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UID:8219@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20141208T153000
DTEND;TZID=Europe/Paris:20141208T163000
DTSTAMP:20241120T210112Z
URL:https://www.i2m.univ-amu.fr/evenements/a-khaleghi-institut-curie-infer
 ence-in-the-stationary-ergodic-framework/
SUMMARY: (...): A. Khaleghi (Institut Curie): Inference in the Stationary E
 rgodic framework
DESCRIPTION::  Inference in the Stationary Ergodic framework\n\nby Azadeh K
 haleghi (Institut Curie)\n\nAbstract: We consider two fundamental unsuperv
 ised learning problems\\\, namely change point estimation and time-series 
 clustering\\\, in the case where the data are assumed to have been generat
 ed by arbitrary\\\, unknown stationary ergodic process distributions. This
  is one of the weakest assumptions in statistics\\\, because it is more ge
 neral than the parametric and model-based settings\\\, and it subsumes mos
 t of the non-parametric frameworks considered for this class of problems. 
 Statistical analysis in the stationary ergodic framework is extremely chal
 lenging. In general\\\, rates of convergence (even of frequencies to respe
 ctive probabilities) are provably impossible to obtain for this class of p
 rocesses. 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 proce
 ss or by two different ones. This in turn implies that such problems as ti
 me se!\n ries clus\n t\nering with unknown number of clusters\\\, or onlin
 e change point detection\\\, cannot possibly admit consistent solutions. T
 hus\\\, a challenging task is to discover the problem formulations which a
 dmit consistent solutions in this general framework. Our main contribution
  is to constructively demonstrate that despite these theoretical impossibi
 lity results\\\, natural formulations of the considered problems exist whi
 ch do indeed admit consistent solutions in this general framework. Specifi
 cally\\\, 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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