9,811 research outputs found
Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables
We investigate the challenging task of learning causal structure in the
presence of latent variables, including locating latent variables and
determining their quantity, and identifying causal relationships among both
latent and observed variables. To address this, we propose a Generalized
Independent Noise (GIN) condition for linear non-Gaussian acyclic causal models
that incorporate latent variables, which establishes the independence between a
linear combination of certain measured variables and some other measured
variables. Specifically, for two observed random vectors and ,
GIN holds if and only if and are
independent, where is a non-zero parameter vector determined by the
cross-covariance between and . We then give necessary
and sufficient graphical criteria of the GIN condition in linear non-Gaussian
acyclic causal models. Roughly speaking, GIN implies the existence of an
exogenous set relative to the parent set of (w.r.t.
the causal ordering), such that d-separates from
. Interestingly, we find that the independent noise condition
(i.e., if there is no confounder, causes are independent of the residual
derived from regressing the effect on the causes) can be seen as a special case
of GIN. With such a connection between GIN and latent causal structures, we
further leverage the proposed GIN condition, together with a well-designed
search procedure, to efficiently estimate Linear, Non-Gaussian Latent
Hierarchical Models (LiNGLaHs), where latent confounders may also be causally
related and may even follow a hierarchical structure. We show that the
underlying causal structure of a LiNGLaH is identifiable in light of GIN
conditions under mild assumptions. Experimental results show the effectiveness
of the proposed approach
Robust causal structure learning with some hidden variables
We introduce a new method to estimate the Markov equivalence class of a
directed acyclic graph (DAG) in the presence of hidden variables, in settings
where the underlying DAG among the observed variables is sparse, and there are
a few hidden variables that have a direct effect on many of the observed ones.
Building on the so-called low rank plus sparse framework, we suggest a
two-stage approach which first removes the effect of the hidden variables, and
then estimates the Markov equivalence class of the underlying DAG under the
assumption that there are no remaining hidden variables. This approach is
consistent in certain high-dimensional regimes and performs favourably when
compared to the state of the art, both in terms of graphical structure recovery
and total causal effect estimation
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