arXiv subjects

Judea Pearl

Publications and source records attributed to Judea Pearl.

63 records · Page 4Linked to original sources

arXiv2012

Graphical Condition for Identification in recursive SEM

The paper concerns the problem of predicting the effect of actions or interventions on a system from a combination of (i) statistical data on a set of observed variables, and (ii) qualitative causal knowledge encoded in the form of a directed acyclic graph (DAG). The DAG represents a set of linear equations called Structural Equations Model (SEM), whose coefficients are parameters representing direct causal effects. Reliable quantitative conclusions can only be obtained from the model if the causal effects are uniquely determined by the data. That is, if there exists a unique parametrization for the model that makes it compatible with the data. If this is the case, the model is called identified. The main result of the paper is a general sufficient condition for identification of recursive SEM models.

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arXiv2012

Identification of Conditional Interventional Distributions

The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting conditional distributions resulting from performing an action on a set of variables and, subsequently, taking measurements of another set. We provide a necessary and sufficient graphical condition for the cases where such distributions can be uniquely computed from the available information, as well as an algorithm which performs this computation whenever the condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995] for the same identification problem.

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arXiv2012

What Counterfactuals Can Be Tested

Counterfactual statements, e.g., "my headache would be gone had I taken an aspirin" are central to scientific discourse, and are formally interpreted as statements derived from "alternative worlds". However, since they invoke hypothetical states of affairs, often incompatible with what is actually known or observed, testing counterfactuals is fraught with conceptual and practical difficulties. In this paper, we provide a complete characterization of "testable counterfactuals," namely, counterfactual statements whose probabilities can be inferred from physical experiments. We provide complete procedures for discerning whether a given counterfactual is testable and, if so, expressing its probability in terms of experimental data.

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arXiv2012

Effects of Treatment on the Treated: Identification and Generalization

Many applications of causal analysis call for assessing, retrospectively, the effect of withholding an action that has in fact been implemented. This counterfactual quantity, sometimes called "effect of treatment on the treated," (ETT) have been used to to evaluate educational programs, critic public policies, and justify individual decision making. In this paper we explore the conditions under which ETT can be estimated from (i.e., identified in) experimental and/or observational studies. We show that, when the action invokes a singleton variable, the conditions for ETT identification have simple characterizations in terms of causal diagrams. We further give a graphical characterization of the conditions under which the effects of multiple treatments on the treated can be identified, as well as ways in which the ETT estimand can be constructed from both interventional and observational distributions.

stat.ME↗

arXiv2012

On a Class of Bias-Amplifying Variables that Endanger Effect Estimates

This note deals with a class of variables that, if conditioned on, tends to amplify confounding bias in the analysis of causal effects. This class, independently discovered by Bhattacharya and Vogt (2007) and Wooldridge (2009), includes instrumental variables and variables that have greater influence on treatment selection than on the outcome. We offer a simple derivation and an intuitive explanation of this phenomenon and then extend the analysis to non linear models. We show that: 1. the bias-amplifying potential of instrumental variables extends over to non-linear models, though not as sweepingly as in linear models; 2. in non-linear models, conditioning on instrumental variables may introduce new bias where none existed before; 3. in both linear and non-linear models, instrumental variables have no effect on selection-induced bias.

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arXiv2012

On Measurement Bias in Causal Inference

This paper addresses the problem of measurement errors in causal inference and highlights several algebraic and graphical methods for eliminating systematic bias induced by such errors. In particulars, the paper discusses the control of partially observable confounders in parametric and non parametric models and the computational problem of obtaining bias-free effect estimates in such models.

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arXiv2012

Confounding Equivalence in Causal Inference

The paper provides a simple test for deciding, from a given causal diagram, whether two sets of variables have the same bias-reducing potential under adjustment. The test requires that one of the following two conditions holds: either (1) both sets are admissible (i.e., satisfy the back-door criterion) or (2) the Markov boundaries surrounding the manipulated variable(s) are identical in both sets. Applications to covariate selection and model testing are discussed.

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arXiv2005

Causes and Explanations: A Structural-Model Approach. Part II: Explanations

We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion paper. Essentially, an explanation is a fact that is not known for certain but, if found to be true, would constitute an actual cause of the fact to be explained, regardless of the agent's initial uncertainty. We show that the definition handles well a number of problematic examples from the literature.

cs.AI↗

arXiv2005

Causes and Explanations: A Structural-Model Approach, Part I: Causes

We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for other definitions and resolves major difficulties in the traditional account.

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