Random Objects and Metric Statistics for Connectomics

Description

The focus is on the statistical analysis of non-Euclidean data, where random objects denote random variables and data samples that take values in general metric spaces. Data of such general type are increasingly prevalent in statistics and machine learning. The workshop covers theory,  methodology and applications, with emphasis on applications to brain connectomics.  Methodology for metric statistics is aimed at samples of networks, distributions, compositional data, covariance matrices and surfaces, tree data and data on manifolds,  as well as complex Euclidean data such as high-dimensional and functional data that can be viewed as elements of a metric space.

Topics of interest include quantification of means, barycenters and variance and conditional Fréchet means and their implementation by regression models such as
Fréchet regression and its variants. The workshop will also cover extensions of  metric statistics and the analysis of random objects towards metric versions of principal component analysis,  uncertainty quantification, deep learning, causal inference and longitudinal and time series methodology.