Nonparametric Identifiability of Causal Representations from Unknown Interventions

• URL: http://arxiv.org/abs/2306.00542v2
• Date: Sat, 28 Oct 2023 11:54:37 GMT
• Title: Nonparametric Identifiability of Causal Representations from Unknown Interventions
• Authors: Julius von K\"ugelgen, Michel Besserve, Liang Wendong, Luigi Gresele, Armin Keki\'c, Elias Bareinboim, David M. Blei, Bernhard Sch\"olkopf
• Abstract summary: 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.
• Score: 63.1354734978244
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional mixtures of the variables. Prior work relies on weak supervision, in the form of counterfactual pre- and post-intervention views or temporal structure; places restrictive assumptions, such as linearity, on the mixing function or latent causal model; or requires partial knowledge of the generative process, such as the causal graph or intervention targets. We instead consider the general setting in which both the causal model and the mixing function are nonparametric. The learning signal takes the form of multiple datasets, or environments, arising from unknown interventions in the underlying causal model. 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. We study the fundamental setting of two causal variables and prove that the observational distribution and one perfect intervention per node suffice for identifiability, subject to a genericity condition. This condition rules out spurious solutions that involve fine-tuning of the intervened and observational distributions, mirroring similar conditions for nonlinear cause-effect inference. For an arbitrary number of variables, we show that at least one pair of distinct perfect interventional domains per node guarantees identifiability. Further, we demonstrate that the strengths of causal influences among the latent variables are preserved by all equivalent solutions, rendering the inferred representation appropriate for drawing causal conclusions from new data. Our study provides the first identifiability results for the general nonparametric setting with unknown interventions, and elucidates what is possible and impossible for causal representation learning without more direct supervision.

Related papers

• Identifiability Guarantees for Causal Disentanglement from Purely Observational Data [10.482728002416348]
  Causal disentanglement aims to learn about latent causal factors behind data. Recent advances establish identifiability results assuming that interventions on (single) latent factors are available. We provide a precise characterization of latent factors that can be identified in nonlinear causal models.
  arXiv  Detail & Related papers  (2024-10-31T04:18:29Z)
• 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)
• A Sparsity Principle for Partially Observable Causal Representation Learning [28.25303444099773]
  Causal representation learning aims at identifying high-level causal variables from perceptual data. We focus on learning from unpaired observations from a dataset with an instance-dependent partial observability pattern. We propose two methods for estimating the underlying causal variables by enforcing sparsity in the inferred representation.
  arXiv  Detail & Related papers  (2024-03-13T08:40:49Z)
• 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)
• Identifiability Guarantees for Causal Disentanglement from Soft Interventions [26.435199501882806]
  Causal disentanglement aims to uncover a representation of data using latent variables that are interrelated through a causal model. In this paper, we focus on the scenario where unpaired observational and interventional data are available, with each intervention changing the mechanism of a latent variable. When the causal variables are fully observed, statistically consistent algorithms have been developed to identify the causal model under faithfulness assumptions.
  arXiv  Detail & Related papers  (2023-07-12T15:39:39Z)
• A Causal Ordering Prior for Unsupervised Representation Learning [27.18951912984905]
  Causal representation learning argues that factors of variation in a dataset are, in fact, causally related. We propose a fully unsupervised representation learning method that considers a data generation process with a latent additive noise model.
  arXiv  Detail & Related papers  (2023-07-11T18:12:05Z)
• Learning nonparametric latent causal graphs with unknown interventions [18.6470340274888]
  We establish conditions under which latent causal graphs are nonparametrically identifiable. We do not assume the number of hidden variables is known, and we show that at most one unknown intervention per hidden variable is needed.
  arXiv  Detail & Related papers  (2023-06-05T14:06:35Z)
• 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)
• 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)
• Disentangling Observed Causal Effects from Latent Confounders using Method of Moments [67.27068846108047]
  We provide guarantees on identifiability and learnability under mild assumptions. We develop efficient algorithms based on coupled tensor decomposition with linear constraints to obtain scalable and guaranteed solutions.
  arXiv  Detail & Related papers  (2021-01-17T07:48:45Z)

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.