2019/07/17 by Maël Chiapino, Chiapino, Maël, Stéphan Clémençon +5
Computer Science · Economics, Econometrics and Finance · Environmental Science · #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Hydrology and Drought Analysis #Machine Learning (stat.ML) #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.1907.07523
openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a wide variety of situations, anomalies in the behaviour of a complex\nsystem, whose health is monitored through the observation of a random vector X\n= (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of\nextreme values for certain subgroups \α \⊂ 1,. .. , d of\nvariables Xj. Under the heavy-tail assumption, which is precisely appropriate\nfor modeling these phenomena, statistical methods relying on multivariate\nextreme value theory have been developed in the past few years for identifying\nsuch events/subgroups. This paper exploits this approach much further by means\nof a novel mixture model that permits to describe the distribution of extremal\nobservations and where the anomaly type \α is viewed as a latent\nvariable. One may then take advantage of the model by assigning to any extreme\npoint a posterior probability for each anomaly type \α, defining\nimplicitly a similarity measure between anomalies. It is explained at length\nhow the latter permits to cluster extreme observations and obtain an\ninformative planar representation of anomalies using standard graph-mining\ntools. The relevance and usefulness of the clustering and 2-d visual display\nthus designed is illustrated on simulated datasets and on real observations as\nwell, in the aeronautics application domain.\n