G-Meta Plus

Overview

In this paper, I, alongside my collaborators Gian Marco Visani and Mert Erden, present our enhanced framework, G-Meta+, which builds upon the original G-Meta framework. My specific contributions to this work include overseeing the overall infrastructure and tooling required for our experiments. Thank you to all our collaborators for their invaluable contributions to this project.

Enhancing Graph Neural Networks with G-Meta+

Recent advancements in Graph Neural Networks (GNNs) and Meta Learning have led to the exciting new field of meta learning on graphs. This convergence has been propelled by the increasing collection of high throughput data using Biological Interaction Networks. One standout framework in this domain is G-Meta, a state-of-the-art method for Model-Agnostic Meta-Learning that facilitates the rapid adaptation of deep networks.

Introduction to G-Meta

G-Meta operates by creating subgraphs from a collection of graphs and leverages the local neighborhood information of these subgraphs to generate a prototypical support embedding. This embedding is formed by averaging the individual subgraph embeddings, and predictions are made using Probabilistic Nearest Neighbor (PrNN) classification between the prototypical support embedding and the subgraph embedding being used for prediction.

However, we identified areas for improvement in the G-Meta framework. Specifically, we believe that incorporating connectivity information between subgraphs can prevent the loss of crucial information and enhance prediction accuracy. Additionally, replacing the PrNN classification with a more effective technique from the metric learning literature can further boost performance.

Our Contributions: G-Meta+

Our approach, termed G-Meta+, aims to intelligently integrate the global graph structure into the existing G-Meta framework. This integration is achieved through two primary enhancements:

1. Expanding Subgraphs with Shortest Paths: We enhance the support data subgraphs by incorporating the shortest path between the support subgraphs we generate. This step ensures that connectivity within the network is captured, theoretically preserving the global structure.

   \[\text{Shortest Path}(s_i, s_j) \in n_k \Rightarrow \text{Expanded Subgraph}(s_i) \cup \text{Expanded Subgraph}(s_j)\]

2. Substituting Prototypical Networks with Relation Networks: We replace the prototypical network component used in G-Meta with a relation network component for label prediction. Relation networks create support embeddings by combining all support embeddings, and instead of using PrNN, they train a relation function to compare support data with query data.

   For each label \(( l )\), given \(( K )\) support embeddings \(( s_l^1, \ldots, s_l^K )\), we compute a prototypical support embedding:

   \[ps_l = \frac{1}{K} \sum_{i=1}^{K} s_l^i\]

   The support embedding \(( ps_l )\) and query embedding \(( q )\) are concatenated and fed into a relation module \(( g_{\phi} )\), parameterized by \(( \phi )\), which outputs a relation score \(( r_{ql} )\):

   \[r_{ql} = g_{\phi}(\text{concat}(ps_l, q))\]

   A prediction across labels is made via:

   \[\text{argmax}(r_{ql} \text{ for } l \text{ in labels})\]

   Mean Squared Error (MSE) is used as the loss function, viewing the prediction of relation scores as a regression problem.

Methodology

G-Meta+ applies the meta-learning framework to node classification and link prediction problems by meta-learning GNNs on subgraphs. Our enhancements are summarized as follows:

• Data Partitioning: The dataset \((\mathcal{D})\) is partitioned into \((\mathcal{D}_{train})\), \((\mathcal{D}_{validate})\), and \((\mathcal{D}_{test})\), with tasks \((\tau_i)\) divided into \((\tau_i^{\text{support}})\) and \((\tau_i^{\text{query}})\).

• Embedding Computation: For each support subgraph pair \(((s_i, s_j))\), the shortest path in the network \(( n_k )\) joining these subgraphs is included. The relation module \(( g_{\phi} )\) optimizes within the MAML framework to enhance prediction accuracy.

Experiments

We evaluated G-Meta+ on two datasets that G-Meta was previously evaluated on: Tissue-PPI and Tree-of-Life. Tissue-PPI consists of 24 protein-protein interaction networks from different tissues, while Tree-of-Life consists of 1,840 protein-protein interaction networks from different species. We defined two meta-learning tasks: link prediction and node classification, and compared the performance of G-Meta+ with the original G-Meta.

Results

Discussion

Our results show that on the Tissue-PPI dataset, both our modifications to the G-Meta framework individually improve performance to an accuracy higher than G-Meta’s average accuracy by one standard deviation. Specifically, incorporating the shortest paths between subgraphs (G-Meta + paths) and using relation networks for label prediction (G-Meta + relation) both lead to significant performance gains.

Furthermore, when combining both modifications in G-Meta-Plus, we observed an additional boost in performance, reaching a test accuracy of 0.828. This performance is more than two standard deviations above G-Meta’s average performance, indicating a substantial improvement.

However, on the Tree-of-Life dataset, our modifications did not lead to a significant performance improvement. While the accuracy slightly increased with the inclusion of paths, the combined G-Meta-Plus approach did not outperform the original G-Meta framework. Importantly, our modifications never degraded the performance of G-Meta on this dataset.

These results suggest that our enhancements are particularly effective for node classification tasks, as demonstrated by the Tissue-PPI results. The lack of significant improvement on the Tree-of-Life dataset may be due to the nature of the link prediction task and the features used (node degrees). Further investigation is needed to understand how to better utilize global graph structure for different types of graph-based tasks.

Conclusion

G-Meta-Plus extends the G-Meta framework by increasing its complexity through modifications to its subgraph and meta-learning computations. Despite these modifications, G-Meta-Plus maintains the same computational complexity as the original G-Meta. Our experimental results indicate that G-Meta-Plus outperforms the original G-Meta on node classification problems, particularly on the Tissue-PPI dataset.

Our findings highlight the importance of leveraging global graph structures and advanced metric learning techniques to improve the performance of graph neural networks. While our current approach shows promising results, future work should focus on optimizing hyperparameters and exploring additional methods for incorporating global graph information. This could lead to further improvements in both node classification and link prediction tasks.

Overall, our work demonstrates the potential of G-Meta-Plus to advance the field of meta-learning on graphs, providing a robust framework for rapid adaptation and accurate predictions in graph-based applications.