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SUMMARY:Linear-Cost Covariance Functions for Gaussian Random Fields - Jie 
 Chen (IBM Research)
DTSTART:20180307T094500Z
DTEND:20180307T103000Z
UID:TALK102220@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-author: Michael L. Stein		(University of Chicago)    
     <br></span><span><br>Gaussian random fields (GRF) are a fundamental st
 ochastic model for spatiotemporal data analysis. An essential ingredient o
 f GRF is the covariance function that characterizes the joint Gaussian dis
 tribution of the field. Commonly used covariance functions give rise to fu
 lly dense and unstructured covariance matrices\, for which required calcul
 ations are notoriously expensive to carry out for large data. In this work
 \, we propose a construction of covariance functions that result in matric
 es with a hierarchical structure. Empowered by matrix algorithms that scal
 e linearly with the matrix dimension\, the hierarchical structure is prove
 d to be efficient for a variety of random field computations\, including s
 ampling\, kriging\, and likelihood evaluation. Specifically\, with n scatt
 ered sites\, sampling and likelihood evaluation has an O(n) cost and krigi
 ng has an O(logn) cost after preprocessing\, particularly favorable for th
 e kriging of an extremely large number of sites (e.g.\, predict ing on mor
 e sites than observed). We demonstrate comprehensive numerical experiments
  to show the use of the constructed covariance functions and their appeali
 ng computation time. Numerical examples on a laptop include simulated data
  of size up to one million\, as well as a climate data product with over t
 wo million observations.</span>
LOCATION:Seminar Room 1\, Newton Institute
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