Multiresolution Gaussian Processes

W e propose a multiresolution Gaussian process to capture lo ng-range, non-Markovian dependencies while allowing for abrupt changes a nd non-stationarity. The multiresolution GP hierarchically couples a collectio n of smooth GPs, each defined over an element of a random nested partition. Long-ra nge dependencies are captured by the top-level GP while the partition poi nts define the abrupt changes. Due to the inherent conjugacy of the GPs, one can analytically marginalize the GPs and compute the marginal likelihood of the observations given the partition tree. This property allows for efficient inference of the partition itself, for which we employ graph-theoretic techniques. W e apply the multiresolution GP to the analysis of magnetoencephalography (MEG) recordings of brain activity.