Sparse pairwise Markov model learning for anomaly detection in heterogeneous data
Résumé
An important challenge in the aeronautic industry is to cope with maintenance issues of the products , notably detection and localization of components breakdowns. Modern equipments enjoy better recording and processing capacities, allowing the storage of a large amount of data, on which better maintenance systems are expected to be built. Efficient probabilistic models able to represent the statistic distribution of the collected variables in the " normal state " of the system are needed in order to derive anomaly detection algorithms. Graphical models constitute a rich class of models and are natural candidates to address this task. This article proposes a method for learning undirected hybrid graphical models from heterogeneous data. The data are heterogeneous as they include physical (quantitative) measures as well as a collection of inherently discrete variables for instance describing the state of electronic devices. The model we propose is adapted from the Ising and Gaussian models so that the data don't require to be translated from their original space, allowing the user to easily interpret the dependency graph learned from data. The learning step is carried out by minimizing the negative pseudo-log-likelihood using a proximal gradient algorithm with Lasso and group Lasso penalization for addressing the high dimension of variables. Once the model is learned, we use the penalized negative pseudo-log likelihood as a test statistics for detecting anomalous events.
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