8 research outputs found
Probabilistic Reasoning across the Causal Hierarchy
We propose a formalization of the three-tier causal hierarchy of association,
intervention, and counterfactuals as a series of probabilistic logical
languages. Our languages are of strictly increasing expressivity, the first
capable of expressing quantitative probabilistic reasoning -- including
conditional independence and Bayesian inference -- the second encoding
do-calculus reasoning for causal effects, and the third capturing a fully
expressive do-calculus for arbitrary counterfactual queries. We give a
corresponding series of finitary axiomatizations complete over both structural
causal models and probabilistic programs, and show that satisfiability and
validity for each language are decidable in polynomial space.Comment: AAAI-2
A Topological Perspective on Causal Inference
This paper presents a topological learning-theoretic perspective on causal
inference by introducing a series of topologies defined on general spaces of
structural causal models (SCMs). As an illustration of the framework we prove a
topological causal hierarchy theorem, showing that substantive assumption-free
causal inference is possible only in a meager set of SCMs. Thanks to a known
correspondence between open sets in the weak topology and statistically
verifiable hypotheses, our results show that inductive assumptions sufficient
to license valid causal inferences are statistically unverifiable in principle.
Similar to no-free-lunch theorems for statistical inference, the present
results clarify the inevitability of substantial assumptions for causal
inference. An additional benefit of our topological approach is that it easily
accommodates SCMs with infinitely many variables. We finally suggest that the
framework may be helpful for the positive project of exploring and assessing
alternative causal-inductive assumptions.Comment: NeurIPS 202
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
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A Characterization of Interventional Distributions in Semi-Markovian Causal Models
We offer a complete characterization of the set of distributions that could be induced by local interventions on variables governed by a causal Bayesian network of unknown structure, in which some of the variables remain unmeasured. We show that such distributions are constrained by a simply formulated set of inequalities, from which bounds can be derived on causal effects that are not directly measured in randomized experiments
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A Characterization of Interventional Distributions in Semi-Markovian Causal Models
We offer a complete characterization of the set of distributions that could be induced by local interventions on variables governed by a causal Bayesian network of unknown structure, in which some of the variables remain unmeasured. We show that such distributions are constrained by a simply formulated set of inequalities, from which bounds can be derived on causal effects that are not directly measured in randomized experiments
A Characterization of Interventional Distributions in Semi-Markovian Causal Models
We offer a complete characterization of the set of distributions that could be induced by local interventions on variables governed by a causal Bayesian network of unknown structure, in which some of the variables remain unmeasured. We show that such distributions are constrained by a simply formulated set of inequalities, from which bounds can be derived on causal effects that are not directly measured in randomized experiments