Complex-time Representation of Repeated Measurement Longitudinal Data and Space-kime Analytics

This presentation will describe the novel complex-time (kime) representation of repeated measurement longitudinal data and introduce space-kime artificial intelligence (AI) techniques. By translating fundamental quantum mechanics principles into statistical inference models of time-varying processes, we generalize the classical 4D spatiotemporal sampling to a 5D space-kime manifold, where the phase of complex-time encodes repeated random drawings at fixed spatiotemporal locations. Many AI applications and statistical inference techniques involving temporal data can be formulated in a Bayesian space-kime analytics framework. We explore alternative strategies for translating time-series observations into kime-surfaces, which are richer, computationally tractable, objects amenable to tensor-based linear modeling and model-free inference. Simulated and observed neuroimaging and macroeconomics data will be used to demonstrate space-kime analytics. We will discuss space-kime analytic duality between theoretical model inference, based on generalized functions (distributions), and experimental data inference, based on replicated finite samples as proxy measures of the underlying probability distributions. Several theoretical, experimental, computational, and data-analytic open problems will be presented.