Multiresolution Gaussian Processes
This method addresses the challenge of modeling non-Markovian dependencies with abrupt changes in time-series data, such as brain activity recordings, offering a novel inference approach for researchers in neuroscience and signal processing.
The authors tackled the problem of modeling data with long-range dependencies and abrupt changes by proposing a multiresolution Gaussian process, which hierarchically couples smooth GPs over a random nested partition to capture these features efficiently. They applied it to Magnetoencephalography (MEG) recordings of brain activity, demonstrating its utility in analyzing complex temporal patterns.
We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP while the partition points define the abrupt changes. Due to the inherent conjugacy of the GPs, one can analytically marginalize the GPs and compute the conditional 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. We apply the multiresolution GP to the analysis of Magnetoencephalography (MEG) recordings of brain activity.