Interventional Causal Discovery in a Mixture of DAGs

• URL: http://arxiv.org/abs/2406.08666v1
• Date: Wed, 12 Jun 2024 22:12:03 GMT
• Title: Interventional Causal Discovery in a Mixture of DAGs
• Authors: Burak Varıcı, Dmitriy Katz-Rogozhnikov, Dennis Wei, Prasanna Sattigeri, Ali Tajer,
• Abstract summary: This paper addresses the hitherto unknown role of interventions in learning causal interactions among variables governed by a mixture of causal systems. It aims to identify edges that exist in at least one component DAG of the mixture, referred to as true edges.
• Score: 34.82590796630406
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Causal interactions among a group of variables are often modeled by a single causal graph. In some domains, however, these interactions are best described by multiple co-existing causal graphs, e.g., in dynamical systems or genomics. This paper addresses the hitherto unknown role of interventions in learning causal interactions among variables governed by a mixture of causal systems, each modeled by one directed acyclic graph (DAG). Causal discovery from mixtures is fundamentally more challenging than single-DAG causal discovery. Two major difficulties stem from (i) inherent uncertainty about the skeletons of the component DAGs that constitute the mixture and (ii) possibly cyclic relationships across these component DAGs. This paper addresses these challenges and aims to identify edges that exist in at least one component DAG of the mixture, referred to as true edges. First, it establishes matching necessary and sufficient conditions on the size of interventions required to identify the true edges. Next, guided by the necessity results, an adaptive algorithm is designed that learns all true edges using ${\cal O}(n^2)$ interventions, where $n$ is the number of nodes. Remarkably, the size of the interventions is optimal if the underlying mixture model does not contain cycles across its components. More generally, the gap between the intervention size used by the algorithm and the optimal size is quantified. It is shown to be bounded by the cyclic complexity number of the mixture model, defined as the size of the minimal intervention that can break the cycles in the mixture, which is upper bounded by the number of cycles among the ancestors of a node.

Related papers

• Causality is all you need [63.10680366545293]
  Causal Graph Routing (CGR) is an integrated causal scheme relying entirely on the intervention mechanisms to reveal the cause-effect forces hidden in data. CGR can surpass the current state-of-the-art methods on both Visual Question Answer and Long Document Classification tasks.
  arXiv  Detail & Related papers  (2023-11-21T02:53:40Z)
• DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets [81.75973217676986]
  Gene regulatory networks (GRN) describe interactions between genes and their products that control gene expression and cellular function. Existing methods either focus on challenge (1), identifying cyclic structure from dynamics, or on challenge (2) learning complex Bayesian posteriors over DAGs, but not both. In this paper we leverage the fact that it is possible to estimate the "velocity" of gene expression with RNA velocity techniques to develop an approach that addresses both challenges.
  arXiv  Detail & Related papers  (2023-02-08T16:36:40Z)
• Subset verification and search algorithms for causal DAGs [13.108039226223793]
  We study the problem of identifying the smallest set of interventions required to learn the causal relationships between a subset of edges (target edges) We prove several interesting structural properties of interventional causal graphs that we believe have applications beyond the subset verification/search problems studied here.
  arXiv  Detail & Related papers  (2023-01-09T06:25:44Z)
• Large-Scale Differentiable Causal Discovery of Factor Graphs [3.8015092217142223]
  We introduce the notion of factor directed acyclic graphs (f-DAGs) as a way to the search space to non-linear low-rank causal interaction models. We propose a scalable implementation of f-DAG constrained causal discovery for high-dimensional interventional data.
  arXiv  Detail & Related papers  (2022-06-15T21:28:36Z)
• 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)
• Shared Independent Component Analysis for Multi-Subject Neuroimaging [107.29179765643042]
  We introduce Shared Independent Component Analysis (ShICA) that models each view as a linear transform of shared independent components contaminated by additive Gaussian noise. We show that this model is identifiable if the components are either non-Gaussian or have enough diversity in noise variances. We provide empirical evidence on fMRI and MEG datasets that ShICA yields more accurate estimation of the components than alternatives.
  arXiv  Detail & Related papers  (2021-10-26T08:54:41Z)
• 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)
• Active Structure Learning of Causal DAGs via Directed Clique Tree [28.637447727749]
  We develop a universal lower bound for single-node interventions that establishes that the largest clique is always a fundamental impediment to structure learning. Specifically, we present a decomposition of a DAG into independently orientable components through directed clique trees. We also present a two-phase intervention design algorithm that matches the optimal number of interventions up to a multiplicative logarithmic factor in the number of maximal cliques.
  arXiv  Detail & Related papers  (2020-11-01T23:11:17Z)
• Causal inference of brain connectivity from fMRI with $\psi$-Learning Incorporated Linear non-Gaussian Acyclic Model ($\psi$-LiNGAM) [27.32225635737671]
  We propose a $psi$-learning incorporated a linear non-Gaussian acyclic model ($psi$-LiNGAM) to facilitate causal inferences. We use the association model ($psi$-learning) to facilitate causal inferences and the model works well especially for high-dimensional cases.
  arXiv  Detail & Related papers  (2020-06-16T21:56:40Z)

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.