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SUMMARY:Estimating sparse additive auto-regressive network models - Garves
 h Raskutti (University of Wisconsin-Madison)
DTSTART:20180627T100000Z
DTEND:20180627T104500Z
UID:TALK107431@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Consider a multi-variate time series\, which may correspond to
  spike train responses for multiple neurons in a brain\, crime event data 
 across multiple regions\, and many others. An important challenge associat
 ed with these time series models is to estimate an influence network betwe
 en the d variables\, especially when the number of variables d is large me
 aning we are in the high-dimensional setting. Prior work has focused on pa
 rametric vector auto-regressive models. However\, parametric approaches ar
 e somewhat restrictive in practice. In this paper\, we use the non-paramet
 ric sparse additive model (SpAM) framework to address this challenge. Usin
 g a combination of beta and phi-mixing properties of Markov chains and emp
 irical process techniques for reproducing kernel Hilbert spaces (RKHSs)\, 
 we provide upper bounds on mean-squared error in terms of the sparsity s\,
  logarithm of the dimension logd\, number of time points T\, and the smoot
 hness of the RKHSs. Our rates are sharp up to logarithm factors in many ca
 ses. We also provide numerical experiments that support our theoretical re
 sults and display potential advantages of using our non-parametric SpAM fr
 amework for a Chicago crime dataset.
LOCATION:Seminar Room 1\, Newton Institute
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