Graph Embedding in Minkowski Spacetime for Causal Link Prediction
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Solution Overview
Problem
Current methods for large-scale causal inference based on observational data fail to accurately account for causality due to confounders and intermediaries, leading to incorrect causal relationship assignments and missed relationships in machine learning applications, particularly in link prediction tasks.
Innovation Solution
The method involves embedding knowledge graphs into non-Euclidean geometries such as pseudo-Riemannian manifolds using a unique loss function, like the Triple Fermi-Dirac function, to capture directionality and temporal relationships, enabling more accurate directed link prediction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Euclidean geometry is used for graph embedding, then the embedding process is simple and computationally efficient, but the accuracy of causal inference and link prediction deteriorates due to inability to capture directionality and temporal relationships
Solution Approach 1:
The patent transitions from Euclidean geometry to Minkowski spacetime geometry, adding a time dimension to the embedding space. This dimensional change enables the representation of temporal relationships and causal directionality through the time coordinate, while spatial coordinates capture semantic similarities. The loss function incorporates both spatial distance and time difference to predict directed edges accurately.
Solution Approach 2:
The patent changes the metric parameters of the embedding space by using Minkowski metric instead of Euclidean metric. This parameter change allows the geometry to distinguish between temporal and spatial separations, enabling accurate representation of causal relationships where directionality matters. The metric signature change from positive-definite to indefinite is key to capturing causal structure.
2Reliability
If traditional distance-based approaches are used in Euclidean space, then computational simplicity is maintained, but false positives increase due to mistaken ascription of direct causal relationships
Solution Approach 1:
By embedding nodes in Minkowski spacetime rather than Euclidean space, the patent introduces a time dimension that enables distinction between direct and indirect causal relationships. The time coordinate provides an additional degree of freedom to represent temporal precedence, reducing false positives in link prediction while maintaining computational tractability through standard optimization techniques.
Solution Approach 2:
The patent uses the time coordinate as an intermediary variable to mediate causal inference. Instead of directly measuring spatial distance between nodes, the model uses temporal separation combined with spatial distance to infer causal relationships. This intermediary time parameter helps distinguish direct edges from indirect paths through confounders.
3Measurement precision
If Euclidean embedding is used, then computational efficiency is maintained, but causal relationships are missed due to confounders and intermediaries
Solution Approach 1:
The addition of time as a separate dimension in Minkowski spacetime allows the model to represent causal chains with intermediaries as sequences of events separated in time. Direct causal relationships show strong temporal correlation, while spurious correlations through confounders show weaker or different temporal patterns, enabling more accurate detection of true causal relationships.
Solution Approach 2:
The patent segments the causal inference problem into spatial similarity (captured by spatial coordinates) and temporal dependency (captured by time coordinate). This segmentation allows independent optimization of each aspect and enables the model to distinguish between semantic similarity and causal relationship, reducing interference from confounders.
Data Source
AI summary
Methods and apparatus are provided for generating an embedding of a graph. The graph includes a plurality of nodes and each node includes a connection to another one or more of the nodes. The method including and/or apparatus configured to: receiving data representative of at least a portion of the graph; transforming the nodes of the graph into a non-Euclidean geometry; iteratively updating an embedding model based the transformed nodes in the non-Euclidean geometry based on a causal loss function and a link prediction function associated with the non-Euclidean geometry.