Causal Dependency Graphs for High-Dimensional Data Processing

The patent segments the causal structure discovery process into two distinct phases: (1) learning the skeleton graph structure using graphical Lasso algorithm to identify conditional independence relationships, and (2) determining edge directions using intervention data and dependency relationships. This segmentation divides the originally intractable super-exponential search space into manageable sub-problems with polynomial complexity, resolving the contradiction between accuracy and computational complexity.

The patent performs preliminary action by first learning the skeleton graph structure and conditional independence relationships before determining the final causal directions. By pre-establishing the undirected skeleton structure using intervention data and graphical Lasso, the method narrows down the search space significantly before performing the direction assignment, thereby reducing overall computational complexity while maintaining accuracy.

The patent segments the causal discovery process into skeleton learning and direction determination phases, allowing the method to scale to hundreds or thousands of factors. The skeleton learning phase using graphical Lasso has computational complexity that scales polynomially with the number of factors, enabling high adaptability while maintaining productivity even as the number of factors increases to large scales.

The patent changes the parameter representation by using conditional independence relationships and intervention data to constrain the search space. By parameterizing the problem in terms of conditional independencies rather than exhaustive causal structure enumeration, the method achieves both high adaptability to large numbers of factors and maintained productivity through efficient algorithmic complexity.