Likelihood-Based Dynamic Graph Prediction Using GNNs And MLE
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Solution Overview
Problem
Existing graph prediction methods fail to capture the correlation among changes to nodes, edges, and attributes in dynamic graphs, leading to inaccurate predictions and inability to report the relative likelihood of various possible sets of changes.
Innovation Solution
A statistical model combining graph neural networks (GNNs) and maximum likelihood estimation (MLE) is used to map input graphs onto embeddings, with a feedforward neural network (FNN) predicting future graph embeddings and a statistical distribution modeling the differences between these embeddings, allowing for relative probability calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing graph prediction methods are used, then the prediction process is simple, but the prediction accuracy is low and correlation among changes to nodes, edges, and attributes is not captured
Solution Approach 1:
The patent combines graph neural networks (GNNs) with maximum likelihood estimation (MLE) to create a unified statistical model. The GNN processes graph structure and node features, while MLE provides the probabilistic framework for predicting future graph states. This merging allows the model to capture correlations among changes to nodes, edges, and attributes simultaneously, resolving the contradiction between prediction accuracy and model complexity by integrating multiple approaches into a cohesive system.
Solution Approach 2:
The patent employs a composite modeling approach by combining different computational components: GNNs for graph representation learning, FNNs for temporal prediction, and statistical distributions for uncertainty modeling. This composite structure enables the system to achieve high prediction accuracy by leveraging the strengths of each component while maintaining a manageable complexity through modular architecture.
2Reliability
If a statistical model combining GNNs and MLE is used, then correlation structures in graph changes are captured, but the computational complexity increases
Solution Approach 1:
The patent segments the prediction task into distinct computational stages: (1) GNN processes current graph state to extract features, (2) FNN predicts future graph embedding, (3) Statistical distribution models the prediction uncertainty. This segmentation allows each component to be optimized independently and enables parallel computation where possible, reducing overall computational complexity while maintaining prediction reliability through the coordinated operation of specialized sub-components.
Solution Approach 2:
The patent introduces graph embeddings as an intermediary representation that bridges the input graph data and the prediction output. By transforming the graph into a compact embedding space, the model reduces the dimensionality of subsequent computations while preserving essential structural information. This intermediary representation significantly decreases computational complexity in the prediction step while maintaining the reliability needed to capture correlation structures.
3Loss of information
If graph embeddings and forward images are computed, then relative probabilities of future graphs can be determined, but the processing time increases
Solution Approach 1:
The patent transforms the graph data into an embedding space, effectively changing from the original high-dimensional graph structure to a lower-dimensional continuous vector representation. This dimensional transformation compresses the graph information while preserving essential patterns and relationships. By operating in this compressed embedding space, the model can compute forward images and determine relative probabilities of future graphs with reduced computational overhead, thus decreasing processing time while retaining critical information.
Data Source
AI summary
Dynamic graph prediction can be achieved using a statistical model of graph dynamics that combines neural networks, including graph neural networks (GNNs), with maximum likelihood estimation. More specifically, in some embodiments, a GNN is used to compute graph embeddings representing an evolving graph at two different points in time, an additional neural network is used to create a forward image of the graph embedding associated with the first point in time, and a statistical distribution of the difference between the forward image and the graph embedding associated with the second point in time is evaluated. The GNN, additional neural network, and statistical distribution collectively constitute the statistical model, which can be trained on training data comprising pairs of graphs from one or more time series of evolving graphs. Such a statistical model may be employed, for example, to predict graph changes in a cybersecurity incident graph.