mlsanityData to 14 Oct 2026

Causal Inference Despite Limited Global Confounding via Mixture Models

arXiv 2112.11602 ↗First posted 22 Dec 2021cs.LG cs.DS eess.SPcited by 9

Not on the map. Why?

Abstract (arXiv)

A Bayesian Network is a directed acyclic graph (DAG) on a set of n random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite k-mixture of such models is graphically represented by a larger graph which has an additional ``hidden'' (or ``latent'') random variable U, ranging in 1,ldots,k, and a directed edge from U to every other vertex. Models of this type are fundamental to causal inference, where U models an unobserved confounding effect of multiple populations, obscuring the causal relationships in the observable DAG. By solving the mixture problem and recovering the joint probability distribution with U, traditionally unidentifiable causal relationships become identifiable. Using a reduction to the more well-studied ``product'' case on empty graphs, we give the first algorithm to learn mixtures of non-empty DAGs.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 10 of its 47 references that are in the map. First posted on arXiv 22 Dec 2021.

Builds on

10 of 47 references.

References · 10

  1. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
  2. 2018The Blessings of Multiple Causescited by 104
  3. 2021Learning latent causal graphs via mixture oraclescited by 55
  4. 2019Comment on "Blessings of Multiple Causes"cited by 16
  5. 2018Beyond the Low-Degree Algorithm: Mixtures of Subcubes and Their Applicationscited by 15
  6. 2018Multiple Causal Inference with Latent Confoundingcited by 14
  7. 2020Source Identification for Mixtures of Product Distributionscited by 11
  8. 2013Learning Mixtures of DAG Modelscited by 10
  9. 2017Learning Overcomplete HMMscited by 9
  10. 2021Hadamard Extensions and the Identification of Mixtures of Product Distributionscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 1; 2026: 2.

9 papers.

  1. 2023Identification of Mixtures of Discrete Product Distributions in Near-Optimal Sample and Time Complexitycited by 4
  2. 2023Causal Discovery in Mixtures of Populationscited by 4
  3. 2023Identifiability of Product of Experts Modelscited by 3
  4. 2024Synthetic Potential Outcomes and Causal Mixture Identifiabilitycited by 3
  5. 2024Learning Discrete Latent Variable Structures with Tensor Rank Conditionscited by 3
  6. 2024Controlling for discrete unmeasured confounding in nonlinear causal modelscited by 1
  7. 2025On Theoretical Identifiability of Discrete Latent Causal Graphical Modelscited by 0
  8. 2026Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independencecited by 0
  9. 2026Causal Inference with Unobserved Confounding: A Mixture Learning Perspectivecited by 0