A Mathematical Framework for Topological Causal Data Analysis

• URL: http://arxiv.org/abs/2607.28161v1
• Date: Thu, 30 Jul 2026 13:02:11 GMT
• Title: A Mathematical Framework for Topological Causal Data Analysis
• Abstract summary: We introduce emphTopological Causal Data Analysis, a framework separating the observation space, causal-model class, topological representation, and causal query.<n>Topology does not define interventions; it supplies stable, shape-sensitive summaries after causal assumptions have been specified.<n>At the distribution level, we identify targets through the standard causal (g)-formula and derive stability-transfer bounds and plug-in consistency.
• Score: 5.8010446129208155
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many modern outcomes, including images, point clouds, networks, and spatial fields, are structured objects for which \(Y^1-Y^0\) may be undefined or scientifically inadequate. We introduce \emph{Topological Causal Data Analysis} (TCDA), a framework separating the observation space, causal-model class, topological representation, and causal query. Topology does not define interventions; it supplies stable, shape-sensitive summaries after causal assumptions have been specified. We distinguish outcome-level TCDA, which transforms individual potential outcomes, from distribution-level TCDA, which transforms interventional outcome laws, and characterize when outcome and distribution level contrasts agree. Building on recent outcome-level theory, we formulate identification and doubly robust representations for Banach-space-valued summaries. At the distribution level, we identify targets through the standard causal \(g\)-formula and derive stability-transfer bounds and plug-in consistency. We also place target-specific topological ignorability within the framework, clarifying when a covariate-standardized coarse effect can be identified without identifying the full interventional laws. Finally, we delimit the role of observational topology in causal discovery: it can assist diagnosis on restricted model classes but cannot by itself identify causal structure.

Related papers

• Adversarial Causal Intervention Falsification [0.0]
  We study a sequential game in which a structural causal generator proposes observational and interventional distributions.<n>An adversarial experimentalist selects interventions intended to maximally falsify the generator.<n>The discriminator is indexed by an intervention and tests whether the generator reproduces the corresponding post-intervention law.
  arXiv  Detail & Related papers  (2026-08-05T20:01:26Z)
• Relational Structural Causal Models [52.818153111470394]
  We develop relational structural causal models, extending structural causal models to settings where objects and their relations vary.<n>We propose relational neural causal models, a provably correct approach that outperforms non-relational baselines on simulated traffic scenes.
  arXiv  Detail & Related papers  (2026-06-12T18:54:06Z)
• Topological Ignorability for Structural Causal Effects Beyond Means [0.0]
  Interventions alter the structure of an outcome distribution rather than its mean.<n>Mean-based causal estimands such as the average treatment effect may miss important structural effects.<n>We introduce topological-geometrical causal metrics based on summaries of interventional outcome laws.
  arXiv  Detail & Related papers  (2026-05-31T11:56:53Z)
• Scalable Contrastive Causal Discovery under Unknown Soft Interventions [3.165716101116899]
  We propose a scalable causal discovery model for paired observational and interventional settings with shared underlying causal structure and unknown soft interventions.<n> Experiments on synthetic data demonstrate improved causal structure recovery, generalization to unseen graphs with held-out causal mechanisms, and scalability to larger graphs.
  arXiv  Detail & Related papers  (2026-03-03T18:16:16Z)
• Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning [26.3914014514629]
  In scientific domains -- from biology to the social sciences -- many questions boil down to textitWhat effect will we observe if we intervene on a particular variable?<n>We propose using meta-learning to create an end-to-end model: the Model-Averaged Causal Estimation Transformer Neural Process (MACE-TNP)<n>Our work establishes meta-learning as a flexible and scalable paradigm for approximating complex Bayesian causal inference.
  arXiv  Detail & Related papers  (2025-07-07T22:48:32Z)
• 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 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)
• The Combinatorics of Causality [0.0]
  We introduce and explore the notion of "spaces of input histories" In the simplest case of binary inputs, the number of available "causally complete" spaces grows from 7 on 2 events, to 2644 on 3 events, to an unknown number on 4 events (likely around a billion) For perspective, previous literature on non-locality and contextuality used a single one of the 2644 available spaces on 3 events, work on definite causality used 19 spaces, derived from partial orders, and work on indefinite causality used only 6 more, for a grand total of 25.
  arXiv  Detail & Related papers  (2022-06-17T17:42:17Z)
• Effect Identification in Cluster Causal Diagrams [51.42809552422494]
  We introduce a new type of graphical model called cluster causal diagrams (for short, C-DAGs) C-DAGs allow for the partial specification of relationships among variables based on limited prior knowledge. We develop the foundations and machinery for valid causal inferences over C-DAGs.
  arXiv  Detail & Related papers  (2022-02-22T21:27:31Z)
• Variational Causal Networks: Approximate Bayesian Inference over Causal Structures [132.74509389517203]
  We introduce a parametric variational family modelled by an autoregressive distribution over the space of discrete DAGs. In experiments, we demonstrate that the proposed variational posterior is able to provide a good approximation of the true posterior.
  arXiv  Detail & Related papers  (2021-06-14T17:52:49Z)
• Structural Causal Models Are (Solvable by) Credal Networks [70.45873402967297]
  Causal inferences can be obtained by standard algorithms for the updating of credal nets. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks. Experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.
  arXiv  Detail & Related papers  (2020-08-02T11:19:36Z)

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.