Graph Probabilistic Pooling: From Bernoulli to Poisson Distribution.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Graph Neural Networks

Background:

• Graph pooling is essential for enhancing receptive fields and reducing computational costs in deep graph representation learning.
• Existing methods often rely on deterministic selection or random dropping, which can limit flexibility and performance.

Purpose of the Study:

• To propose a simple yet effective graph probabilistic pooling (GP-Pool) framework for improved graph feature learning.
• To develop novel pooling strategies that capture salient substructures and global topology.

Main Methods:

• Developed a probabilistic subgraph sampling approach using a variational bound to achieve expected distributions.
• Introduced Bernoulli graph pooling (BernPool) for sampling nodes and local structures via a learnable reference set.
• Derived Poisson-distributed pooling (PoissonPool) for controllable node quantity and proposed a hybrid graph pooling (HGP) combining sampling and clustering.

Main Results:

• BernPool captures salient graph substructures with diverse node sampling due to its nondeterministic nature.
• PoissonPool offers explicit control over node quantity with fewer variational learning variables.
• The proposed HGP paradigm effectively combines subgraph compactness and graph coarsening, retaining both representative substructures and global topology.

Conclusions:

• The GP-Pool framework demonstrates superior performance compared to various graph pooling methods.
• GP-Pool achieves state-of-the-art results on multiple public graph classification datasets.
• Probabilistic approaches offer a more effective and flexible alternative to deterministic or random pooling in deep graph learning.