3-4pm A1.01, Dec 8, 2017 - Richard Samworth

Title: High-dimensional changepoint estimation via sparse projection

Abstract: Changepoints are a very common feature of big data that arrive in the form of a data stream. We study high dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the co-ordinates. The challenge is to borrow strength across the co-ordinates to detect smaller changes than could be observed in any individual component series. We propose a two-stage procedure called inspect for estimation of the changepoints: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimization problem derived from the cumulative sum transformation of the time series. We then apply an existing univariate changepoint estimation algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated changepoints and the rates of convergence of their locations, and our numerical studies validate its highly competitive empirical performance for a wide range of data-generating mechanisms. Software implementing the methodology is available in the R package InspectChangepoint.

4-5pm A1.01, Dec 8, 2017 - Simon R. White, MRC Biostatistics Unit, University of Cambridge

Title: Spatio-temporal modelling and heterogeneity in neuroimaging

 Abstract: Neuroimaging allows us to gain insight into the structure and activity of the brain. Clearly, there is significant spatial structure that leads to dependencies across measurements that must be accounted for. Further, the brain as an organ is never idle, thus the local temporal behaviour is important when characterising long-term functional connectivity.

 In this talk we will discuss several approaches to modelling neuroimaging that account for these key features, namely spatio-temporal heterogeneity: a novel approach to spatial modelling as an extension to the commonly used dimension reduction technique independent component analysis (ICA) for tasked-based functional magnetic resonance imaging (fMRI); propagating subject-level heterogeneity through multi-stage analyses of dynamic functional connectivity (dFC) using resting-state fMRI (rs-fMRI), and structural development using structural MRI.