A high dimensional Directed information estimation using data-dependent partitioning

Directed Information (DI) is used to quantify the causal and dynamic relations between two signals. The main advantage of using DI compared to other measures of causality is that it does not assume an underlying signal model and thus can capture both linear and nonlinear interactions between signals. However, one major problem in computing the DI from data is the high computational cost and the unreliability of the probability density function (pdf) estimation methods. In this paper, we propose a high dimensional DI estimation method based on computing multi-information by an adaptive data-dependent partitioning technique. The proposed estimation method does not assume any distribution for the data under consideration and requires no pdf estimation. The proposed method is applied on simulated data and is compared with other DI estimation methods to verify its effectiveness.