Statistical Foundations for the Analysis of Non-Euclidean Data

Description

The goal of this workshop is to introduce exploratory data analysis and basic descriptive summary statistics for samples of data residing in non-Euclidean metric spaces.  Motivating applications span various scientific disciplines, with an abundance of such examples to be found in brain connectomics.  These include networks and graphs, shapes, and probability distributions quantifying functional connectivity.

Topics of interest include foundational tools for exploratory data analysis and statistical inference for non-Euclidean data.  For instance, the Fréchet mean and variance typically serve as quantifications of the center and spread of data distributions, both at the population and sample level.   Theory and practice will each be emphasized throughout the workshop to justify the methodologies. Theoretical properties of interest include finite-sample concentration bounds and asymptotic properties for the evaluation of estimators.  Computational algorithms that implement the methodologies will also be demonstrated using complex, real-world data sets.

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