A. Khaleghi (Institut Curie): Inference in the Stationary Ergodic framework

Date(s) : 08/12/2014   iCal
15 h 30 min - 16 h 30 min

Inference in the Stationary Ergodic framework\n\nby Azadeh Khaleghi (Institut Curie)\n\nAbstract: We consider two fundamental unsupervised learning problems\, namely change point estimation and time-series clustering\, in the case where the data are assumed to have been generated by arbitrary\, unknown stationary ergodic process distributions. This is one of the weakest assumptions in statistics\, because it is more general than the parametric and model-based settings\, and it subsumes most of the non-parametric frameworks considered for this class of problems. Statistical analysis in the stationary ergodic framework is extremely challenging. In general\, rates of convergence (even of frequencies to respective probabilities) are provably impossible to obtain for this class of processes. As a result\, given a pair of samples generated independently by stationary ergodic process distributions\, it is provably impossible to distinguish between the case where they are generated by the same process or by two different ones. This in turn implies that such problems as time se!\n ries clus\n t\nering with unknown number of clusters\, or online change point detection\, cannot possibly admit consistent solutions. Thus\, a challenging task is to discover the problem formulations which admit consistent solutions in this general framework. Our main contribution is to constructively demonstrate that despite these theoretical impossibility results\, natural formulations of the considered problems exist which do indeed admit consistent solutions in this general framework. Specifically\, we propose natural formulations as well as efficient algorithms which we further show to be asymptotically consistent under the assumption that the process distributions are stationary ergodic. \n\n

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