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This paper addresses how to calculate and interpret the time-delayed mutual information for a complex, diversely and sparsely measured, possibly non-stationary population of time-series of unknown composition and origin. The primary vehicle used for this analysis is a comparison between the time-delayed mutual information averaged over the population and the time-delayed mutual information of an aggregated population (here aggregation implies the population is conjoined before any statistical estimates are implemented). Through the use of information theoretic tools, a sequence of practically implementable calculations are detailed that allow for the average and aggregate time-delayed mutual information to be interpreted. Moreover, these calculations can be also be used to understand the degree of homo- or heterogeneity present in the population. To demonstrate that the proposed methods can be used in nearly any situation, the methods are applied and demonstrated on the time series of glucose measurements from two different subpopulations of individuals from the Columbia University Medical Center electronic health record repository, revealing a picture of the composition of the population as well as physiological features.
Nonparametric estimation of mutual information is used in a wide range of scientific problems to quantify dependence between variables. The k-nearest neighbor (knn) methods are consistent, and therefore expected to work well for large sample size. Th
We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of new infor
Let $T_{epsilon}$ be the noise operator acting on Boolean functions $f:{0, 1}^nto {0, 1}$, where $epsilonin[0, 1/2]$ is the noise parameter. Given $alpha>1$ and fixed mean $mathbb{E} f$, which Boolean function $f$ has the largest $alpha$-th moment $m
Correlation function and mutual information are two powerful tools to characterize the correlations in a quantum state of a composite system, widely used in many-body physics and in quantum information science, respectively. We find that these two to
External and internal factors may cause a systems parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a time-delayed