mlsanityData to 14 Oct 2026

Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Models

arXiv 2102.10440 ↗First posted 20 Feb 2021cs.LGcited by 22

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Abstract (arXiv)

While probabilistic models are an important tool for studying causality, doing so suffers from the intractability of inference. As a step towards tractable causal models, we consider the problem of learning interventional distributions using sum-product networks (SPNs) that are over-parameterized by gate functions, e.g., neural networks. Providing an arbitrarily intervened causal graph as input, effectively subsuming Pearl's do-operator, the gate function predicts the parameters of the SPN. The resulting interventional SPNs are motivated and illustrated by a structural causal model themed around personal health. Our empirical evaluation on three benchmark data sets as well as a synthetic health data set clearly demonstrates that interventional SPNs indeed are both expressive in modelling and flexible in adapting to the interventions.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). Builds on 24 of its 59 references that are in the map. First posted on arXiv 20 Feb 2021.

Builds on

24 of 59 references.

References · 24

  1. 2017Counterfactual Fairnesscited by 804
  2. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 307
  3. 2019Causality for Machine Learningcited by 243
  4. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  5. 2013Learning Bayesian Networks: The Combination of Knowledge and Statistical Datacited by 187
  6. 2019Counterfactual Off-Policy Evaluation with Gumbel-Max Structural Causal Modelscited by 117
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  9. 2020Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuitscited by 103
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12 more
  1. 2020CausalML: Python Package for Causal Machine Learningcited by 74
  2. 2015Learning Causal Graphs with Small Interventionscited by 63
  3. 2018Morpho-MNIST: Quantitative Assessment and Diagnostics for Representation Learningcited by 56
  4. 2019Causal Reasoning from Meta-reinforcement Learningcited by 53
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  6. 2019Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architecturescited by 24
  7. 2019Bayesian Learning of Sum-Product Networkscited by 24
  8. 2020Sum-product networks: A surveycited by 15
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  12. 2020Interventions and Counterfactuals in Tractable Probabilistic Models: Limitations of Contemporary Transformationscited by 3

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Citing papers per year: 2021: 4; 2022: 4; 2023: 5; 2024: 4; 2025: 2; 2026: 3.

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  2. 2022Can Foundation Models Talk Causality?cited by 30
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  4. 2021HyperSPNs: Compact and Expressive Probabilistic Circuitscited by 14
  5. 2023Compositional Probabilistic and Causal Inference using Tractable Circuit Modelscited by 10
  6. 2024A Compositional Atlas for Algebraic Circuitscited by 10
  7. 2025Scaling Probabilistic Circuits via Monarch Matricescited by 9
  8. 2023Characteristic Circuitscited by 8
  9. 2024Restructuring Tractable Probabilistic Circuitscited by 7
  10. 2024Conditional Generative Models are Sufficient to Sample from Any Causal Effect Estimandcited by 4
  11. 2025CausalMan: A physics-based simulator for large-scale causalitycited by 4
  12. 2022Pearl Causal Hierarchy on Image Data: Intricacies & Challengescited by 3
10 more
  1. 2024chiSPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domainscited by 3
  2. 2022GT-CausIn: a novel causal-based insight for traffic predictioncited by 2
  3. 2026Context-specific Credibility-aware Multimodal Fusion with Conditional Probabilistic Circuitscited by 2
  4. 2021Explaining Deep Tractable Probabilistic Models: The sum-product network casecited by 1
  5. 2021A Taxonomy for Inference in Causal Model Familiescited by 1
  6. 2021The Causal Loss: Driving Correlation to Imply Causationcited by 1
  7. 2026Geometry-Aware Probabilistic Circuits via Voronoi Tessellationscited by 1
  8. 2022Continual Causal Abstractionscited by 0
  9. 2023MCNS: Mining Causal Natural Structures Inside Time Series via A Novel Internal Causality Schemecited by 0
  10. 2026Interventional Causal Circuits for Safe Robot Action Testing and Failure Recoverycited by 0