Papers by Austin Vandegriffe
The presentation covers prerequisite results from Topology and Measure Theory. This is then follo... more The presentation covers prerequisite results from Topology and Measure Theory. This is then followed by an introduction into couplings and basic definitions for optimal transport. The Kantrorovich problem is then introduced and an existence theorem is presented. Following the setup of optimal transport is a brief overview of the Wasserstein distance and a short proof of how it metrizes the space of probability measures on a COMPACT domain. This presentation is a detailed examination of Villani's "Optimal Transport: Old and New" chapters 1-4 and part of 6.
279 WACSAW: A Statistical and Individually Adaptive Method to Determine Sleep and Wakefulness from Activity
Technological innovations have broadened the type and amount of activity data that can be capture... more Technological innovations have broadened the type and amount of activity data that can be captured in the home and under normal living conditions. Yet, converting naturalistic activity patterns into sleep and wakefulness states has remained a challenge. Despite the successes of current algorithms, they do not fill all actigraphy needs. We have developed a novel statistical approach to determine sleep and wakefulness times, called the Wasserstein Algorithm for Classifying Sleep and Wakefulness (WACSAW), and validated the algorithm in a small cohort of healthy participants. WACSAW functional routines: 1) Conversion of the triaxial movement data into a univariate time series; 2) Construction of a Wasserstein weighted sum (WSS) time series by measuring the Wasserstein distance between equidistant distributions of movement data before and after the time-point of interest; 3) Segmenting the time series by identifying changepoints based on the behavior of the WSS series; 4) Merging segment...
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Papers by Austin Vandegriffe