Additive Noise Model Structure Learning Based on Spatial Coordinates

Discovering causal relationships from a large amount of observational data is an important research direction in data mining. To address the challenges of discovering and constructing causal networks on nonlinear and high-dimensional data, this article proposes a new structural learning algorithm called spatial coordinates based (SCB). The SCB algorithm effectively discovers causal networks from large scale nonlinear data. In this article, we make three main contributions. Firstly, based on the Hilbert–Schmidt independence criterion (HSIC), we propose new independence test coefficients: spatial coordinate (SC) coefficient and conditional spatial coordinate (CSC) coefficient. We also prove that the statistical distribution of the CSC coefficient follows a standard normal distribution. Secondly, using the statistical distribution of the CSC coefficient, we redefine the correlation of variables and combine it with local learning to propose the SCB algorithm. Finally, we demonstrate the effectiveness of the algorithm through experiments on data generated from various nonlinear function dependencies. Compared to existing algorithms, the causal network models constructed using the SCB algorithm exhibit significant improvements in accuracy and time performance. The effectiveness of the proposed method is further validated on real power plant data.