Linear Causal Disentanglement via Interventions
- URL: http://arxiv.org/abs/2211.16467v3
- Date: Sun, 11 Jun 2023 21:35:42 GMT
- Title: Linear Causal Disentanglement via Interventions
- Authors: Chandler Squires, Anna Seigal, Salil Bhate, Caroline Uhler
- Abstract summary: Causal disentanglement seeks a representation of data involving latent variables that relate to one another via a causal model.
We study observed variables that are a linear transformation of a linear latent causal model.
- Score: 8.444187296409051
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Causal disentanglement seeks a representation of data involving latent
variables that relate to one another via a causal model. A representation is
identifiable if both the latent model and the transformation from latent to
observed variables are unique. In this paper, we study observed variables that
are a linear transformation of a linear latent causal model. Data from
interventions are necessary for identifiability: if one latent variable is
missing an intervention, we show that there exist distinct models that cannot
be distinguished. Conversely, we show that a single intervention on each latent
variable is sufficient for identifiability. Our proof uses a generalization of
the RQ decomposition of a matrix that replaces the usual orthogonal and upper
triangular conditions with analogues depending on a partial order on the rows
of the matrix, with partial order determined by a latent causal model. We
corroborate our theoretical results with a method for causal disentanglement
that accurately recovers a latent causal model.
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