1968), 1030-1039.
30. Quentin Stout, Optimal algorithms for unimodal regression, Computer Science and Statistics, vol. 32, 2000.
31. M. Stylianou and N. Flournoy, Dose-finding using the biased coin up-and-down design and isotonic regression, Biometrics 58 (2002), 171-177.
32. T.R. Turner, S function unfit to calculate the unimodal isotornic regression of a set of data, Univ. New Brunswichk Dept. Math, and Stat., 1983.
33. V. A. Ubhaya, Isotonic optimization I, Approx. Theory 12 (1974), 146-159.
34. _, Isotonic optimization II, Approx. Theory 12 (1974), 315-331.
35. K. Ulm, Nonparametric analysis of dose-response relationships, Ann. N.Y. Acad. Sci. 895 (1999), 223-231.