Polytope samplers for inference in ill-posed inverse problems

Journal of Machine Learning Research

Volumn 15, Issue , 2011, Pages 110-118

  Airoldi, Edoardo M ^a   Haas, Bertrand ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINGENCY TABLE ANALYSIS; HERMITE NORMAL FORM; ILL-POSED INVERSE PROBLEM; NETWORK TOMOGRAPHY; POLYTOPES; SOLUTION SPACE; TESTING RESULTS; UNIFORM DISTRIBUTION; UNIMODULARITY;

ARTIFICIAL INTELLIGENCE; DIFFERENTIAL EQUATIONS; INVERSE PROBLEMS;

MATRIX ALGEBRA;

EID: 84862270520     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (26)

1. E. M. Airoldi and C. Faloutsos. Recovering latent time-series from their observed sums: network tomography with particle filters. In Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, volume 10, pages 30-39, 2004.
2. D. Avis, D. Bremner, and A. Deza. Polyhedral Computation. American Mathematical Society, 2009.
3. Y. Bishop, S. E. Fienberg, and P. Holland. Discrete multivariate analysis: theory and practice. The MIT press, 1975.
4. A. W. Blocker and E. M. Airoldi. Deconvolution of mixing time series on a graph. Manuscript no. 1105.2526 on arXiv.org, May 2011.
5. J. Cao, D. Davis, S. Van Der Viel, and B. Yu. Timevarying network tomography: router link data. Journal of the American Statistical Association, 95: 1063-75, 2000.
6. J. Cao, D. Davis, S. Van Der Viel, B. Yu, and Z. Zu. A scalable method for estimating network traffic matrices from link counts. Technical report, Bell Labs, 2001.
7. Y. Chen, P. Diaconis, S.P. Holmes, and J.S. Liu. Sequential Monte Carlo methods for statistical analysis of tables. Journal of the American Statistical Association, 100(469):109-120, 2005.
8. J. A. De Loera, J. Rambau, and F. Santos. Triangulations: Structures for Algorithms and Applications. Springer, 1st edition, 2010.
9. P. Diaconis and B. Sturmfels. Algebraic algorithms for sampling from conditional distributions. The Annals of Statistics, 26(1):363-397, 1998.
10. A. Dobra and S.E. Fienberg. The generalized shuttle algorithm. In P. Gibilisco, E. Riccomagno, M. P. Rogantin, and H. P. Wynn, editors, Algebraic and geometric methods in statistics, pages 135-156. Cambridge University Press, 2008.
11. A. Dobra, C. Tebaldi, and M. West. Data augmentation in multi-way contingency tables with fixed marginal totals. Journal of Statistical Planning and Inference, 136:355-372, 2006.
12. A. Dobra, S. E. Fienberg, A. Rinaldo, S. Slavkovic, and Y. Zhou. Algebraic statistics and contingency table problems: Estimation and disclosure limitation. In S. Sullivant and M. Putinar, editors, Emerging applications of algebraic geometry, volume 149 of IMA, pages 63-88. Springer, 2009.
13. J. Fang, Y. Vardi, and C.-H. Zhang. An iterative tomogravity algorithm for the estimation of network traffic. In R. Liu, W. Strawderman, and C.-H. Zhang, editors, Complex Datasets and Inverse Problems: Tomography, Networks and Beyond, volume 54 of Lecture Notes-Monograph Series. IMS, 2007.
14. W. Fulton. Introduction to Toric Varieties. Princeton University Press, 1993.
15. E. Lawrence, G. Michailidis, V. Nair, and B. Xi. Network tomography: A review and recent developments,. In J. Fan and H. L. Koul, editors, Frontiers in Statistics. Imperial College Press, 2006.
16. T.-W. Lee, M. S. Lewicki, M. Girolami, and T. J. Sejnowski. Blind source separation of more sources than mixtures using overcomplete representations. IEEE Signal Processing Letters, 6(4):87-90, 1999.
17. G. Liang and B. Yu. Pseudo-likelihood estimations in network tomography. In Proceedings of IEEE INFOCOM, 2003.
18. A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot. Traffic matrix estimation: existing techniques and new directions. SIGCOMM Computer Communication Review, 32(4):161-174, 2002.
19. L. Parra and P. Sajda. Blind source separation via generalized eigenvalue decomposition. Journal of Machine Learning Resaerch, 4:1261-1269, 2003.
20. A. Schrijver. Theory of Linear and Integer Programming. Interscience Series in Discrete Mathematics and Optimization. J. Wiley, 1998.
21. L. A. Shepp and J. B. Kruskal. Computerized tomography: The new medical x-ray technology. The American Mathematical Monthly, 85(6):420-439, 1978.
22. C. Tebaldi and M. West. Bayesian inference on network traffic using link count data. Journal of the American Statistical Association, 93(442):557-573, 1998.
23. R. J. Vanderbei and J. Iannone. An em approach to od matrix estimation. Technical Report SOR 94-04, Princeton University, 1994.
24. Y. Vardi. Network tomography: estimating sourcedestination traffic intensities from link data. Journal of the American Statistical Association, 91:365-377, 1996.
25. Y. Vardi, L. A. Shepp, and L. Kaufman. A statistical model for positron emission tomography. Journal of the American Statistical Association, 80(389):8-20, 1985.
26. Y. Zhang, M. Roughan, C. Lund, and D. Donoho. An information-theoretic approach to traffic matrix estimation. In Proceedings of SIGCOMM, 2003.