On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features (2111.12128v3)

Abstract: While Graph Neural Networks (GNNs) have recently become the de facto standard for modeling relational data, they impose a strong assumption on the availability of the node or edge features of the graph. In many real-world applications, however, features are only partially available; for example, in social networks, age and gender are available only for a small subset of users. We present a general approach for handling missing features in graph machine learning applications that is based on minimization of the Dirichlet energy and leads to a diffusion-type differential equation on the graph. The discretization of this equation produces a simple, fast and scalable algorithm which we call Feature Propagation. We experimentally show that the proposed approach outperforms previous methods on seven common node-classification benchmarks and can withstand surprisingly high rates of missing features: on average we observe only around 4% relative accuracy drop when 99% of the features are missing. Moreover, it takes only 10 seconds to run on a graph with $\sim$2.5M nodes and $\sim$123M edges on a single GPU.

• The paper proposes a novel feature propagation method based on Dirichlet energy minimization to effectively reconstruct missing node features.
• Experiments across seven benchmarks show only a 4% accuracy drop even when 99% of node features are missing, outperforming classic imputation methods.
• The approach is scalable and versatile, integrating seamlessly with any GNN architecture to enhance performance in real-world incomplete data scenarios.

Feature Propagation in Graphs with Missing Node Features

The paper "On the Unreasonable Effectiveness of Feature Propagation in Learning on Graphs with Missing Node Features" explores an innovative method to address one of the predominant challenges in graph neural networks (GNNs): the handling of missing node features. Given the widespread use of GNNs in processing relational data across various applications, tackling the problem of incomplete node features is crucial for broadening their applicability to real-world scenarios where data is often incomplete.

Problem Context

GNNs have become the standard for modeling relational data, leveraging both node and edge features to learn representations. However, they typically assume that the feature matrix is fully observed, an assumption that seldom holds in practical applications, such as social networks where demographic information might be sparsely available. Classic feature imputation methods do not utilize graph structure, limiting their effectiveness in graph-based machine learning tasks.

Proposed Solution: Feature Propagation

The paper introduces a novel approach termed Feature Propagation (FP), based on the minimization of the Dirichlet energy, a criterion that promotes feature smoothness across the graph. Feature Propagation operates through a diffusion-type differential equation, which, when discretized, yields an iterative algorithm for feature reconstruction. Crucially, FP distinguishes itself by efficiently propagating known features across the graph while ensuring scalability.

Numerical Results and Analysis

The empirical evaluation of Feature Propagation spans seven node-classification benchmarks, demonstrating its robustness against remarkably high rates of missing features. For instance, experiments reveal only a 4% relative accuracy drop when 99% of features are missing. This marks a significant improvement over competing methods, which suffer from much more substantial degradation in performance. Moreover, FP is computationally efficient, able to run on large graphs with millions of nodes and edges in a matter of seconds on a single GPU.

Advantages and Implications

FP is theoretically motivated, deriving naturally from Dirichlet energy minimization as a continuous-time diffusion model on graphs. This not only fortifies its theoretical foundation but also aligns with contemporary pursuits in continuous-time models for machine learning on graphs. Furthermore, its versatility allows it to be paired with any GNN architecture, broadening the scope of tasks it can handle beyond node classification.

The key implications of the paper are twofold. Practically, FP enables GNNs to operate effectively in high missing feature scenarios, empowering applications across domains with stringent privacy constraints or sparse data availability. Theoretically, the paper paves the way for future exploration into energy-based methods and diffusion models within graph-based learning systems.

Speculations on Future Developments

Looking ahead, the paper's methodology encourages further exploration into adaptive diffusion processes capable of learning and integrating node features with variable levels of homophily and heterophily. Additionally, melding the diffusion-based feature reconstruction with advanced GNN architectures could unlock new potential for real-time graph analytics amidst incomplete data landscapes.

In summary, the paper provides a profound contribution to graph machine learning, offering insights and techniques that enhance the robustness and scalability of GNNs in scenarios with incomplete node features. The approach promises significant value for both researchers and practitioners looking to advance the effectiveness of graph-based systems in complex, real-world environments.