Identification of Nonlinear Latent Hierarchical Models

• URL: http://arxiv.org/abs/2306.07916v2
• Date: Tue, 31 Oct 2023 14:54:09 GMT
• Title: Identification of Nonlinear Latent Hierarchical Models
• Authors: Lingjing Kong, Biwei Huang, Feng Xie, Eric Xing, Yuejie Chi, Kun Zhang
• Abstract summary: We develop an identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models.
• Score: 38.925635086396596
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of causal structures and latent variables (up to invertible transformations) can be achieved under mild assumptions: on causal structures, we allow for multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we permit general nonlinearity and multi-dimensional continuous variables, alleviating existing work's parametric assumptions. Specifically, we first develop an identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models.

Related papers

• Score matching through the roof: linear, nonlinear, and latent variables causal discovery [18.46845413928147]
  Causal discovery from observational data holds great promise. Existing methods rely on strong assumptions about the underlying causal structure. We propose a flexible algorithm for causal discovery across linear, nonlinear, and latent variable models.
  arXiv  Detail & Related papers  (2024-07-26T14:09:06Z)
• Learning Discrete Latent Variable Structures with Tensor Rank Conditions [30.292492090200984]
  Unobserved discrete data are ubiquitous in many scientific disciplines, and how to learn the causal structure of these latent variables is crucial for uncovering data patterns. Most studies focus on the linear latent variable model or impose strict constraints on latent structures, which fail to address cases in discrete data involving non-linear relationships or complex latent structures. We explore a tensor rank condition on contingency tables for an observed variable set $mathbfX_p$, showing that the rank is determined by the minimum support of a specific conditional set. One can locate the latent variable through probing the rank on different observed variables
  arXiv  Detail & Related papers  (2024-06-11T07:25:17Z)
• Parameter identification in linear non-Gaussian causal models under general confounding [8.273471398838533]
  We study identification of the linear coefficients when such models contain latent variables. Our main result is a graphical criterion that is necessary and sufficient for deciding generic identifiability of direct causal effects. We report on estimations based on the identification result, explore a generalization to models with feedback loops, and provide new results on the identifiability of the causal graph.
  arXiv  Detail & Related papers  (2024-05-31T14:39:14Z)
• 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)
• 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)
• Causal Discovery in Linear Structural Causal Models with Deterministic Relations [27.06618125828978]
  We focus on the task of causal discovery form observational data. We derive a set of necessary and sufficient conditions for unique identifiability of the causal structure.
  arXiv  Detail & Related papers  (2021-10-30T21:32:42Z)
• Discovering Latent Causal Variables via Mechanism Sparsity: A New Principle for Nonlinear ICA [81.4991350761909]
  Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse.
  arXiv  Detail & Related papers  (2021-07-21T14:22:14Z)
• 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.