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Paper · 2407.16975 · 2024

On the Parameter Identifiability of Partially Observed Linear Causal Models

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 9 functions out of this paper's own repositories and ran 8 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
dongxinshuai/scm-identify canonical 8 of 9
FunctionStatusWhere it lives
extract_graph_edges Ran dongxinshuai/scm-identify/pytetrad/utils.py
code served (permissive licence) · get_code("023237ccf04802f6")
extract_graph_nodes Ran dongxinshuai/scm-identify/pytetrad/utils.py
code served (permissive licence) · get_code("571d798439a11843")
generate_adjacency_matrix_ordered Ran dongxinshuai/scm-identify/pytetrad/utils.py
code served (permissive licence) · get_code("eb9db603347e0c5e")
get_cov_V_by_trek Ran dongxinshuai/scm-identify/ParameterLearning/linear_parameter_identification.py
code served (permissive licence) · get_code("2c0303ade8044f0f")
graphs_to_probs Ran dongxinshuai/scm-identify/pytetrad/visualize.py
code served (permissive licence) · get_code("06611de7ad2b51b0")
parameter_by_trek Ran dongxinshuai/scm-identify/ParameterLearning/linear_parameter_identification.py
code served (permissive licence) · get_code("8b9e6f041fd74427")
tetrad_graph_to_pcalg Ran dongxinshuai/scm-identify/pytetrad/translate.py
code served (permissive licence) · get_code("6868e44567fe9ad5")
write_gdot Ran dongxinshuai/scm-identify/pytetrad/visualize.py
code served (permissive licence) · get_code("94192dfd38028e02")
parameter_standard Not yet run dongxinshuai/scm-identify/ParameterLearning/linear_parameter_identification.py
code served (permissive licence) · get_code("8dae5f0ad0668279")

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Abstract

Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether the edge coefficients can be recovered given the causal structure and partially observed data. Our setting is more general than that of prior research - we allow all variables, including both observed and latent ones, to be flexibly related, and we consider the coefficients of all edges, whereas most existing works focus only on the edges between observed variables. Theoretically, we identify three types of indeterminacy for the parameters in partially observed linear causal models. We then provide graphical conditions that are sufficient for all parameters to be identifiable and show that some of them are provably necessary. Methodologically, we propose a novel likelihood-based parameter estimation method that addresses the variance indeterminacy of latent variables in a specific way and can asymptotically recover the underlying parameters up to trivial indeterminacy. Empirical studies on both synthetic and real-world datasets validate our identifiability theory and the effectiveness of the proposed method in the finite-sample regime. Code: https://github.com/dongxinshuai/scm-identify.

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