메뉴 건너뛰기




Volumn 7, Issue , 2006, Pages 665-704

Learning minimum volume sets

Author keywords

Anomaly detection; Minimum volume sets; Sample complexity; Statistical learning theory; Uniform deviation bounds; Universal consistency

Indexed keywords

DECISION MAKING; OPTIMIZATION; PARAMETER ESTIMATION; PROBABILITY; RISK ASSESSMENT; SET THEORY; TREES (MATHEMATICS);

EID: 33646350762     PISSN: 15337928     EISSN: 15337928     Source Type: Journal    
DOI: 10.1016/j.neuron.2006.05.014     Document Type: Short Survey
Times cited : (138)

References (42)
  • 1
    • 18044402908 scopus 로고    scopus 로고
    • Convergence rates in nonparametric estimation of level sets
    • A. Baillo, J. A. Cuesta-Albertos, and A. A. Cuevas. Convergence rates in nonparametric estimation of level sets. Stat. Prob. Letters, 53:27-35, 2001.
    • (2001) Stat. Prob. Letters , vol.53 , pp. 27-35
    • Baillo, A.1    Cuesta-Albertos, J.A.2    Cuevas, A.A.3
  • 3
    • 0031208638 scopus 로고    scopus 로고
    • Learning distributions by their density levels: A paradigm for learning without a teacher
    • S. Ben-David and M. Lindenbaum. Learning distributions by their density levels: a paradigm for learning without a teacher. J. Comp. Sys. Sci., 55:171-182, 1997.
    • (1997) J. Comp. Sys. Sci. , vol.55 , pp. 171-182
    • Ben-David, S.1    Lindenbaum, M.2
  • 4
    • 9444269346 scopus 로고    scopus 로고
    • Oracle bounds and exact algorithm for dyadic classification trees
    • J. Shawe-Taylor and Y. Singer, editors, Springer-Verlag, Heidelberg
    • G. Blanchard, C. Schäfer, and Y. Rozenholc. Oracle bounds and exact algorithm for dyadic classification trees. In J. Shawe-Taylor and Y. Singer, editors, Learning Theory: 17th Annual Conference on Learning Theory, COLT 2004, pages 378-392. Springer-Verlag, Heidelberg, 2004.
    • (2004) Learning Theory: 17th Annual Conference on Learning Theory, COLT 2004 , pp. 378-392
    • Blanchard, G.1    Schäfer, C.2    Rozenholc, Y.3
  • 5
    • 33846313242 scopus 로고    scopus 로고
    • Introduction to statistical learning theory
    • O. Bousquet, U.v. Luxburg, and G. Rtsch, editors, Springer
    • O. Bousquet, S. Boucheron, and G. Lugosi. Introduction to statistical learning theory. In O. Bousquet, U.v. Luxburg, and G. Rtsch, editors, Advanced Lectures in Machine Learning, pages 169-207. Springer, 2004.
    • (2004) Advanced Lectures in Machine Learning , pp. 169-207
    • Bousquet, O.1    Boucheron, S.2    Lugosi, G.3
  • 7
    • 27744586991 scopus 로고    scopus 로고
    • Learning with the Neyman-Pearson and min-max criteria
    • Los Alamos National Laboratory
    • A. Cannon, J. Howse, D. Hush, and C. Scovel. Learning with the Neyman-Pearson and min-max criteria. Technical Report LA-UR 02-2951, Los Alamos National Laboratory, 2002. URL http: //www.c3.lanl.gov/~kelly/ml/pubs/ 2002_minmax/paper.pdf.
    • (2002) Technical Report , vol.LA-UR 02-2951
    • Cannon, A.1    Howse, J.2    Hush, D.3    Scovel, C.4
  • 10
    • 0031329212 scopus 로고    scopus 로고
    • A plug-in approach to support estimation
    • A. Cuevas and R. Fraiman. A plug-in approach to support estimation. Ann. Stat., 25:2300-2312, 1997.
    • (1997) Ann. Stat. , vol.25 , pp. 2300-2312
    • Cuevas, A.1    Fraiman, R.2
  • 12
    • 85009724776 scopus 로고    scopus 로고
    • Nonlinear approximation
    • R. A. DeVore. Nonlinear approximation. Acta Numerica, 7:51-150, 1998.
    • (1998) Acta Numerica , vol.7 , pp. 51-150
    • DeVore, R.A.1
  • 14
    • 0033248623 scopus 로고    scopus 로고
    • Wedgelets: Nearly minimax estimation of edges
    • D. Donoho. Wedgelets: Nearly minimax estimation of edges. Ann. Stat., 27:859-897, 1999.
    • (1999) Ann. Stat. , vol.27 , pp. 859-897
    • Donoho, D.1
  • 16
    • 0001341972 scopus 로고
    • Estimation of a convex density contour in two dimensions
    • J. Hartigan. Estimation of a convex density contour in two dimensions. J. Amer. Statist. Assoc., 82 (397):267-270, 1987.
    • (1987) J. Amer. Statist. Assoc. , vol.82 , Issue.397 , pp. 267-270
    • Hartigan, J.1
  • 17
    • 2142811065 scopus 로고    scopus 로고
    • A network flow approach in finding maximum likelihood estimate of high concentration regions
    • X. Huo and J. Lu. A network flow approach in finding maximum likelihood estimate of high concentration regions. Computational Statistics and Data Analysis, 46(1):33-56, 2004.
    • (2004) Computational Statistics and Data Analysis , vol.46 , Issue.1 , pp. 33-56
    • Huo, X.1    Lu, J.2
  • 18
    • 0346961497 scopus 로고    scopus 로고
    • Complexity penalized support estimation
    • J. Klemelä. Complexity penalized support estimation. J. Multivariate Anal., 88:274-297, 2004.
    • (2004) J. Multivariate Anal. , vol.88 , pp. 274-297
    • Klemelä, J.1
  • 19
    • 0035397715 scopus 로고    scopus 로고
    • Rademacher penalties and structural risk minimization
    • V. Koltchinskii. Rademacher penalties and structural risk minimization. IEEE Trans. Inform. Theory, 47:1902-1914, 2001.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 1902-1914
    • Koltchinskii, V.1
  • 20
    • 21844462365 scopus 로고    scopus 로고
    • Tutorial on practical prediction theory for classification
    • J. Langford. Tutorial on practical prediction theory for classification. J. Machine Learning Research, 6:273-306, 2005.
    • (2005) J. Machine Learning Research , vol.6 , pp. 273-306
    • Langford, J.1
  • 22
    • 0029754587 scopus 로고    scopus 로고
    • Concept learning using complexity regularization
    • G. Lugosi and K. Zeger. Concept learning using complexity regularization. IEEE Trans. Inform. Theory, 42(1):48-54, 1996.
    • (1996) IEEE Trans. Inform. Theory , vol.42 , Issue.1 , pp. 48-54
    • Lugosi, G.1    Zeger, K.2
  • 23
    • 0029307575 scopus 로고
    • Nonparametric estimation using empirical risk minimization
    • G. Lugosi and K. Zeger. Nonparametric estimation using empirical risk minimization. IEEE Trans. Inform. Theory, 41(3):677-687, 1995.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , Issue.3 , pp. 677-687
    • Lugosi, G.1    Zeger, K.2
  • 24
    • 0000371878 scopus 로고
    • Excess mass estimates and tests for multimodality
    • D. Müller and G Sawitzki. Excess mass estimates and tests for multimodality. J. Amer. Statist. Assoc., 86(415):738-746, 1991.
    • (1991) J. Amer. Statist. Assoc. , vol.86 , Issue.415 , pp. 738-746
    • Müller, D.1    Sawitzki, G.2
  • 25
    • 31544483334 scopus 로고    scopus 로고
    • Estimation of high-density regions using one-class neighbor machines
    • A. Muñoz and J. M. Moguerza. Estimation of high-density regions using one-class neighbor machines. IEEE Trans. Patt. Anal. Mach. Intell., 28:476-480, 2006.
    • (2006) IEEE Trans. Patt. Anal. Mach. Intell. , vol.28 , pp. 476-480
    • Muñoz, A.1    Moguerza, J.M.2
  • 26
    • 0001642186 scopus 로고
    • The excess mass ellipsoid
    • D. Nolan. The excess mass ellipsoid. J. Multivariate Analysis, 39:348-371, 1991.
    • (1991) J. Multivariate Analysis , vol.39 , pp. 348-371
    • Nolan, D.1
  • 28
    • 0001030653 scopus 로고
    • Measuring mass concentrations and estimating density contour cluster-an excess mass approach
    • W. Polonik. Measuring mass concentrations and estimating density contour cluster-an excess mass approach. Ann. Stat., 23(3):855-881, 1995.
    • (1995) Ann. Stat. , vol.23 , Issue.3 , pp. 855-881
    • Polonik, W.1
  • 29
    • 0031592717 scopus 로고    scopus 로고
    • Minimum volume sets and generalized quantile processes
    • W. Polonik. Minimum volume sets and generalized quantile processes. Stochastic Processes and their Applications, 69:1-24, 1997.
    • (1997) Stochastic Processes and Their Applications , vol.69 , pp. 1-24
    • Polonik, W.1
  • 30
    • 85144895276 scopus 로고
    • An iterative method for estimating a multivariate mode and isopleth
    • T. W. Sager. An iterative method for estimating a multivariate mode and isopleth. J. Am. Stat. Asso., 74:329-339, 1979.
    • (1979) J. Am. Stat. Asso. , vol.74 , pp. 329-339
    • Sager, T.W.1
  • 32
    • 33646367811 scopus 로고    scopus 로고
    • Learning minimum volume sets
    • UW-Madison
    • C. Scott and R. Nowak. Learning minimum volume sets. Technical Report ECE-05-2, UW-Madison, 2005a. URL http://www.stat.rice.edu/~cscott.
    • (2005) Technical Report , vol.ECE-05-2
    • Scott, C.1    Nowak, R.2
  • 33
    • 27744553952 scopus 로고    scopus 로고
    • A Neyman-Pearson approach to statistical learning
    • C. Scott and R. Nowak. A Neyman-Pearson approach to statistical learning. IEEE Trans. Inform. Theory, 51(8):3806-3819, 2005b.
    • (2005) IEEE Trans. Inform. Theory , vol.51 , Issue.8 , pp. 3806-3819
    • Scott, C.1    Nowak, R.2
  • 34
    • 33645724205 scopus 로고    scopus 로고
    • Minimax-optimal classification with dyadic decision trees
    • April
    • C. Scott and R. Nowak. Minimax-optimal classification with dyadic decision trees. IEEE Trans. Inform. Theory, pages 1335-1353, April 2006.
    • (2006) IEEE Trans. Inform. Theory , pp. 1335-1353
    • Scott, C.1    Nowak, R.2
  • 36
    • 0031478562 scopus 로고    scopus 로고
    • On nonparametric estimation of density level sets
    • A. B. Tsybakov. On nonparametric estimation of density level sets. Ann. Stat., 25:948-969, 1997.
    • (1997) Ann. Stat. , vol.25 , pp. 948-969
    • Tsybakov, A.B.1
  • 39
    • 32544452547 scopus 로고    scopus 로고
    • Consistency and convergence rates of one-class SVM and related algorithms
    • Universit Paris-Sud
    • R. Vert and J.-P. Vert. Consistency and convergence rates of one-class SVM and related algorithms. Technical Report 1414, Universit Paris-Sud, 2005.
    • (2005) Technical Report , vol.1414
    • Vert, R.1    Vert, J.-P.2
  • 40
    • 0031316270 scopus 로고    scopus 로고
    • Granulometric smoothing
    • G. Walther. Granulometric smoothing. Ann. Stat., 25:2273-2299, 1997.
    • (1997) Ann. Stat. , vol.25 , pp. 2273-2299
    • Walther, G.1
  • 41
    • 33646382278 scopus 로고    scopus 로고
    • Minimax optimal level set estimation
    • submitted to
    • R. Willett and R. Nowak. Minimax optimal level set estimation. submitted to IEEE Trans. Image Proc., 2006. URL http://www.ee.duke.edu/~willett/.
    • (2006) IEEE Trans. Image Proc.
    • Willett, R.1    Nowak, R.2
  • 42
    • 30844435040 scopus 로고    scopus 로고
    • Minimax optimal level set estimation
    • 31 July - 4 August, San Diego, CA, USA
    • R. Willett and R. Nowak. Minimax optimal level set estimation. In Proc. SPIE, Wavelets XI, 31 July - 4 August, San Diego, CA, USA, 2005.
    • (2005) Proc. SPIE, Wavelets XI
    • Willett, R.1    Nowak, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.