Judea Pearl

Causal diagrams for epidemiologic research.

We explored the relation between various potential sources of maternal periconceptional pregnancy exposures to pesticides and congenital anomalies in offspring. Data were derived from a case-control study of fetuses and liveborn infants with orofacial clefts, neural tube defects, conotruncal defects, or limb anomalies, among 1987-1989 California births and fetal deaths. We conducted telephone interviews with mothers of 662 (85% of eligible) orofacial cleft cases, 265 (84%) neural tube defect cases, 207 (87%) conotruncal defect cases, 165 (84%) limb cases, and 734 (78%) nonmalformed controls. The odds ratio (OR) estimates did not indicate increased risk for any of the studied anomaly groups among women whose self-reported occupational tasks were considered by an industrial hygienist likely to involve pesticide exposures. Paternal occupational exposure to pesticides, as reported by the mother, revealed elevated ORs for only two of the cleft phenotypes [OR = 1.7 [95% confidence interval (CI) = 0.9-3.4] for multiple cleft lip with/without cleft palate and OR = 1.6 [95% CI = 0.7-3.4] for multiple cleft palate]. Use of pesticide products for household gardening, by mothers or by professional applicators, was associated with ORs > or =1.5 for most of the studied anomalies. Use of pesticide products for the control of pests in or around homes was not associated with elevated risks for most of the studied anomalies, although women who reported that a professional applied pesticides to their homes had increased risks for neural tube defect-affected pregnancies [OR = 1.6 (95% CI = 1.1-2.5)] and limb anomalies [OR = 1.6 (95% CI = 1.0-2.7)]. Having a pet cat or dog and treating its fleas was not associated with increased anomaly risk. Women who reported living within 0.25 miles of an agricultural crop revealed increased risks for offspring with neural tube defects [OR = 1.5 (95%CI = 1.1-2.1)]. For many of the comparisons, data were sparse, resulting in imprecise effect estimation. Despite our investigating multiple sources of potential pesticide exposures, without more specific information on chemical and level of exposure, we could not adequately discriminate whether the observed effects are valid, whether biased exposure reporting contributed to the observed elevated risks, or whether nonspecific measurement of exposure was responsible for many of the observed estimated risks not being elevated.Causal diagrams have a long history of informal use and, more recently, have undergone formal development for applications in expert systems and robotics. We provide an introduction to these developments and their use in epidemiologic research. Causal diagrams can provide a starting point for identifying variables that must be measured and controlled to obtain unconfounded effect estimates. They also provide a method for critical evaluation of traditional epidemiologic criteria for confounding. In particular, they reveal certain heretofore unnoticed shortcomings of those criteria when used in considering multiple potential confounders. We show how to modify the traditional criteria to correct those shortcomings.

Network-based heuristics for constraint satisfaction problems

Abstract Many AI tasks can be formulated as constraint-satisfaction problems (CSP), i.e., the assignment of values to variables subject to a set of constraints. While some CSPs are hard, those that are easy can often be mapped into sparse networks of constraints which, in the extreme case, are trees. This paper identifies classes of problems that lend themselves to easy solutions, and develops algorithms that solve these problems optimally. The paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree-structured CSPs. The advice is generated by simplifying the pending subproblems into trees, counting the number of consistent solutions in each simplified subproblem, and comparing these counts to decide among the choices pending in the original problem.

Generalized best-first search strategies and the optimality of A*

This paper reports several properties of heuristic best-first search strategies whose scoring functions ƒ depend on all the information available from each candidate path, not merely on the current cost g and the estimated completion cost h. It is shown that several known properties of A* retain their form (with the minmax of f playing the role of the optimal cost), which helps establish general tests of admissibility and general conditions for node expansion for these strategies. On the basis of this framework the computational optimality of A*, in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that A* uses, is examined. A hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered. Computational performances relative to these algorithms and domains are appraised. For each class-domain combination, we then identify the strongest type of optimality that exists and the algorithm for achieving it. The main results of this paper relate to the class of algorithms that, like A*, return optimal solutions (i.e., admissible) when all cost estimates are optimistic (i.e., h ≤ h*). On this class, A* is shown to be not optimal and it is also shown that no optimal algorithm exists, but if the performance tests are confirmed to cases in which the estimates are also consistent, then A* is indeed optimal. Additionally, A* is also shown to be optimal over a subset of the latter class containing all best-first algorithms that are guided by path-dependent evaluation functions.

Tree clustering for constraint networks (research note)

Abstract The paper offers a systematic way of regrouping constraints into hierarchical structures capable of supporting search without backtracking. The method involves the formation and preprocessing of an acyclic database that permits a large variety of queries and local perturbations to be processed swiftly, either by sequential backtrack-free procedures, or by distributed constraint propagation processes.

A theory of inferred causation

Publisher Summary This chapter discusses the theory of inferred causation. The study of causation is central to the understanding of human reasoning. Inferences involving changing environments require causal theories that make formal distinctions between beliefs based on passive observations and those reflecting intervening actions. In applications such as diagnosis, qualitative physics, and plan recognition, a central task is that of finding a satisfactory explanation to a given set of observations, and the meaning of explanation is intimately related to the notion of causation. In some systems, causal ordering is defined as the ordering at which subsets of variables can be solved independently of others; in other systems, it follows the way a disturbance is propagated from one variable to others. An empirical semantics for causation is important for several reasons. The notion of causation is often associated with those of necessity and functional dependence; causal expressions often tolerate exceptions, primarily because of missing variables and coarse description. Temporal precedence is normally assumed essential for defining causation, and it is one of the most important clues that people use to distinguish causal from other types of associations.

Identifying independence in bayesian networks

An important feature of Bayesian networks is that they facilitate explicit encoding of information about independencies in the domain, information that is indispensable for efficient inferencing. This article characterizes all independence assertions that logically follow from the topology of a network and develops a linear time algorithm that identifies these assertions. The algorithms correctness is based on the soundness of a graphical criterion, called d-separation, and its optimality stems from the completeness of d-separation. An enhanced version of d-separation, called D-separation, is defined, extending the algorithm to networks that encode functional dependencies. Finally, the algorithm is shown to work for a broad class of nonprobabilistic independencies.

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

We propose a new definition of actual causes, 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. 1. Introduction2. Causal models: a review 2.1Causal models 2.2Syntax and semantics3. The definition of cause4. Examples5. A more refined definition6. Discussion AAppendix: Some Technical Issues A.1The active causal process A.2A closer look at AC2(b) A.3Causality with infinitely many variables A.4Causality in nonrecursive models Introduction Causal models: a review 2.1Causal models 2.2Syntax and semantics 2.1Causal models 2.2Syntax and semantics The definition of cause Examples A more refined definition Discussion AAppendix: Some Technical Issues A.1The active causal process A.2A closer look at AC2(b) A.3Causality with infinitely many variables A.4Causality in nonrecursive models

Evidential reasoning using stochastic simulation of causal models

Abstract Stochastic simulation is a method of computing probabilities by recording the fraction of time that events occur in a random series of scenarios generated from some causal model. This paper presents an efficient, concurrent method of conducting the simulation which guarantees that all generated scenarios will be consistent with the observed data. It is shown that the simulation can be performed by purely local computations, involving products of parameters given with the initial specification of the model. Thus, the method proposed renders stochastic simulation a powerful technique of coherent inferencing, especially suited for tasks involving complex, nondecomposable models where “ballpark” estimates of probabilities will suffice.

Research noteTree clustering for constraint networks

Abstract The paper offers a systematic way of regrouping constraints into hierarchical structures capable of supporting search without backtracking. The method involves the formation and preprocessing of an acyclic database that permits a large variety of queries and local perturbations to be processed swiftly, either by sequential backtrack-free procedures, or by distributed constraint propagation processes.

Qualitative probabilities for default reasoning, belief revision, and causal modeling

Abstract This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering on rules which is syntactically derived from the knowledge base. This ordering accounts for rule interactions, respects specificity considerations and facilitates the construction of coherent states of beliefs. Practical algorithms are developed and analyzed for testing consistency, computing rule ordering, and answering queries. Imprecise observations are incorporated using qualitative versions of Jeffreys rule and Bayesian updating, with the result that coherent belief revision is embodied naturally and tractably. Finally, causal rules are interpreted as imposing Markovian conditions that further constrain world rankings to reflect the modularity of causal organizations. These constraints are shown to facilitate reasoning about causal projections, explanations, actions and change.