Estimators and tail bounds for dimension reduction in l α (0 < α ≤ 2) using stable random projections

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2008, Pages 10-19

  Li, Ping ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CAUCHY DENSITY; DATASTREAM (CO); DIMENSION REDUCTION (DR); MACHINE-LEARNING; RANDOM PROJECTIONS; SAMPLE SIZES;

COMPUTATIONAL FLUID DYNAMICS; DATA MINING; ELECTRIC NETWORK ANALYSIS; HARMONIC ANALYSIS; INFORMATION MANAGEMENT; INFORMATION SERVICES; LEARNING SYSTEMS; PARAMETER ESTIMATION;

ALGORITHMS;

EID: 51849147253     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (44)

1. Diinitris Achlioptas. Database-friendly random projections: Johnson-Lindenstrauss with binary coins. Journal of Computer and System Sciences, 66(4):671-687, 2003.
2. Nir Ailon and Bernard Chazelle. Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform. In STOC, pages 557-563, 2006.
3. Rosa Arriaga and Santosh Veinpala. An algorithmic theory of learning: Robust concepts and random projection. Machine Learning, 63(2): 161-182, 2006.
4. B. Babcock, S. Babu, M. Datar, R. Motwani, and J. Widom. Models and issues in data stream systems. In PODS, pages 1-16, 2002.
5. M. S. Bartlett. Approximate confidence intervals, II. Biometrika, 40(3/4):306-317, 1953.
6. 1. In FOCS, pages 514-523, 2003.
7. 1. Journal of ACM, 52(2):766-788, 2005.
8. Andrei Z. Broder. On the resemblance and containment of documents. In the Compression and Complexity of Sequences, pages 21-29, 1997.
9. Andrei Z. Broder, Moses Charikar, Alan M. Frieze, and Michael Mitzenmacher. Min-wise independent permutations (extended abstract). In STOC, pages 327-336, 1998.
10. Moses S. Charikar. Similarity estimation techniques from rounding algorithms. In STOC, pages 380-388, 2002.
11. Herman Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. The Annals of Mathematical Statistics, 23(4):493-507, 1952.
12. Graham Cormode, Mayur Datar, Piotr Indyk, and S. Muthukrishnan. Comparing data streams using hamming norms (how to zero in). IEEE Transactions on Knowledge and Data Engineering, 15(3):529-540, 2003.
13. Graham Cormode and S. Muthukrishnan. Estimating dominance norms of multiple data streams. In ESA, pages 148-160, 2003.
14. N. Cressie. A note on the behaviour of the stable distributions for small index. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 31(1):61-64, 1975.
15. Sanjoy Dasgupta and Anupam Gupta. An elementary proof of a theorem of Johnson and Lindenstrauss. Random Structures and Algorithms, 22(1):60-65, 2003.
16. Mayur Datar, Nicole Immorlica, Piotr Indyk, and Vahab S. Mirrokn. Locality-sensitive hashing scheme based on pstable distributions. In SCG, pages 253-262, 2004.
17. David L. Donoho. Compressed sensing. IEEE Trans. Inform. Theory, 52(4): 1289-1306, 2006.
18. Eugene F. Fama and Richard Roll. Some properties of symmetric stable distributions. Journal of the American Statistical Association, 63(323):817-836, 1968.
19. Eugene F. Fama and Richard Roll. Parameter estimates for symmetric stable distributions. Journal of the American Statistical Association, 66(334):331-338, 1971.
20. 1 - difference algorithm for massive data streams. In FOCS, pages 501-511, 1999.
21. P. Frankl and H. Maehara. The Johnson-Lindenstrauss lemma and the sphericity of some graphs. Journal of Combinatorial Theory A, 44(3):355-362, 1987.
22. Sumit Ganguly and Graham Cormode. On estimating frequency moments of data streams. In APPROX-RANDOM, pages 479-493, 2007.
23. I. S. Gradshteyn and I. M. Ryzhik. Table of Integrals, Series, and Products. Academic Press, sixth edition, 2000.
24. Monika R. Henzinger, Prabhakar Raghavan, and Sridhar Rajagopalan. Computing on data streams. American Mathematical Society, 1999.
25. Piotr Indyk. Stable distributions, pseudorandom generators, embeddings and data stream computation. In FOCS, pages 189-197, 2000.
26. Piotr Indyk. Algorithmic applications of low-distortion geometric embeddings. In FOCS, pages 10-33, 2001.
27. Piotr Indyk. Stable distributions, pseudorandom generators, embeddings, and data stream computation. Journal of ACM, 53(3):307-323, 2006.
28. Piotr Indyk and Rajeev Motwani. Approximate nearest neighbors: Towards removing the curse of dimensionality. In STOC, pages 604-613, 1998.
29. W. B. Johnson and J. Lindenstrauss. Extensions of Lipschitz mapping into Hilbert space. Contemporary Mathematics, 26:189-206, 1984.
30. 1. Acta. Math., 149:71-85, 1982.
31. 1. Geometric And Functional Analysis, 14(4):745-747, 2004.
32. Erich L. Lehmann and George Casella. Theory of Point Estimation. Springer, second edition, 1998.
33. α (0 < α ≤ 2) norm. In KDD, 2007.
34. Ping Li and Kenneth W. Church. Using sketches to estimate associations. In HLT/EMNLP, pages 708-715, 2005.
35. Ping Li and Kenneth W. Church. A sketch algorithm for estimating two-way and multi-way associations. Computational Linguistics, 33(3):305-354, 2007.
36. Ping Li, Kenneth W. Church, and Trevor J. Hastie. Conditional random sampling: A sketch-based sampling technique for sparse data. In NIPS, pages 873-880, 2007.
37. α (0 < α ≤ 2) using stable random projections. In NIPS, 2008.
38. Ping Li, Trevor J. Hastie, and Kenneth W. Church. Improving random projections using marginal information. In COLT, pages 635-649, 2006.
39. 1 using Cauchy random projections. In COLT, 2007.
40. 1 using cauchy random projections. Journal of Machine Learning Research. To appear.
41. J. Huston McCulloch. Simple consistent estimators of stable distribution parameters. Communications on Statistics-Simulation, 15(4):1109-1136, 1986.
42. L. R. Shenton and K. Bowman. Higher moments of a maximum-likelihood estimate. Journal of Royal Statistical Society B, 25(2):305-317, 1963.
43. Santosh Vempala. The Random Projection Method. American Mathematical Society, Providence, RI, 2004.
44. V. M. Zolotarev. One-dimensional Stable Distributions. American Mathematical Society, Providence, RI, 1986.