Score-based Causal Representation Learning: Linear and General Transformations

• URL: http://arxiv.org/abs/2402.00849v3
• Date: Wed, 30 Oct 2024 01:47:27 GMT
• Title: Score-based Causal Representation Learning: Linear and General Transformations
• Authors: Burak Varıcı, Emre Acartürk, Karthikeyan Shanmugam, Abhishek Kumar, Ali Tajer,
• Abstract summary: The paper addresses both the identifiability and achievability aspects. It designs a score-based class of algorithms that ensures both identifiability and achievability. Results are empirically validated via experiments on structured synthetic data and image data.
• Score: 31.786444957887472
• License:
• Abstract: This paper addresses intervention-based causal representation learning (CRL) under a general nonparametric latent causal model and an unknown transformation that maps the latent variables to the observed variables. Linear and general transformations are investigated. The paper addresses both the identifiability and achievability aspects. Identifiability refers to determining algorithm-agnostic conditions that ensure recovering the true latent causal variables and the latent causal graph underlying them. Achievability refers to the algorithmic aspects and addresses designing algorithms that achieve identifiability guarantees. By drawing novel connections between score functions (i.e., the gradients of the logarithm of density functions) and CRL, this paper designs a score-based class of algorithms that ensures both identifiability and achievability. First, the paper focuses on linear transformations and shows that one stochastic hard intervention per node suffices to guarantee identifiability. It also provides partial identifiability guarantees for soft interventions, including identifiability up to ancestors for general causal models and perfect latent graph recovery for sufficiently non-linear causal models. Secondly, it focuses on general transformations and shows that two stochastic hard interventions per node suffice for identifiability. Notably, one does not need to know which pair of interventional environments have the same node intervened. Finally, the theoretical results are empirically validated via experiments on structured synthetic data and image data.

Related papers

• A General Causal Inference Framework for Cross-Sectional Observational Data [0.4972323953932129]
  General Causal Inference (GCI) framework specifically designed for cross-sectional observational data. This paper proposes a GCI framework specifically designed for cross-sectional observational data.
  arXiv  Detail & Related papers  (2024-04-28T14:26:27Z)
• Learning Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity [27.630223763160515]
  We provide the first identifiability results based on data that stem from general environments. We show that for linear causal models, while the causal graph can be fully recovered, the latent variables are only identified up to the surrounded-node ambiguity (SNA) We also propose an algorithm, textttLiNGCReL which provably recovers the ground-truth model up to SNA.
  arXiv  Detail & Related papers  (2023-11-21T01:09:11Z)
• Identifiable Latent Polynomial Causal Models Through the Lens of Change [82.14087963690561]
  Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as identifiability.
  arXiv  Detail & Related papers  (2023-10-24T07:46:10Z)
• General Identifiability and Achievability for Causal Representation Learning [33.80247458590611]
  The paper establishes identifiability and achievability results using two hard uncoupled interventions per node in the latent causal graph. For identifiability, the paper establishes that perfect recovery of the latent causal model and variables is guaranteed under uncoupled interventions. The analysis, additionally, recovers the identifiability result for two hard coupled interventions, that is when metadata about the pair of environments that have the same node intervened is known.
  arXiv  Detail & Related papers  (2023-10-24T01:47:44Z)
• Learning Linear Causal Representations from Interventions under General Nonlinear Mixing [52.66151568785088]
  We prove strong identifiability results given unknown single-node interventions without access to the intervention targets. This is the first instance of causal identifiability from non-paired interventions for deep neural network embeddings.
  arXiv  Detail & Related papers  (2023-06-04T02:32:12Z)
• 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)
• Score-based Causal Representation Learning with Interventions [54.735484409244386]
  This paper studies the causal representation learning problem when latent causal variables are observed indirectly. The objectives are: (i) recovering the unknown linear transformation (up to scaling) and (ii) determining the directed acyclic graph (DAG) underlying the latent variables.
  arXiv  Detail & Related papers  (2023-01-19T18:39:48Z)
• 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)
• 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)
• Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables [13.299431908881425]
  Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs is well studied. corresponding algorithms are underused due to the complexity of estimating the identifying functionals they output. We bridge the gap between identification and estimation of population-level causal effects involving a single treatment and a single outcome.
  arXiv  Detail & Related papers  (2020-03-27T22:29:04Z)

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.