Runtime guarantees for regression problems

ITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science

Volumn , Issue , 2013, Pages 269-282

  Chin, Hui Han ^a   Madry, Aleksander ^b   Miller, Gary L ^a   Peng, Richard ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b EPFL   (Switzerland)

Author keywords

image processing; optimization; regression

Indexed keywords

GRAPH ALGORITHMS; INFERENCE PROBLEM; LEAST SQUARES PROBLEMS; OPTIMIZATION PROBLEMS; QUADRATIC MINIMIZATION; REGRESSION; REGRESSION PROBLEM; RUNTIMES;

ALGORITHMS; COMPUTER SCIENCE; COMPUTER VISION; GRAPH THEORY; IMAGE PROCESSING; LINEAR SYSTEMS; OPTIMIZATION;

PROBLEM SOLVING;

EID: 84873329588     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2422436.2422469     Document Type: Conference Paper

References (44)

1. S. Arora, E. Hazan, and S. Kale. The multiplicative weights update method: a meta algorithm and applications. Technical report, Princeton University, 2005. 5
2. H. Avron, G. Shklarski, and S. Toledo. On element SDD approximability. CoRR, abs/0911.0547, 2009. 2.1
3. S. R. Becker, E. J. Candes, and M. Grant. Templates for convex cone problems with applications to sparse signal recovery. MATHEMATICAL PROGRAMMING COMPUTATION, 3:165, 2011. 1, 4.4
4. G. E. Blelloch, A. Gupta, I. Koutis, G. L. Miller, R. Peng, and K. Tangwongsan. Near linear-work parallel SDD solvers, low-diameter decomposition, and low-stretch subgraphs. In Proceedings of the 23rd ACM symposium on Parallelism in algorithms and architectures, SPAA '11, pages 13-22, New York, NY, USA, 2011. ACM. 2.1
5. E. G. Boman, B. Hendrickson, and S. A. Vavasis. Solving elliptic finite element systems in near-linear time with support preconditioners. CoRR, cs.NA/0407022, 2004. 2.1
6. S. Boyd and L. Vandenberghe. Convex Optimization. Camebridge University Press, 2004. 1, 4.1, C, C.1
7. J. Candes, E. Compressive sampling. Proceedings of the International Congress of Mathematicians, 2006. 1, 1
8. T. Chan and J. Shen. Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods. SIAM, 2005. 3.1, 6.1
9. P. Christiano, J. A. Kelner, A. Ma̧dry, D. Spielman, and S.-H. Teng. Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs. In Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC), 2011. 1, 2.1, 4.2, 5, 5, 5, 7, B, B
10. E. Cohen. Polylog-time and near-linear work approximation scheme for undirected shortest paths. J. ACM, 47(1):132-166, 2000. 1
11. D. Coppersmith and S. Winograd. Matrix multiplication via arithmetical progressions. J. Symbolic Computation, 9:251-280, 1990. 2.1
12. S. I. Daitch and D. A. Spielman. Support-graph preconditioners for 2-dimensional trusses. CoRR, abs/cs/0703119, 2007. 2.1
13. S. I. Daitch and D. A. Spielman. Faster approximate lossy generalized flow via interior point algorithms. In Proceedings of the 40th annual ACM symposium on Theory of computing, STOC '08, pages 451-460, New York, NY, USA, 2008. ACM. 1, 5, A, C
14. J. Darbon and M. Sigelle. Image restoration with discrete constrained total variation part i: Fast and exact optimization. Journal of Mathematical Imaging and Vision, 26(3):261-276, 2006. 4.2
15. Y. Freund and R. E. Schapire. Adaptive game playing using multiplicative weights. Games and Economic Behavior, 29(1-2):79-103, October 1999. 5
16. A. V. Goldberg and S. Rao. Beyond the flow decomposition barrier. J. ACM, 45:783-797, September 1998. 4.2
17. D. Goldfarb and W. Yin. Second-order cone programming methods for total variation-based image restoration. SIAM J. Sci. Comput, 27:622-645, 2004. 4.1, C
18. T. Goldstein and S. Osher. The split bregman method for l1-regularized problems. SIAM J. Img. Sci., 2:323-343, April 2009. 6.1, 1
19. T. Hocking, J.-P. Vert, F. Bach, and A. Joulin. Clusterpath: an algorithm for clustering using convex fusion penalties. In L. Getoor and T. Scheffer, editors, Proceedings of the 28th International Conference on Machine Learning (ICML-11), ICML '11, pages 745-752, New York, NY, USA, June 2011. ACM. 3.4
20. D. S. Johnson and C. C. McGeoch, editors. Network Flows and Matching: First DIMACS Implementation Challenge. American Mathematical Society, Boston, MA, USA, 1993. 1
21. J. A. Kelner, G. L. Miller, and R. Peng. Faster approximate multicommodity flow using quadratically coupled flows. In Proceedings of the 44th symposium on Theory of Computing, STOC '12, pages 1-18, New York, NY, USA, 2012. ACM. 2.1, 3.2
22. V. Kolmogorov and R. Zabih. What energy functions can be minimized via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26:65-81, 2004. 4.2
23. I. Koutis and G. Miller. The combinatorial multigrid solver. Conference Talk, March 2009. 6
24. 1/6) time, parallel algorithm for solving planar Laplacians. In Proc. 18th ACM-SIAM Symposium on Discrete Algorithms (SODA 2007), 2007. 3.1
25. I. Koutis, G. L. Miller, and R. Peng. Approaching optimality for solving sdd linear systems. In Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS '10, pages 235-244, Washington, DC, USA, 2010. IEEE Computer Society. 2.1
26. I. Koutis, G. L. Miller, and R. Peng. A nearly-m log n time solver for sdd linear systems. In Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS '11, pages 590-598, Washington, DC, USA, 2011. IEEE Computer Society. 2.1
27. I. Koutis, G. L. Miller, and D. Tolliver. Combinatorial preconditioners and multilevel solvers for problems in computer vision and image processing. In International Symposium of Visual Computing, pages 1067-1078, 2009. 6
28. S. Kullback and R. A. Leibler. On information and sufficiency. Ann. Math. Statist., 22(1):79-86, 1951. 5
29. N. Littlestone and M. K. Warmuth. The weighted majority algorithm. Inf. Comput., 108(2):212-261, Feb. 1994. 5
30. C. A. Micchelli, L. Shen, and Y. Xu. Proximity algorithms for image models: denoising. Inverse Problems, 27(4):045009, 2011. 6.1, 1
31. K. Mulmuley, U. V. Vazirani, and V. V. Vazirani. Matching is as easy as matrix inversion. Combinatorica, 7(1):105-113, Jan. 1987. A
32. D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics, 42:577-685, 1989. 2, 7
33. Y. NESTEROV. Gradient methods for minimizing composite objective function. CORE Discussion Papers 2007076, UniversitÃl' catholique de Louvain, Center for Operations Research and Econometrics (CORE), 2007. 1, 4.4
34. P. Pérez, M. Gangnet, and A. Blake. Poisson image editing. ACM Transactions on Graphics (SIGGRAPH'03), 22(3):313-318, 2003. 3.3, 6.2
35. L. Rosasco, E. De, V. A. Caponnetto, M. Piana, and A. Verri. Are loss functions all the same. Neural Computation, 15, 2004. 7
36. L. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithm. Physica D, 1(60):259-268, 1992. 1, 1, 6.1
37. D. A. Spielman and S.-H. Teng. Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pages 81-90, June 2004. 2.1
38. D. A. Spielman and S.-H. Teng. Nearly-linear time algorithms for preconditioning and solving symmetric, diagonally dominant linear systems. CoRR, abs/cs/0607105, 2006. 1, 2.1
39. V. Strassen. Gaussian elimination is not optimal. Numerische Mathematik, 13:354-356, 1969. 2.1
40. R. Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society (Series B), 58:267-288, 1996. 1
41. R. Tibshirani, M. Saunders, S. Rosset, J. Zhu, and K. Knight. Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society Series B, 67(1):91-108, 2005. 2
42. V. Vassilevska Williams. Breaking the Coppersmith-Winograd barrier. In Proceedings of the 44th symposium on Theory of Computing, STOC '12, 2012. 2.1
43. B. Wohlberg and P. Rodriguez. An iteratively reweighted norm algorithm for minimization of total variation functionals. Signal Processing Letters, IEEE, 14(12):948 -951, dec. 2007. 4.3
44. M. Yuan and Y. Lin. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society, Series B, 68:49-67, 2006. 2