RBF MMD Metrics

MMD metrics using RBF kernels with dynamic bandwidths, as proposed by Thompson et al. [1].

The following graph descriptors are available:

Graph Descriptors

OrbitCounts: Counts of different graphlet orbits
ClusteringHistogram: Distribution of clustering coefficients
SparseDegreeHistogram: Distribution of node degrees
EigenvalueHistogram: Distribution of graph Laplacian eigenvalues
RandomGIN: Graph Neural Network embedding of the graph, combined with a normalization layer (NormalizedDescriptor). Proposed by Thompson et al. [1].

Below, we demonstrate how to evaluate all metrics in the benchmark with point estimates and with uncertainty quantification.

from polygraph.datasets import PlanarGraphDataset, SBMGraphDataset
from polygraph.metrics import RBFMMD2Benchmark, RBFMMD2BenchmarkInterval

reference = list(PlanarGraphDataset("val").to_nx())
generated = list(SBMGraphDataset("val").to_nx())

# Evaluate the benchmark with point estimates
benchmark = RBFMMD2Benchmark(reference[:20])
print(benchmark.compute(generated[:20]))

# Evaluate the benchmark with uncertainty quantification
benchmark_with_uncertainty = RBFMMD2BenchmarkInterval(
    reference,
    subsample_size=20,
    num_samples=100,
    coverage=0.95,
)
print(benchmark_with_uncertainty.compute(generated))

References

[1] Thompson, R., Knyazev, B., Ghalebi, E., Kim, J., & Taylor, G. W. (2022). On Evaluation Metrics for Graph Generative Models. In International Conference on Learning Representations (ICLR).

Summary Benchmark

`polygraph.metrics.RBFMMD2Benchmark`

Bases: MetricCollection[Graph]

Collection of MMD2 metrics using RBF kernels with dynamic bandwidths.

Parameters:	`reference_graphs` (`Collection[Graph]`) – Collection of reference networkx graphs.

`polygraph.metrics.RBFMMD2BenchmarkInterval`

Bases: MetricCollection[Graph]

Collection of MMD2 metrics using RBF kernels with dynamic bandwidths and uncertainty quantification.

Parameters:

reference_graphs (Collection[Graph]) –

Collection of reference networkx graphs.
subsample_size (int) –

Number of graphs used in each individual MMD2 sample. Should be consistent with the sample size in point estimates.
num_samples (int, default: 500 ) –

Number of MMD2 samples used to compute the uncertainty interval.
coverage (Optional[float], default: 0.95 ) –

Coverage of the uncertainty interval.