The Observational Partial Order of Causal Structures with Latent Variables

• URL: http://arxiv.org/abs/2502.07891v1
• Date: Tue, 11 Feb 2025 19:00:58 GMT
• Title: The Observational Partial Order of Causal Structures with Latent Variables
• Authors: Marina Maciel Ansanelli, Elie Wolfe, Robert W. Spekkens,
• Abstract summary: We consider the problem of determining the partial order of equivalence classes of causal structures with latent variables. We find evidence that as one increases the number of visible variables, the equivalence classes satisfying nontrivial inequality constraints become ubiquitous.
• Score: 0.9217021281095907
• License:
• Abstract: For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the visible variables realizable by the second. Knowing such dominance relations is useful for adjudicating between these structures given observational data. We here consider the problem of determining the partial order of equivalence classes of causal structures with latent variables relative to observational dominance. We provide a complete characterization of the dominance order in the case of three visible variables, and a partial characterization in the case of four visible variables. Our techniques also help to identify which observational equivalence classes have a set of realizable distributions that is characterized by nontrivial inequality constraints, analogous to Bell inequalities and instrumental inequalities. We find evidence that as one increases the number of visible variables, the equivalence classes satisfying nontrivial inequality constraints become ubiquitous. (Because such classes are the ones for which there can be a difference in the distributions that are quantumly and classically realizable, this implies that the potential for quantum-classical gaps is also ubiquitous.) Furthermore, we find evidence that constraint-based causal discovery algorithms that rely solely on conditional independence constraints have a significantly weaker distinguishing power among observational equivalence classes than algorithms that go beyond these (i.e., algorithms that also leverage nested Markov constraints and inequality constraints).

Related papers

• On the Significance of Intermediate Latents: Distinguishing Quantum Causal Scenarios with Indistinguishable Classical Analogs [1.03590082373586]
  We consider directed acyclic graphs each of which contains both nodes representing observed variables as well as nodes representing latent or hidden variables. We highlight how the change to a quantum interpretation of the latent nodes induces distinctions between causal scenarios that would be classically indistinguishable.
  arXiv  Detail & Related papers  (2024-12-13T16:08:30Z)
• Linear causal disentanglement via higher-order cumulants [0.0]
  We study the identifiability of linear causal disentanglement, assuming access to data under multiple contexts. We show that one perfect intervention on each latent variable is sufficient and in the worst case necessary to recover parameters under perfect interventions.
  arXiv  Detail & Related papers  (2024-07-05T15:53:16Z)
• Everything that can be learned about a causal structure with latent variables by observational and interventional probing schemes [0.9217021281095907]
  We find that two causal structures remain indistinguishable if they are both associated with the same mDAG structure. We also consider the question of when one causal structure dominates another in the sense that it can realize all of the joint distributions probability.
  arXiv  Detail & Related papers  (2024-07-01T18:01:07Z)
• Identifiable Latent Neural Causal Models [82.14087963690561]
  Causal representation learning seeks to uncover latent, high-level causal representations from low-level observed data. We determine the types of distribution shifts that do contribute to the identifiability of causal representations. We translate our findings into a practical algorithm, allowing for the acquisition of reliable latent causal representations.
  arXiv  Detail & Related papers  (2024-03-23T04:13:55Z)
• Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies [58.179981892921056]
  This work introduces a novel principle for disentanglement we call mechanism sparsity regularization. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors. We show that the latent factors can be recovered by regularizing the learned causal graph to be sparse.
  arXiv  Detail & Related papers  (2024-01-10T02:38:21Z)
• A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables [28.51579090194802]
  We introduce a novel framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network. We develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases.
  arXiv  Detail & Related papers  (2023-12-18T07:57:39Z)
• Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities [0.0]
  We develop methods for detecting causal scenarios that impose inequality constraints versus those which do not. Many scenarios with exclusively equality constraints can be detected via a condition articulated by Henson, Lal and Pusey. We are able to resolve all but three causal scenarios, providing evidence that the HLP condition is, in fact, exhaustive.
  arXiv  Detail & Related papers  (2023-08-04T15:23:55Z)
• Nonparametric Identifiability of Causal Representations from Unknown Interventions [63.1354734978244]
  We study causal representation learning, the task of inferring latent causal variables and their causal relations from mixtures of the variables. Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data.
  arXiv  Detail & Related papers  (2023-06-01T10:51:58Z)
• Identifying Weight-Variant Latent Causal Models [82.14087963690561]
  We find that transitivity acts as a key role in impeding the identifiability of latent causal representations. Under some mild assumptions, we can show that the latent causal representations can be identified up to trivial permutation and scaling. We propose a novel method, termed Structural caUsAl Variational autoEncoder, which directly learns latent causal representations and causal relationships among them.
  arXiv  Detail & Related papers  (2022-08-30T11:12:59Z)
• Nested Counterfactual Identification from Arbitrary Surrogate Experiments [95.48089725859298]
  We study the identification of nested counterfactuals from an arbitrary combination of observations and experiments. Specifically, we prove the counterfactual unnesting theorem (CUT), which allows one to map arbitrary nested counterfactuals to unnested ones.
  arXiv  Detail & Related papers  (2021-07-07T12:51:04Z)
• Learning from Aggregate Observations [82.44304647051243]
  We study the problem of learning from aggregate observations where supervision signals are given to sets of instances. We present a general probabilistic framework that accommodates a variety of aggregate observations. Simple maximum likelihood solutions can be applied to various differentiable models.
  arXiv  Detail & Related papers  (2020-04-14T06:18:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.