160 research outputs found
Surrogate Outcomes and Transportability
Identification of causal effects is one of the most fundamental tasks of
causal inference. We consider an identifiability problem where some
experimental and observational data are available but neither data alone is
sufficient for the identification of the causal effect of interest. Instead of
the outcome of interest, surrogate outcomes are measured in the experiments.
This problem is a generalization of identifiability using surrogate experiments
and we label it as surrogate outcome identifiability. We show that the concept
of transportability provides a sufficient criteria for determining surrogate
outcome identifiability for a large class of queries.Comment: This is the version published in the International Journal of
Approximate Reasonin
Polynomial Constraints in Causal Bayesian Networks
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce the complexity of the implicitization problem and make the problem tractable in certain causal Bayesian networks. We also show some preliminary results on the algebraic structure of polynomial constraints. The results have applications in distinguishing between causal models and in testing causal models with combined observational and experimental data
Model testing for causal models
Finding cause-effect relationships is the central aim of many studies in the physical, behavioral, social and biological sciences. We consider two well-known mathematical causal models: Structural equation models and causal Bayesian networks. When we hypothesize a causal model, that model often imposes constraints on the statistics of the data collected. These constraints enable us to test or falsify the hypothesized causal model. The goal of our research is to develop efficient and reliable methods to test a causal model or distinguish between causal models using various types of constraints.
For linear structural equation models, we investigate the problem of generating a small number of constraints in the form of zero partial correlations, providing an efficient way to test hypothesized models. We study linear structural equation models with correlated errors focusing on the graphical aspects of the models. We provide a set of local Markov properties and prove that they are equivalent to the global Markov property.
For causal Bayesian networks, we study equality and inequality constraints imposed on data and investigate a way to use these constraints for model testing and selection. For equality constraints, we formulate an implicitization problem and show how we may reduce the complexity of the problem. We also study the algebraic structure of the equality constraints. For inequality constraints, we present a class of inequality constraints on both nonexperimental and interventional distributions
Quantifying causal influences
Many methods for causal inference generate directed acyclic graphs (DAGs)
that formalize causal relations between variables. Given the joint
distribution on all these variables, the DAG contains all information about how
intervening on one variable changes the distribution of the other
variables. However, quantifying the causal influence of one variable on another
one remains a nontrivial question. Here we propose a set of natural, intuitive
postulates that a measure of causal strength should satisfy. We then introduce
a communication scenario, where edges in a DAG play the role of channels that
can be locally corrupted by interventions. Causal strength is then the relative
entropy distance between the old and the new distribution. Many other measures
of causal strength have been proposed, including average causal effect,
transfer entropy, directed information, and information flow. We explain how
they fail to satisfy the postulates on simple DAGs of nodes. Finally,
we investigate the behavior of our measure on time-series, supporting our
claims with experiments on simulated data.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1145 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Axiomatization of Interventional Probability Distributions
Causal intervention is an essential tool in causal inference. It is
axiomatized under the rules of do-calculus in the case of structure causal
models. We provide simple axiomatizations for families of probability
distributions to be different types of interventional distributions. Our
axiomatizations neatly lead to a simple and clear theory of causality that has
several advantages: it does not need to make use of any modeling assumptions
such as those imposed by structural causal models; it only relies on
interventions on single variables; it includes most cases with latent variables
and causal cycles; and more importantly, it does not assume the existence of an
underlying true causal graph as we do not take it as the primitive object--in
fact, a causal graph is derived as a by-product of our theory. We show that,
under our axiomatizations, the intervened distributions are Markovian to the
defined intervened causal graphs, and an observed joint probability
distribution is Markovian to the obtained causal graph; these results are
consistent with the case of structural causal models, and as a result, the
existing theory of causal inference applies. We also show that a large class of
natural structural causal models satisfy the theory presented here. We note
that the aim of this paper is axiomatization of interventional families, which
is subtly different from "causal modeling."Comment: 39 pages, 4 figure
The Causal-Neural Connection: Expressiveness, Learnability, and Inference
One of the central elements of any causal inference is an object called
structural causal model (SCM), which represents a collection of mechanisms and
exogenous sources of random variation of the system under investigation (Pearl,
2000). An important property of many kinds of neural networks is universal
approximability: the ability to approximate any function to arbitrary
precision. Given this property, one may be tempted to surmise that a collection
of neural nets is capable of learning any SCM by training on data generated by
that SCM. In this paper, we show this is not the case by disentangling the
notions of expressivity and learnability. Specifically, we show that the causal
hierarchy theorem (Thm. 1, Bareinboim et al., 2020), which describes the limits
of what can be learned from data, still holds for neural models. For instance,
an arbitrarily complex and expressive neural net is unable to predict the
effects of interventions given observational data alone. Given this result, we
introduce a special type of SCM called a neural causal model (NCM), and
formalize a new type of inductive bias to encode structural constraints
necessary for performing causal inferences. Building on this new class of
models, we focus on solving two canonical tasks found in the literature known
as causal identification and estimation. Leveraging the neural toolbox, we
develop an algorithm that is both sufficient and necessary to determine whether
a causal effect can be learned from data (i.e., causal identifiability); it
then estimates the effect whenever identifiability holds (causal estimation).
Simulations corroborate the proposed approach.Comment: 10 pages main body (53 total pages with references and appendix), 5
figures in main body (20 total figures including appendix
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