3,228 research outputs found
Switching Regression Models and Causal Inference in the Presence of Discrete Latent Variables
Given a response and a vector of predictors,
we investigate the problem of inferring direct causes of among the vector
. Models for that use all of its causal covariates as predictors enjoy
the property of being invariant across different environments or interventional
settings. Given data from such environments, this property has been exploited
for causal discovery. Here, we extend this inference principle to situations in
which some (discrete-valued) direct causes of are unobserved. Such cases
naturally give rise to switching regression models. We provide sufficient
conditions for the existence, consistency and asymptotic normality of the MLE
in linear switching regression models with Gaussian noise, and construct a test
for the equality of such models. These results allow us to prove that the
proposed causal discovery method obtains asymptotic false discovery control
under mild conditions. We provide an algorithm, make available code, and test
our method on simulated data. It is robust against model violations and
outperforms state-of-the-art approaches. We further apply our method to a real
data set, where we show that it does not only output causal predictors, but
also a process-based clustering of data points, which could be of additional
interest to practitioners.Comment: 46 pages, 14 figures; real-world application added in Section 5.2;
additional numerical experiments added in the Appendix
Group invariance principles for causal generative models
The postulate of independence of cause and mechanism (ICM) has recently led
to several new causal discovery algorithms. The interpretation of independence
and the way it is utilized, however, varies across these methods. Our aim in
this paper is to propose a group theoretic framework for ICM to unify and
generalize these approaches. In our setting, the cause-mechanism relationship
is assessed by comparing it against a null hypothesis through the application
of random generic group transformations. We show that the group theoretic view
provides a very general tool to study the structure of data generating
mechanisms with direct applications to machine learning.Comment: 16 pages, 6 figure
A Logical Characterization of Constraint-Based Causal Discovery
We present a novel approach to constraint-based causal discovery, that takes
the form of straightforward logical inference, applied to a list of simple,
logical statements about causal relations that are derived directly from
observed (in)dependencies. It is both sound and complete, in the sense that all
invariant features of the corresponding partial ancestral graph (PAG) are
identified, even in the presence of latent variables and selection bias. The
approach shows that every identifiable causal relation corresponds to one of
just two fundamental forms. More importantly, as the basic building blocks of
the method do not rely on the detailed (graphical) structure of the
corresponding PAG, it opens up a range of new opportunities, including more
robust inference, detailed accountability, and application to large models
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