mlsanityData to 7 Oct 2026

Testing Bayesian Networks

arXiv 1612.03156 ↗First posted 9 Dec 2016cs.DS cs.IT cs.LGcited by 23

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Abstract (arXiv)

This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a directed acyclic graph, where we associate a random variable with each node. The value at any particular node is conditionally independent of all the other non-descendant nodes once its parents are fixed. Specifically, we study the properties of identity testing and closeness testing of Bayesian networks. Our main contribution is the first non-trivial efficient testing algorithms for these problems and corresponding information-theoretic lower bounds. For a wide range of parameter settings, our testing algorithms have sample complexity sublinear in the dimension and are sample-optimal, up to constant factors.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Dec 2016.

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

23 papers.

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  1. 2022Private High-Dimensional Hypothesis Testingcited by 12
  2. 2023Testing Closeness of Multivariate Distributions via Ramsey Theorycited by 8
  3. 2022Learning and Testing Latent-Tree Ising Models Efficientlycited by 7
  4. 2022Independence Testing for Bounded Degree Bayesian Networkcited by 5
  5. 2023Learning bounded-degree polytrees with known skeletoncited by 5
  6. 2022Complexity of High-Dimensional Identity Testing with Coordinate Conditional Samplingcited by 4
  7. 2024Replicable Uniformity Testingcited by 4
  8. 2022Gaussian Mean Testing Made Simplecited by 3
  9. 2023Near-Optimal Degree Testing for Bayes Netscited by 3
  10. 2021Learning Sparse Fixed-Structure Gaussian Bayesian Networkscited by 2
  11. 2023Uniformity Testing over Hypergrids with Subcube Conditioningcited by 2
  12. 2025Monotonicity Testing of High-Dimensional Distributions with Subcube Conditioningcited by 2
11 more
  1. 2025Replicable Distribution Testingcited by 2
  2. 2021Robust Learning of Fixed-Structure Bayesian Networks in Nearly-Linear Timecited by 1
  3. 2021Efficient inference of interventional distributionscited by 1
  4. 2024Causal Contextual Bandits with Adaptive Contextcited by 1
  5. 2025Product distribution learning with imperfect advicecited by 1
  6. 2026Total Variation Distance Estimation in Autoregressive Modelscited by 1
  7. 2024Efficient Sample-optimal Learning of Gaussian Tree Models via Sample-optimal Testing of Gaussian Mutual Informationcited by 0
  8. 2025Dimension Agnostic Testing of Survey Data Credibility through the Lens of Regressioncited by 0
  9. 2026Entropy Equivalence Testingcited by 0
  10. 2026Falsifying Causal Graphs With Outlier Eventscited by 0
  11. 2026Testing Distributions Against Bounded Distinguisherscited by 0