Causal Discovery via Diffusion Model Leaf Node Removal
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Solution Overview
Problem
Current methods for causal discovery in high-dimensional datasets are computationally intensive and do not scale well, making them impractical for large datasets, as they require costly acyclicity checks and greedy combinatorial optimization.
Innovation Solution
A data processing apparatus and method using a trained diffusion model to determine the order of variables by iteratively removing leaf nodes, leveraging the score and Hessian variance to efficiently find and remove leaf nodes, thereby reducing the search space and enabling scalable causal discovery without re-training the model at each iteration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If greedy combinatorial optimization is used for causal discovery, then causal relationships can be discovered, but computational cost increases and scalability to high-dimensional problems is lost
Solution Approach 1:
The patent segments the causal discovery problem into two distinct phases: (1) topological ordering phase that determines the sequence of variables, and (2) structure selection phase that identifies specific causal relationships. This segmentation allows the computationally intensive acyclicity checks to be performed only once during ordering, rather than at each step of structure search, thereby resolving the contradiction between reliability and productivity.
Solution Approach 2:
The patent performs preliminary topological ordering before conducting the actual causal structure search. By pre-establishing the correct ordering of variables, the method eliminates the need for repeated acyclicity verification during subsequent structure identification steps, significantly reducing computational cost while maintaining causal discovery accuracy.
2Productivity
If topological ordering is performed first followed by structure selection, then search space is reduced and computational cost decreases, but the method still does not scale to large datasets
Solution Approach 1:
The patent replaces the traditional mechanical combinatorial search approach with a diffusion probabilistic model that learns causal structures through probabilistic inference. This substitution enables the method to scale to large datasets by leveraging the efficiency of diffusion models in high-dimensional spaces, while maintaining the benefits of reduced search space through preliminary topological ordering.
Data Source
AI summary
A data processing apparatus comprises: a memory configured to store a trained model; and processing circuitry configured to: receive at least one dataset that comprises d variables and n samples; determine variances associated with the variables by processing the dataset using the model; determine an order of the variables based on the determined variances, including iteratively removing at least one node or variable represented by said at least one node thereby to determine the order.