Inferring rankings using constrained sensing

IEEE Transactions on Information Theory

Volumn 57, Issue 11, 2011, Pages 7288-7306

  Jagabathula, Srikanth ^a   Shah, Devavrat ^b  

^a NEW YORK UNIVERSITY   (United States)

^b Department of Electrical Engineering and Computer Science   (United States)

Author keywords

Compressive sensing; Fourier analysis over symmetric group; functions over permutations; sparsest fit

Indexed keywords

COMPRESSIVE SENSING; CONVEX RELAXATION; DISCRETE-TIME; DOMAIN SIZE; GENERATION OF FUNCTIONS; HIGH PROBABILITY; ITERATIVE ALGORITHM; MULTI-OBJECT TRACKING; PARTIAL INFORMATION; RANDOM MODEL; RANKING SYSTEM; RECOVERABILITY; RECOVERY OF FUNCTIONS; SPARSEST-FIT; SUFFICIENT CONDITIONS; SYMMETRIC GROUPS;

ALGORITHMS; FOURIER ANALYSIS; INFORMATION THEORY; OPTIMIZATION; RELAXATION PROCESSES; SIGNAL RECONSTRUCTION;

RECOVERY;

EID: 81255188956     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2165827     Document Type: Article

References (26)

1. D. Donoho and P. Stark, "Uncertainty principles and signal recovery," SIAM J. Appl. Math., pp. 906-931, 1989.
2. C. Dwork, R. Kumar, M. Naor, and D. Sivakumar, "Rank aggregation methods for the web," WWW, pp. 613-622, 2001.
3. P. Diaconis, "Group representations in probability and statistics," IMS Lecture Notes-Monograph Ser., vol. 11, 1988.
4. J. Huang, C. Guestrin, and L. Guibas, "Efficient inference for distributions on permutations," Adv. Neur. Inf. Process. Syst., vol. 20, pp. 697-704, 2008.
5. R. Kondor, A. Howard, and T. Jebara, "Multi-object tracking with representations of the symmetric group," presented at the 11th Int. Conf. Artificial Intelligence and Statistics, 2007.
6. P. Dangauthier, R. Herbrich, T. Minka, and T. Graepel, "Trueskill through time: Revisiting the history of chess," Adv. Neur. Inf. Process. Syst., vol. 20, 2007.
7. K. Kueh, T. Olson, D. Rockmore, and K. Tan, "Nonlinear approximation theory on compact groups," J. Fourier Anal. Appl., vol. 7, no. 3, pp. 257-281, 2001. (Pubitemid 33658732)
8. C. Shannon, "Communication in the presence of noise," Proc. IRE, vol. 37, no. 1, pp. 10-21, 1949.
9. H. Nyquist, "Certain topics in telegraph transmission theory," Proc. IEEE, vol. 90, no. 2, pp. 280-305, Feb. 2002. (Pubitemid 43779308)
10. E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. (Pubitemid 41800353)
11. E. Candes, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol. 59, no. 8, 2006.
12. E. Candes and J. Romberg, "Quantitative robust uncertainty principles and optimally sparse decompositions," Found. Comput. Math., vol. 6, no. 2, pp. 227-254, 2006. (Pubitemid 43824483)
13. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006. (Pubitemid 43174093)
14. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
15. R. Gallager, "Low-density parity-check codes," IRE Trans. Inf. Theory, vol. 8, no. 1, pp. 21-28, 1962.
16. M. Sipser and D. A. Spielman, "Expander codes," IEEE Trans. Inf. Theory, vol. 42, pp. 1710-1722, 1996. (Pubitemid 126769170)
17. M. Luby, M. Mitzenmacher, M. Shokrollahi, and D. Spielman, "Improved low-density parity-check codes using irregular graphs," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 585-598, Feb. 2001. (Pubitemid 32318091)
18. I. Reed and G. Solomon, "Polynomial codes over certain finite fields," J. SIAM, pp. 300-304, 1960.
19. J. Tropp, "Just relax: Convex programming methods for identifying sparse signals in noise," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1030-1051, Mar. 2006. (Pubitemid 46444890)
20. J. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
21. R. Berinde, A. Gilbert, P. Indyk, H. Karloff, and M. Strauss, "Combining geometry and combinatorics: A unified approach to sparse signal recovery," preprint, 2008.
22. G. Cormode and S. Muthukrishnan, "Combinatorial algorithms for compressed sensing," Lecture Notes Comput. Sci., vol. 4056, p. 280, 2006.
23. A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin, "One sketch for all: Fast algorithms for compressed sensing," in Proc. 39th Annu. ACM Symp. Theory of Computing, New York, 2007, pp. 237-246, ACM. (Pubitemid 47630740)
24. S. Muthukrishnan, Data Streams: Algorithms and Applications, ser. Foundations and Trends in Theoretical Computer Science. Boston, MA: Now Publishers, 2005.
25. S. Jagabathula and D. Shah, "Inferring rankings under constrained sensing," in Proc. NIPS, 2008, pp. 7-1.
26. T. M. Cover and J. A. Thomas, Elements of Information Theory, ser. Wiley Series in Telecommunications and Signal Processing, 2nd ed. Hoboken, NJ: Wiley, Jul. 2006 [Online]. Available: http://www.amazon.ca/exec/obidos/redirect?tag= citeulike09-20&path=ASIN/0471241954