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From Geometry to Causality- Ricci Curvature and the Reliability of Causal Inference on Networks

ICML 2024 · Probabilistic and scientific modeling › Treatment effects · approach: Proximal and deep causal effect estimation

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Links graph Ricci curvature to causal identification theoretically (negative curvature hampers identifiability) and proposes Ricci-flow edge reweighting to improve GNN-based network causal effect estimation (f-NetEst).

Problem

Causal effect estimation on networked treatment units is hard because network dependencies violate ignorability and SUTVA, and there is no ground-truth-free way to assess reliability of GNN-based causal estimates.

Approach

Theoretically connects Ollivier-Ricci curvature (via entropy bounds from optimal transport and entropic causal inference) to identifiability of causal parameters, showing negative curvature regions yield less reliable ITE estimates; then applies discrete Ricci flow to reweight edges of the input graph so curvature is flattened, improving NetEst.

Key results

• f-NetEst (Ricci flow adjusted NetEst) achieves the lowest PEHE on all nine datasets, e.g. BC 0.033 vs 0.069 for NetEst (relative gain up to 52%).
• Empirically, summed Ollivier-Ricci curvature around a node is negatively correlated with ITE estimation error across nine networks.
• Ricci flow adjustment also reduces error for T-Learner+GNN, X-Learner+GNN and NetDeconf in most cases.

Measured effects reported in the paper

Surprising findings

• Ricci flow adjustment makes X-Learner+GNN and T-Learner+GNN errors worse on some datasets (e.g., Wisconsin and Cora), so gains are not uniform across models.

Limitations

• Ricci flow is a static graph reweighting and is not updated during training.
• Cannot target specific network neighborhoods for improvement.
• Edge reweighting requires care for conceptual consistency of edge weights with the problem context.

Experimental setup

Datasets: BlogCatalog Flickr Cornell Texas Wisconsin chameleon Cora CiteSeer Actor

Benchmarks: BlogCatalog Flickr Cornell Texas Wisconsin chameleon Cora CiteSeer Actor

Metrics: PEHE ITE error

Baselines: T-Learner+RF X-Learner+RF TARNet CFR T-Learner+GNN X-Learner+GNN NetDeconf NetEst

Builds on: NetEst Ollivier-Ricci curvature discrete Ricci flow entropic causal inference anchor regression

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