C. De, Cette thèse a été réalisée dans l'équipe STA (Statistiques et Applications ) du département Traitement du Signal et de l'Image (TSI) de Télécom ParisTech. Les contributions présentées dans cette thèse ont été soutenues financièrement par l'Ecole Normale Supérieure de Cachan via un contrat doctoral pour normalien ainsi que par la chaire industrielle "Machine Learning for Big Data" de Telecom ParisTech. Les contributions scikit-learn ont été financées par le Center for Data Science de Paris Saclay pour ce qui est de la collaboration avec Alexandre Gramfort et par la chaire industrielle mentionnée ci-dessus en ce qui concerne la collaboration à l

C. Aggarwal and P. Yu, Outlier Detection for High Dimensional Data, SIGMOD REC, pp.37-46, 2001.

Y. Amit and D. Geman, Shape Quantization and Recognition with Randomized Trees, Neural Computation, vol.1, issue.1, pp.1545-1588, 1997.
DOI : 10.1016/0031-3203(90)90098-6

M. Anthony and J. Shawe-taylor, A result of Vapnik with applications, Discrete Applied Mathematics, vol.47, issue.3, pp.207-217, 1993.
DOI : 10.1016/0166-218X(93)90126-9

A. Baillo, Total error in a plug-in estimator of level sets, Statistics & Probability Letters, vol.65, issue.4, pp.411-417, 2003.
DOI : 10.1016/j.spl.2003.08.007

A. Baillo, J. Cuesta-albertos, and A. Cuevas, Convergence rates in nonparametric estimation of level sets, Statistics & Probability Letters, vol.53, issue.1, pp.27-35, 2001.
DOI : 10.1016/S0167-7152(01)00006-2

E. Barron, P. Cardaliaguet, and R. Jensen, Conditional Essential Suprema with Applications, Applied Mathematics and Optimization, vol.48, issue.3, pp.229-253, 2003.
DOI : 10.1007/s00245-003-0776-4

S. Bay and M. Schwabacher, Mining distance-based outliers in near linear time with randomization and a simple pruning rule, Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining , KDD '03, pp.29-38, 2003.
DOI : 10.1145/956750.956758

J. Beirlant, M. Escobar-bach, Y. Goegebeur, and A. Guillou, Bias-corrected estimation of stable tail dependence function, Journal of Multivariate Analysis, vol.143, pp.453-466, 2016.
DOI : 10.1016/j.jmva.2015.10.006

URL : https://hal.archives-ouvertes.fr/hal-01115538

J. Beirlant and Y. Goegebeur, Local polynomial maximum likelihood estimation for Pareto-type distributions, Journal of Multivariate Analysis, vol.89, issue.1, pp.97-118, 2004.
DOI : 10.1016/S0047-259X(03)00125-8

J. Beirlant, Y. Goegebeur, J. Segers, and J. Teugels, Statistics of extremes: theory and applications, 2006.
DOI : 10.1002/0470012382

J. Beirlant, P. Vynckier, and J. L. Teugels, Tail index estimation, pareto quantile plots regression diagnostics, JASA, vol.91, pp.1659-1667, 1996.

G. Biau, L. Devroye, and G. Lugosi, Consistency of random forests and other averaging classifiers, JMLR, vol.9, pp.2015-2033, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00355368

G. Biau and E. Scornet, A random forest guided tour, TEST, vol.4, issue.2, pp.197-227, 2016.
DOI : 10.1002/widm.1114

URL : https://hal.archives-ouvertes.fr/hal-01221748

C. Bishop, Pattern Recognition and Machine Learning, 2006.

G. Blanchard, G. Lee, and C. Scott, Semi-supervised novelty detection, JMLR, vol.11, pp.2973-3009, 2010.

G. Blanchard, C. Schäfer, and Y. Rozenholc, Oracle Bounds and Exact Algorithm for Dyadic Classification Trees, Proc. COLT, pp.378-392, 2004.
DOI : 10.1007/978-3-540-27819-1_26

URL : https://hal.archives-ouvertes.fr/hal-00264995

L. Bottou and C. Lin, Support vector machine solvers. Large scale kernel machines, pp.301-320, 2007.

S. Boucheron, O. Bousquet, and G. Lugosi, Theory of Classification: a Survey of Some Recent Advances, ESAIM: Probability and Statistics, vol.49, pp.323-375, 2005.
DOI : 10.1109/TIT.2003.813564

URL : https://hal.archives-ouvertes.fr/hal-00017923

S. Boucheron, G. Lugosi, and P. Massart, Concentration Inequalities: A Nonasymptotic Theory of Independence, 2013.
DOI : 10.1093/acprof:oso/9780199535255.001.0001

URL : https://hal.archives-ouvertes.fr/hal-00794821

S. Boucheron and M. Thomas, Concentration inequalities for order statistics, Electronic Communications in Probability, vol.17, issue.0, pp.1-12, 2012.
DOI : 10.1214/ECP.v17-2210

URL : https://hal.archives-ouvertes.fr/hal-00777381

S. Boucheron and M. Thomas, Tail index estimation, concentration and adaptivity, Electronic Journal of Statistics, vol.9, issue.2, pp.2751-2792, 2015.
DOI : 10.1214/15-EJS1088

URL : https://hal.archives-ouvertes.fr/hal-01132911

O. Bousquet, S. Boucheron, and G. Lugosi, Introduction to Statistical Learning Theory, Advanced Lectures on Machine Learning, 2004.
DOI : 10.1007/3-540-45435-7_5

L. Breiman, Random forests, Machine Learning, vol.45, issue.1, pp.5-32, 2001.
DOI : 10.1023/A:1010933404324

M. M. Breunig, H. P. Kriegel, R. T. Ng, and J. Sander, LOF: identifying density-based local outliers, SIGMOD REC, pp.93-104, 2000.

L. Buitinck, G. Louppe, M. Blondel, F. Pedregosa, . Mueller et al., API design for machine learning software: experiences from the scikit-learn project, ECML PKDD Workshop: Languages for Data Mining and Machine Learning, pp.108-122, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00856511

B. Cadre, Kernel estimation of density level sets, Journal of Multivariate Analysis, vol.97, issue.4, pp.999-1023, 2006.
DOI : 10.1016/j.jmva.2005.05.004

URL : https://hal.archives-ouvertes.fr/hal-00003898

V. Chandola, A. Banerjee, and V. Kumar, Anomaly detection, ACM Computing Surveys, vol.41, issue.3, 2009.
DOI : 10.1145/1541880.1541882

V. Chernozhukov, Extremal quantile regression, The Annals of Statistics, vol.33, issue.2, pp.806-839, 2005.
DOI : 10.1214/009053604000001165

S. Clémençon and J. Jakubowicz, Scoring anomalies: a m-estimation formulation, Proc. AISTATS, pp.659-667, 2013.

S. Clémençon and S. Robbiano, Anomaly Ranking as Supervised Bipartite Ranking, Proc. ICML, 2014.

S. Clémençon and N. Vayatis, Nonparametric estimation of the precision-recall curve, Proc. ICML, pp.185-192, 2009.

S. Clémençon and N. Vayatis, Tree-Based Ranking Methods, IEEE Transactions on Information Theory, vol.55, issue.9, pp.4316-4336, 2009.
DOI : 10.1109/TIT.2009.2025558

S. Clémençon and N. Vayatis, Overlaying Classifiers: A??Practical Approach to??Optimal Scoring, Constructive Approximation, vol.16, issue.12, pp.619-648, 2010.
DOI : 10.1148/radiology.143.1.7063747

D. A. Clifton, S. Hugueny, and L. Tarassenko, Novelty Detection with Multivariate Extreme Value Statistics, Journal of Signal Processing Systems, vol.259, issue.2, pp.371-389, 2011.
DOI : 10.1006/jsvi.2002.5168

D. A. Clifton, L. Tarassenko, N. Mcgrogan, D. King, S. King et al., Bayesian Extreme Value Statistics for Novelty Detection in Gas-Turbine Engines, 2008 IEEE Aerospace Conference, pp.1-11, 2008.
DOI : 10.1109/AERO.2008.4526423

S. Coles, J. Bawa, L. Trenner, and P. Dorazio, An introduction to statistical modeling of extreme values, 2001.
DOI : 10.1007/978-1-4471-3675-0

S. Coles and J. A. Tawn, Modeling extreme multivariate events, JR Statist. Soc. B, vol.53, pp.377-392, 1991.

D. Cooley, R. A. Davis, and P. Naveau, The pairwise beta distribution: A flexible parametric multivariate model for extremes, Journal of Multivariate Analysis, vol.101, issue.9, pp.2103-2117, 2010.
DOI : 10.1016/j.jmva.2010.04.007

C. Cortes and V. Vapnik, Support-vector networks, Machine Learning, pp.273-297, 1995.
DOI : 10.1007/BF00994018

A. Cuevas and R. Fraiman, A plug-in approach to support estimation, The Annals of Statistics, vol.25, issue.6, pp.2300-2312, 1997.
DOI : 10.1214/aos/1030741073

A. Daouia, L. Gardes, and S. Girard, On kernel smoothing for extremal quantile regression, Bernoulli, vol.19, issue.5B, pp.2557-2589, 2013.
DOI : 10.3150/12-BEJ466

URL : https://hal.archives-ouvertes.fr/hal-00803127

A. Daouia, L. Gardes, S. Girard, and A. Lekina, Kernel estimators of extreme level curves, TEST, vol.73, issue.2, pp.311-333, 2011.
DOI : 10.2307/2286285

URL : https://hal.archives-ouvertes.fr/inria-00393588

J. Davis and M. Goadrich, The relationship between Precision-Recall and ROC curves, Proceedings of the 23rd international conference on Machine learning , ICML '06, 2006.
DOI : 10.1145/1143844.1143874

D. Haan and A. Ferreira, Extreme value theory: an introduction, 2007.

L. De-haan and S. Resnick, Second-order regular variation and rates of convergence in extreme-value theory, The Annals of Probability, vol.24, issue.1, pp.97-124, 1996.
DOI : 10.1214/aop/1042644709

L. De-haan and S. I. Resnick, Limit theory for multivariate sample extremes, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.11, issue.4, pp.317-337, 1977.
DOI : 10.1007/BF00533086

A. L. Dekkers, J. H. Einmahl, and L. De-haan, A Moment Estimator for the Index of an Extreme-Value Distribution, The Annals of Statistics, vol.17, issue.4, pp.1833-1855, 1989.
DOI : 10.1214/aos/1176347397

F. Denis, R. Gilleron, and F. Letouzey, Learning from positive and unlabeled examples, Theoretical Computer Science, vol.348, issue.1, pp.70-83, 2005.
DOI : 10.1016/j.tcs.2005.09.007

URL : https://hal.archives-ouvertes.fr/inria-00538887

L. Devroye, L. Györfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition. Applications of mathematics : stochastic modelling and applied probability, 1996.

R. Díaz-uriarte and S. A. De-andres, Gene selection and classification of microarray data using random forest, BMC bioinformatics, 2006.

H. Drees and X. Huang, Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function, Journal of Multivariate Analysis, vol.64, issue.1, pp.25-47, 1998.
DOI : 10.1006/jmva.1997.1708

M. C. Du-plessis, G. Niu, and M. Sugiyama, Class-prior estimation for learning from positive and unlabeled data, Proc. ACML, 2015.
DOI : 10.1587/transinf.E93.D.2690

C. Désir, S. Bernard, C. Petitjean, and L. Heutte, A New Random Forest Method for One-Class Classification, Structural, Syntactic, and Statistical Pattern Recognition, 2012.
DOI : 10.1007/978-3-642-34166-3_31

J. H. Einmahl, L. De-haan, and D. Li, Weighted approximations of tail copula processes with application to testing the bivariate extreme value condition, The Annals of Statistics, vol.34, issue.4, pp.1987-2014, 2006.
DOI : 10.1214/009053606000000434

J. H. Einmahl, A. Krajina, and J. Segers, An M-estimator for tail dependence in arbitrary dimensions, The Annals of Statistics, vol.40, issue.3, pp.1764-1793, 2012.
DOI : 10.1214/12-AOS1023

J. H. Einmahl, J. Li, and R. Y. Liu, Thresholding Events of Extreme in Simultaneous Monitoring of Multiple Risks, Journal of the American Statistical Association, vol.104, issue.487, pp.982-992, 2009.
DOI : 10.1198/jasa.2009.ap08329

J. H. Einmahl and J. Segers, Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution, The Annals of Statistics, vol.37, issue.5B, pp.2953-2989, 2009.
DOI : 10.1214/08-AOS677

J. Hj-einmahl, L. De-haan, and V. Piterbarg, Nonparametric estimation of the spectral measure of an extreme value distribution, Ann. Stat, vol.29, pp.1401-1423, 2001.

J. Einmahl and D. Mason, Generalized Quantile Processes, The Annals of Statistics, vol.20, issue.2, pp.1062-1078, 1992.
DOI : 10.1214/aos/1176348670

P. Embrechts, L. De-haan, and X. Huang, Modelling multivariate extremes. Extremes and integrated risk management, pp.59-67, 2000.

E. Eskin, Anomaly detection over noisy data using learned probability distributions, Proc. ICML, pp.255-262, 2000.

E. Eskin, A. Arnold, M. Prerau, L. Portnoy, and S. Stolfo, A Geometric Framework for Unsupervised Anomaly Detection, Applications of data mining in computer security, pp.77-101, 2002.
DOI : 10.1007/978-1-4615-0953-0_4

M. Falk, J. Huesler, and R. D. Reiss, Laws of Small Numbers: Extremes and Rare Events, 1994.

T. Fawcett, An introduction to roc analysis. Pattern recognition letters, pp.861-874, 2006.

H. Federer, Geometric Measure Theory, 1969.
DOI : 10.1007/978-3-642-62010-2

B. Finkenstadt and H. Rootzén, Extreme values in finance, telecommunications, and the environment, 2003.
DOI : 10.1201/9780203483350

P. A. Flach, The geometry of ROC space: understanding ML metrics through ROC isometrics, Proc. ICML, 2003.

A. Fougeres, L. De-haan, and C. Mercadier, Bias correction in multivariate extremes, The Annals of Statistics, vol.43, issue.2, pp.903-934, 2015.
DOI : 10.1214/14-AOS1305

URL : https://hal.archives-ouvertes.fr/hal-00942494

A. Fougères, J. Nolan, and H. Rootzén, Models for Dependent Extremes Using Stable Mixtures, Scandinavian Journal of Statistics, vol.65, issue.1987, pp.42-59, 2009.
DOI : 10.6028/jres.099.028

Y. Freund and R. Schapire, Experiments with a new boosting algorithm, Proc. ICML, pp.148-156, 1996.

J. Friedman, T. Hastie, and R. Tibshirani, The elements of statistical learning, 2001.

L. Gardes and S. Girard, A moving window approach for nonparametric estimation of the conditional tail index, Journal of Multivariate Analysis, vol.99, issue.10, pp.2368-2388, 2008.
DOI : 10.1016/j.jmva.2008.02.023

URL : https://hal.archives-ouvertes.fr/inria-00124637

L. Gardes, S. Girard, and A. Lekina, Functional nonparametric estimation of conditional extreme quantiles, Journal of Multivariate Analysis, vol.101, issue.2, pp.419-433, 2010.
DOI : 10.1016/j.jmva.2009.06.007

URL : https://hal.archives-ouvertes.fr/hal-00289996

R. Genuer, J. Poggi, and C. Tuleau, Random forests: some methodological insights, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00340725

R. Genuer, J. Poggi, and C. Tuleau-malot, Variable selection using random forests, Pattern Recognition Letters, vol.31, issue.14, pp.2225-2236, 2010.
DOI : 10.1016/j.patrec.2010.03.014

URL : https://hal.archives-ouvertes.fr/hal-00755489

P. Geurts, D. Ernst, and L. Wehenkel, Extremely randomized trees, Machine Learning, vol.63, issue.1, pp.3-42, 2006.
DOI : 10.1007/s10994-006-6226-1

URL : https://hal.archives-ouvertes.fr/hal-00341932

C. Gini, Variabilita e mutabilita, Memorie di metodologia statistica, 1912.

S. Girard, A Hill Type Estimator of the Weibull Tail-Coefficient, Communications in Statistics - Theory and Methods, vol.10, issue.2, pp.205-234, 2004.
DOI : 10.1214/aos/1176343247

URL : https://hal.archives-ouvertes.fr/hal-00724602

S. Girard and P. Jacob, Frontier estimation via kernel regression on high power-transformed data, Journal of Multivariate Analysis, vol.99, issue.3, pp.403-420, 2008.
DOI : 10.1016/j.jmva.2006.11.006

URL : https://hal.archives-ouvertes.fr/hal-00077683

N. Goix, How to Evaluate the Quality of Unsupervised Anomaly Detection Algorithms, ICML Workshop on Anomaly Detection, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01341809

N. Goix, R. Brault, N. Drougard, and M. Chiapino, One Class Splitting Criteria for Random Forests with Application to Anomaly Detection, 2016.

N. Goix, A. Sabourin, and S. Clémençon, Sparse Representation of Multivariate Extremes, NIPS 2015 Workshop on Nonparametric Methods for Large Scale Representation Learning, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01295301

N. Goix, A. Sabourin, and S. Clémençon, Sparse representation of multivariate extremes with applications to anomaly detection, the reviewing process of JMVA, 2016.
DOI : 10.1016/j.jmva.2017.06.010

N. Goix, A. Sabourin, and S. Clémençon, Learning the dependence structure of rare events: a nonasymptotic study, Proc. COLT, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01148834

N. Goix, A. Sabourin, and S. Clémençon, On Anomaly Ranking and Excess-Mass Curves, Proc. AISTATS, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01113521

N. Goix, A. Sabourin, and S. Clémençon, Sparse Representation of Multivariate Extremes with Applications to Anomaly Ranking, Proc. AISTATS, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01295301

N. Goix and A. Thomas, How to Evaluate the Quality of Unsupervised Anomaly Detection Algorithms? To be submitted, 2016.

J. A. Hartigan, Estimation of a Convex Density Contour in Two Dimensions, Journal of the American Statistical Association, vol.38, issue.397, pp.267-270, 1987.
DOI : 10.1214/aoms/1177698699

B. M. Hill, A Simple General Approach to Inference About the Tail of a Distribution, The Annals of Statistics, vol.3, issue.5, pp.1163-1174, 1975.
DOI : 10.1214/aos/1176343247

T. K. Ho, The random subspace method for constructing decision forests, IEEE transactions on pattern analysis and machine intelligence, vol.20, pp.832-844, 1998.

V. J. Hodge and J. Austin, A Survey of Outlier Detection Methodologies, Artificial Intelligence Review, vol.22, issue.2, pp.85-126, 2004.
DOI : 10.1023/B:AIRE.0000045502.10941.a9

X. Huang, Statistics of bivariate extreme values, 1992.

S. Janson, On concentration of probability. Contemporary combinatorics, 2002.

E. Jones, T. Oliphant, and P. Peterson, Scipy: Open source scientific tools for python, 2001.

. Kddcup, The third international knowledge discovery and data mining tools competition dataset, 1999.

V. Koltchinskii, M -estimation, convexity and quantiles, The Annals of Statistics, vol.25, issue.2, pp.435-477, 1997.
DOI : 10.1214/aos/1031833659

V. Koltchinskii, Local Rademacher complexities and oracle inequalities in risk minimization, The Annals of Statistics, vol.34, issue.6, pp.2593-2706, 2006.
DOI : 10.1214/009053606000001019

M. R. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and related properties of random sequences and processes, 1983.
DOI : 10.1007/978-1-4612-5449-2

H. J. Lee and S. J. Roberts, On-line novelty detection using the Kalman filter and extreme value theory, 2008 19th International Conference on Pattern Recognition, pp.1-4, 2008.
DOI : 10.1109/ICPR.2008.4761918

M. Lichman, UCI machine learning repository, 2013.

R. Lippmann, J. Haines, D. J. Fried, J. Korba, and K. Das, Analysis and Results of the 1999 DARPA Off-Line Intrusion Detection Evaluation, RAID, pp.162-182, 2000.
DOI : 10.1007/3-540-39945-3_11

B. Liu, W. S. Lee, P. Yu, and X. Li, Partially supervised classification of text documents, Proc. ICML, pp.387-394, 2002.

F. T. Liu, K. M. Ting, and Z. Zhou, Isolation-Based Anomaly Detection, ACM Transactions on Knowledge Discovery from Data, vol.6, issue.1, 2012.
DOI : 10.1145/2133360.2133363

F. T. Liu, K. M. Ting, and Z. H. Zhou, Isolation Forest, 2008 Eighth IEEE International Conference on Data Mining, pp.413-422, 2008.
DOI : 10.1109/ICDM.2008.17

G. Louppe, Understanding random forests: From theory to practice, 2014.

M. Markou and S. Singh, Novelty detection: a review part 1: statistical approaches. Signal proc, 2003.

D. M. Mason and W. Polonik, Asymptotic normality of plug-in level set estimates, The Annals of Applied Probability, vol.19, issue.3, pp.1108-1142, 2009.
DOI : 10.1214/08-AAP569

P. Massart, Some applications of concentration inequalities to statistics, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.9, issue.2, pp.245-303, 2000.
DOI : 10.5802/afst.961

P. Massart, Concentration Inequalities and Model Selection: Ecole d'Eté de Probabilités de Saint-Flour XXXIV, Lecture Notes in Mathematics, vol.1896, 2007.

F. Mordelet and J. Vert, A bagging SVM to learn from positive and unlabeled examples, Pattern Recognition Letters, vol.37, pp.201-209, 2014.
DOI : 10.1016/j.patrec.2013.06.010

URL : https://hal.archives-ouvertes.fr/hal-00523336

D. W. Müller and G. Sawitzki, Excess mass estimates and tests for multimodality, JASA, vol.86, pp.738-746, 1991.

P. Panov and S. D?eroski, Combining Bagging and Random Subspaces to Create Better Ensembles, 2007.
DOI : 10.1007/978-3-540-74825-0_11

A. Patcha and J. M. Park, An overview of anomaly detection techniques: Existing solutions and latest technological trends, Computer Networks, vol.51, issue.12, pp.3448-3470, 2007.
DOI : 10.1016/j.comnet.2007.02.001

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion et al., Scikit-learn: Machine learning in Python, JMLR, vol.12, pp.2825-2830, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00650905

W. Polonik, Measuring Mass Concentrations and Estimating Density Contour Clusters-An Excess Mass Approach, The Annals of Statistics, vol.23, issue.3, pp.855-881, 1995.
DOI : 10.1214/aos/1176324626

W. Polonik, Minimum volume sets and generalized quantile processes, Stochastic Processes and their Applications, pp.1-24, 1997.
DOI : 10.1016/S0304-4149(97)00028-8

W. Polonik, The silhouette, concentration functions and ML-density estimation under order restrictions, The Annals of Statistics, vol.26, issue.5, pp.1857-1877, 1998.
DOI : 10.1214/aos/1024691360

F. Provost and T. Fawcett, Analysis and visualization of classifier performance: comparison under imprecise class and cost distributions, KDD, pp.43-48, 1997.

F. Provost, T. Fawcett, and R. Kohavi, The case against accuracy estimation for comparing induction algorithms, Proc. ICML, pp.445-453, 1998.

Y. Qi, Almost sure convergence of the stable tail empirical dependence function in multivariate extreme statistics, Acta Mathematicae Applicatae Sinica, vol.45, issue.2, pp.167-175, 1997.
DOI : 10.1007/BF02015138

J. Quinn and M. Sugiyama, A least-squares approach to anomaly detection in static and sequential data, Pattern Recognition Letters, vol.40, pp.36-40, 2014.
DOI : 10.1016/j.patrec.2013.12.016

S. Resnick, Extreme Values, Regular Variation, and Point Processes, Series in Operations Research and Financial Engineering, 1987.
DOI : 10.1007/978-0-387-75953-1

S. Resnick, Heavy-tail phenomena: probabilistic and statistical modeling, 2007.

P. Rigollet and R. Vert, Optimal rates for plug-in estimators of density level sets, Bernoulli, vol.15, issue.4, pp.1154-1178, 2009.
DOI : 10.3150/09-BEJ184

S. J. Roberts, Novelty detection using extreme value statistics, IEE Proceedings - Vision, Image, and Signal Processing, vol.146, issue.3, pp.124-129, 1999.
DOI : 10.1049/ip-vis:19990428

S. J. Roberts, Extreme value statistics for novelty detection in biomedical data processing, IEE Proceedings - Science, Measurement and Technology, vol.147, issue.6, pp.363-367, 2000.
DOI : 10.1049/ip-smt:20000841

A. Sabourin and P. Naveau, Bayesian Dirichlet mixture model for multivariate extremes: A re-parametrization, Computational Statistics & Data Analysis, vol.71, pp.542-567, 2014.
DOI : 10.1016/j.csda.2013.04.021

URL : https://hal.archives-ouvertes.fr/hal-00880879

B. Schölkopf, J. Platt, J. Shawe-taylor, A. Smola, and R. Williamson, Estimating the Support of a High-Dimensional Distribution, Neural Computation, vol.6, issue.1, pp.1443-1471, 2001.
DOI : 10.1214/aos/1069362732

E. Schubert, R. Wojdanowski, A. Zimek, and H. Kriegel, On Evaluation of Outlier Rankings and Outlier Scores, SDM, pp.1047-1058, 2012.
DOI : 10.1137/1.9781611972825.90

C. Scott and G. Blanchard, Novelty detection: Unlabeled data definitely help, Proc. AISTATS, pp.464-471, 2009.

C. Scott and R. Nowak, Learning minimum volume sets, JMLR, vol.7, pp.665-704, 2006.

J. Segers, Asymptotics of empirical copula processes under non-restrictive smoothness assumptions, Bernoulli, vol.18, issue.3, pp.764-782, 2012.
DOI : 10.3150/11-BEJ387

J. Segers, Max-stable models for multivariate extremes, REVSTAT -Statistical Journal, vol.10, pp.61-82, 2012.

C. E. Shannon, A mathematical theory of communication, ACM SIGMOBILE MC2R, vol.5, pp.3-55, 2001.

J. Shawe-taylor and N. Cristianini, Kernel methods for pattern analysis, 2004.
DOI : 10.1017/CBO9780511809682

T. Shi and S. Horvath, Unsupervised Learning With Random Forest Predictors, Journal of Computational and Graphical Statistics, vol.15, issue.1, 2012.
DOI : 10.1198/106186006X94072

M. L. Shyu, S. C. Chen, K. Sarinnapakorn, and L. Chang, A novel anomaly detection scheme based on principal component classifier, 2003.

R. L. Smith, Estimating Tails of Probability Distributions, The Annals of Statistics, vol.15, issue.3, pp.1174-1207, 1987.
DOI : 10.1214/aos/1176350499

R. Smith, Statistics of extremes, with applications in environment, insurance and finance. Extreme values in finance, telecommunications and the environment, pp.1-78, 2003.

A. J. Smola, L. Song, and C. H. Teo, Relative novelty detection, Proc. AISTATS, pp.536-543, 2009.

I. Steinwart, D. Hush, and C. Scovel, A classification framework for anomaly detection, JMLR, vol.6, pp.211-232, 2005.

A. Stephenson, Simulating multivariate extreme value distributions of logistic type, Extremes, vol.6, issue.1, pp.49-59, 2003.
DOI : 10.1023/A:1026277229992

A. G. Stephenson, HIGH-DIMENSIONAL PARAMETRIC MODELLING OF MULTIVARIATE EXTREME EVENTS, Australian & New Zealand Journal of Statistics, vol.77, issue.1, pp.77-88, 2009.
DOI : 10.1007/978-1-4613-3638-9_14

M. Sugiyama, Superfast-Trainable Multi-Class Probabilistic Classifier by Least-Squares Posterior Fitting, IEICE Transactions on Information and Systems, vol.93, issue.10, pp.2690-2701, 2010.
DOI : 10.1587/transinf.E93.D.2690

V. Svetnik, A. Liaw, C. Tong, J. C. Culberson, R. Sheridan et al., Random Forest:??? A Classification and Regression Tool for Compound Classification and QSAR Modeling, Journal of Chemical Information and Computer Sciences, vol.43, issue.6, pp.1947-1958, 2003.
DOI : 10.1021/ci034160g

M. Tavallaee, E. Bagheri, W. Lu, and A. A. Ghorbani, A detailed analysis of the KDD CUP 99 data set, 2009 IEEE Symposium on Computational Intelligence for Security and Defense Applications, pp.53-58, 2009.
DOI : 10.1109/CISDA.2009.5356528

J. Tawn, Modelling multivariate extreme value distributions, Biometrika, vol.77, issue.2, pp.245-253, 1990.
DOI : 10.1093/biomet/77.2.245

D. Tax and R. Pw-duin, Uniform object generation for optimizing one-class classifiers, JMLR, vol.2, pp.155-173, 2002.

A. Thomas, V. Feuillard, and A. Gramfort, Calibration of One-Class SVM for MV set estimation, 2015 IEEE International Conference on Data Science and Advanced Analytics (DSAA), pp.1-9, 2015.
DOI : 10.1109/DSAA.2015.7344789

URL : https://hal.archives-ouvertes.fr/hal-01188294

M. Thomas, Concentration results on extreme value theory, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01177197

A. B. Tsybakov, On nonparametric estimation of density level sets, The Annals of Statistics, vol.25, issue.3, pp.948-969, 1997.
DOI : 10.1214/aos/1069362732

S. Van-der-walt, G. Colbert, and . Varoquaux, The NumPy Array: A Structure for Efficient Numerical Computation, Computing in Science & Engineering, vol.13, issue.2, pp.22-30, 2011.
DOI : 10.1109/MCSE.2011.37

URL : https://hal.archives-ouvertes.fr/inria-00564007

V. Vapnik, The nature of statistical learning theory, 2013.

V. Vapnik and A. Chervonenkis, Theory of Pattern Recognition, 1974.

J. Vert and R. Vert, Consistency and convergence rates of one-class svms and related algorithms, JMLR, vol.6, pp.828-835, 2006.

R. Vert, Theoretical insights on density level set estimation, application to anomaly detection, 2006.

K. Viswanathan, L. Choudur, V. Talwar, C. Wang, G. Macdonald et al., Ranking anomalies in data centers, 2012 IEEE Network Operations and Management Symposium, pp.79-87, 2012.
DOI : 10.1109/NOMS.2012.6211885

J. Wellner, Limit theorems for the ratio of the empirical distribution function to the true distribution function, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.5, issue.No. 2, pp.73-88, 1978.
DOI : 10.1007/BF00635964

K. Yamanishi, J. I. Takeuchi, G. Williams, and P. Milne, On-line unsupervised outlier detection using finite mixtures with discounting learning algorithms, KDD, pp.275-300, 2000.