Emily Fox (University of Washington): Gaussian Processes on the Brain: Heteroscedasticity, Nonstationarity, and Long-range Dependencies

In this talk, we focus on a set of modeling challenges associated with Magnetoencephalography (MEG) recordings of brain activity: (i) the time series are high dimensional with long-range dependencies, (ii) the recordings are extremely noisy, and (iii) gathering multiple trials for a given stimulus is costly. Our goal then is to harness shared structure both within and between trials. Correlations between sensors arise based on spatial proximity, but also from coactivation patterns of brain activity that change with time. Capturing this unknown and changing correlation structure is crucial in effectively sharing information. Motivated by the structure of our high-dimensional time series, we propose a Bayesian nonparametric dynamic latent factor model based on a sparse combination of Gaussian processes (GPs). Key to the formulation is a time-varying mapping from the lower dimensional embedding of the dynamics to the full observation space, thus capturing time-varying correlations between sensors.Finally, we turn to another challenge: in addition to long-range dependencies, there are abrupt changes in the MEG signal. We propose a multiresolution GP that hierarchically couples GPs over a random nested partition. Long-range dependencies are captured by the top-level GP while the partition points define the abrupt changes in the time series. The inherent conjugacy of the GPs allows for efficient inference of the hierarchical partition, for which we employ graph-theoretic techniques.

Joint work with David Dunson, Alona Fyshe, and Tom Mitchell