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Bayesian Inference with Complex Knowledge Graph Evidence
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Casts incremental belief tracking over unknown KG entities with complex logical evidence as Bayesian filtering, using a SimplE-based Gaussian MRF with MPE and a marginal quantifier (BIKG).
Problem
Reasoning over unobserved knowledge graph entities when complex logical KG evidence (negation, conjunction, disjunction, quantifiers) arrives sequentially, as in incremental KG query answering and critiquing-based recommendation.
Approach
Construct an MRF from complex FOL KG evidence via knowledge-based model construction, with SimplE embeddings as Gaussian factors, and perform closed-form Gaussian Bayesian updating; intermediate variables are handled by MPE beam search, and a Marginal quantifier integrates over multiple paths analytically via Schur complement.
Key results
- On sequential KGQA, BIKG outperforms CQD variants on most query types and sessions, e.g. FB15k 2i session 3 at 0.649 vs 0.593 for CQD-Ł.
- On FB15k-237 2u session 3, BIKG reaches 0.775 hit@10 vs. 0.719 for CQD-M.
- In critiquing experiments, BIKG with the Marginal quantifier yields a larger hit-rate improvement over sessions than CQD and MPE-only BIKG.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BIKG for incremental complex KGQA instead of CQD variants | SimplE-based KG inference · FB15k, FB15k-237, and NELL995 sequential query answering | hit rate@10 | Helped |
| Use BIKG with the Marginal quantifier rather than MPE alone (ablation) | BIKG recommendation inference · Movielens 20M and LFM-1b critique-based recommendation | hit rate@10 | Helped |
| Use BIKG with MPE rather than CQD variants | SimplE-based recommendation inference · Movielens 20M and LFM-1b critique-based recommendation | hit rate@10 | Helped |
| Replace the MPE-only treatment of intermediate variables with MPE plus marginalization (ablation) | BIKG multi-path reasoning · Complex KG evidence with multiple valid intermediate entities | hit rate@10 | Helped |
Surprising findings
- Existential (MPE) instantiation is inadequate for recommendation KGs, where the number of legitimate 2p intermediate entities is much larger (e.g., ~1769 on ML20M+FB vs ~8 on NELL995).
Limitations
- Relies on Gaussian assumptions for all variables and factors.
- MPE beam search restricts intermediate instantiations to top-k candidates, which is inadequate for many-valued relations.
Experimental setup
Datasets: FB15k FB15k-237 NELL995 MovieLens 20M LFM-1b Freebase
Benchmarks: FB15k FB15k-237 NELL995 MovieLens 20M + FB LFM-1b + FB
Metrics: hit rate@10
Baselines: CQD-M CQD-Ł CQD-P
Builds on: SimplE CQD knowledge-based model construction Gaussian belief propagation
Closest papers by meaning
- Context-aware Inductive Knowledge Graph Completion with Latent Type Constraints and Subgraph Reasoning (AAAI 2025 · similarity 0.87)
- Diagnosing and Addressing Pitfalls in KG-RAG Datasets: Toward More Reliable Benchmarking (NeurIPS 2025 · similarity 0.87)
- Is Complex Query Answering Really Complex? (ICML 2025 · similarity 0.86)
- EPERM: An Evidence Path Enhanced Reasoning Model for Knowledge Graph Question and Answering (AAAI 2025 · similarity 0.86)
- A Foundation Model for Zero-shot Logical Query Reasoning (NeurIPS 2024 · similarity 0.86)
- Deliberation on Priors: Trustworthy Reasoning of Large Language Models on Knowledge Graphs (NeurIPS 2025 · similarity 0.86)
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