Approximate computation and implicit regularization for very large-scale data analysis

Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

Volumn , Issue , 2012, Pages 143-154

  Mahoney, Michael W ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

approximate computation; implicit regularization; large scale data analysis

Indexed keywords

APPLICATION DOMAINS; APPROXIMATE COMPUTATION; BI-CRITERIA; COMPUTER SCIENTISTS; DATA BASE THEORY; IMPLICIT REGULARIZATION; INPUT DATAS; LARGE-SCALE DATABASE; MACHINE LEARNERS; NOISE PROPERTIES; NOISY DATA; ONE-FORM; PREDICTIVE PROPERTIES; STATISTICAL DATA ANALYSIS; STATISTICAL PROPERTIES;

COMPUTER SCIENCE; DATABASE SYSTEMS; INPUT OUTPUT PROGRAMS;

ALGORITHMS;

EID: 84862613543     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2213556.2213579     Document Type: Conference Paper

References (42)

1. R. Andersen, F.R.K. Chung, and K. Lang. Local graph partitioning using PageRank vectors. In FOCS '06: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pages 475-486, 2006.
2. R. Andersen and K. Lang. Communities from seed sets. In WWW '06: Proceedings of the 15th International Conference on World Wide Web, pages 223-232, 2006.
3. R. Andersen and K. Lang. An algorithm for improving graph partitions. In SODA '08: Proceedings of the 19th ACM-SIAM Symposium on Discrete algorithms, pages 651-660, 2008.
4. S. Arora, S. Rao, and U. Vazirani. Geometry, flows, and graph-partitioning algorithms. Communications of the ACM, 51(10):96-105, 2008.
5. B. Bahmani, K. Chakrabarti, and D. Xin. Fast personalized PageRank on MapReduce. In Proceedings of the 37th SIGMOD international conference on Management of data, pages 973-984, 2011.
6. B. Bahmani, A. Chowdhury, and A. Goel. Fast incremental and personalized pagerank. Proceedings of the VLDB Endowment, 4(3):173-184, 2010.
7. P. Berkhin. A survey on PageRank computing. Internet Mathematics, 2(1):73-120, 2005.
8. P. Bickel and B. Li. Regularization in statistics. TEST, 15(2):271-344, 2006.
9. L. Blum, F. Cucker, M. Shub, and S. Smale. Complexity and real computation: A manifesto. International Journal of Bifurcation and Chaos, 6(1):3-26, 1996.
10. P. Boldi and S. Vigna. The push algorithm for spectral ranking. Technical report. Preprint: arXiv:1109.4680 (2011).
11. L. Bottou. Large-scale machine learning with stochastic gradient descent. In Proceedings of the 19th International Conference on Computational Statistics (COMPSTAT'2010), pages 177-187, 2010.
12. J. Cheeger. A lower bound for the smallest eigenvalue of the Laplacian. In Problems in Analysis, Papers dedicated to Salomon Bochner, pages 195-199. Princeton University Press, 1969.
13. Z. Chen and S. Haykin. On different facets of regularization theory. Neural Computation, 14(12):2791-2846, 2002.
14. F.R.K. Chung. Spectral graph theory, volume 92 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, 1997.
15. F.R.K. Chung. The heat kernel as the pagerank of a graph. Proceedings of the National Academy of Sciences of the United States of America, 104(50):19735-19740, 2007.
16. J. Cohen, B. Dolan, M. Dunlap, J. M. Hellerstein, and C. Welton. MAD skills: new analysis practices for big data. Proceedings of the VLDB Endowment, 2(2):1481-1492, 2009.
17. J. Dean and S. Ghemawat. MapReduce: Simplified data processing on large clusters. In Proceedings of the 6th conference on Symposium on Operating Systems Design and Implementation, pages 10-10, 2004.
18. R. Agrawal et al. The Claremont report on database research. ACM SIGMOD Record, 37(3):9-19, 2008.
19. J. Friedman, T. Hastie, and R. Tibshirani. Additive logistic regression: a statistical view of boosting. Annals of Statistics, 28(2):337-407, 2000. (Pubitemid 33227445)
20. D.F. Gleich and M.W. Mahoney. Unpublished results, 2012.
21. S. Guattery and G.L. Miller. On the quality of spectral separators. SIAM Journal on Matrix Analysis and Applications, 19:701-719, 1998.
22. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. Springer-Verlag, New York, 2003.
23. S. Hoory, N. Linial, and A. Wigderson. Expander graphs and their applications. Bulletin of the American Mathematical Society, 43:439-561, 2006. (Pubitemid 44448254)
24. G. Jeh and J. Widom. Scaling personalized web search. In WWW '03: Proceedings of the 12th International Conference on World Wide Web, pages 271-279, 2003.
25. J. Langford, L. Li, and T. Zhang. Sparse online learning via truncated gradient. Journal of Machine Learning Research, 10:777-801, 2009.
26. T. Leighton and S. Rao. Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. Journal of the ACM, 46(6):787-832, 1999.
27. J. Leskovec, K.J. Lang, A. Dasgupta, and M.W. Mahoney. Statistical properties of community structure in large social and information networks. In WWW '08: Proceedings of the 17th International Conference on World Wide Web, pages 695-704, 2008.
28. J. Leskovec, K.J. Lang, and M.W. Mahoney. Empirical comparison of algorithms for network community detection. In WWW '10: Proceedings of the 19th International Conference on World Wide Web, pages 631-640, 2010.
29. N. Linial, E. London, and Y. Rabinovich. The geometry of graphs and some of its algorithmic applications. Combinatorica, 15(2):215-245, 1995.
30. M. W. Mahoney. Randomized algorithms for matrices and data. Foundations and Trends in Machine Learning. NOW Publishers, Boston, 2011. Also available at: arXiv:1104.5557.
31. M. W. Mahoney. Algorithmic and statistical perspectives on large-scale data analysis. In U. Naumann and O. Schenk, editors, Combinatorial Scientific Computing, Chapman & Hall/CRC Computational Science. CRC Press, 2012.
32. M. W. Mahoney and L. Orecchia. Implementing regularization implicitly via approximate eigenvector computation. In Proceedings of the 28th International Conference on Machine Learning, pages 121-128, 2011.
33. M. W. Mahoney, L. Orecchia, and N. K. Vishnoi. A local spectral method for graphs: with applications to improving graph partitions and exploring data graphs locally. Technical report. Preprint: arXiv:0912.0681 (2009).
34. A. Neumaier. Solving ill-conditioned and singular linear systems: A tutorial on regularization. SIAM Review, 40:636-666, 1998. (Pubitemid 128619822)
35. L. Page, S. Brin, R. Motwani, and T. Winograd. The PageRank citation ranking: Bringing order to the web. Technical report, Stanford InfoLab, 1999.
36. P. O. Perry and M. W. Mahoney. Regularized Laplacian estimation and fast eigenvector approximation. In Annual Advances in Neural Information Processing Systems 25: Proceedings of the 2011 Conference, 2011.
37. A. Das Sarma, S. Gollapudi, and R. Panigrahy. Estimating PageRank on graph streams. In Proceedings of the 27th ACM Symposium on Principles of Database Systems, pages 69-78, 2008.
38. S. Smale. Some remarks on the foundations of numerical analysis. SIAM Review, 32(2):211-220, 1990. (Pubitemid 20739461)
39. D.A. Spielman and S.-H. Teng. Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In STOC '04: Proceedings of the 36th annual ACM Symposium on Theory of Computing, pages 81-90, 2004.
40. A.N. Tikhonov and V.Y. Arsenin. Solutions of Ill-Posed Problems. W.H. Winston, Washington, D.C., 1977.
41. V.V. Vazirani. Approximation Algorithms. Springer-Verlag, New York, 2001.
42. S. Vigna. Spectral ranking. Technical report. Preprint: arXiv:0912.0238 (2009).