Judea Pearl Research Articles

Programs as Causal Models: Speculations on Mental Programs and Mental Representation

Judea Pearl has argued that counterfactuals and causality are central to intelligence, whether natural or artificial, and has helped create a rich mathematical and computational framework for formally analyzing causality. Here, we draw out connections between these notions and various current issues in cognitive science, including the nature of mental "programs" and mental representation. We argue that programs (consisting of algorithms and data structures) have a causal (counterfactual-supporting) structure; these counterfactuals can reveal the nature of mental representations. Programs can also provide a causal model of the external world. Such models are, we suggest, ubiquitous in perception, cognition, and language processing.

Understanding mechanisms: opening the “black box” in observational studies

Understanding mechanisms: opening the “black box” in observational studies

A Peculiarity in Pearl’s Logic of Interventionist Counterfactuals

We examine a formal semantics for counterfactual conditionals due to Judea Pearl, which formalizes the interventionist interpretation of counterfactuals central to the interventionist accounts of causation and explanation. We show that a characteristic principle validated by Pearl’s semantics, known as the principle of reversibility, states a kind of irreversibility: counterfactual dependence (in David Lewis’s sense) between two distinct events is irreversible. Moreover, we show that Pearl’s semantics rules out only mutual counterfactual dependence, not cyclic dependence in general. This, we argue, suggests that Pearl’s logic is either too weak or too strong.

Counterfactual analyses with graphical models based on local independence

We show that one can perform causal inference in a natural way for continuous-time scenarios using tools from stochastic analysis. This provides new alternatives to the positivity condition for inverse probability weighting. The probability distribution that would govern the frequency of observations in the counterfactual scenario can be characterized in terms of a so-called martingale problem. The counterfactual and factual probability distributions may be related through a likelihood ratio given by a stochastic differential equation. We can perform inference for counterfactual scenarios based on the original observations, re-weighted according to this likelihood ratio. This is possible if the solution of the stochastic differential equation is uniformly integrable, a property that can be determined by comparing the corresponding factual and counterfactual short-term predictions. Local independence graphs are directed, possibly cyclic, graphs that represent short-term prediction among sufficiently autonomous stochastic processes. We show through an example that these graphs can be used to identify and provide consistent estimators for counterfactual parameters in continuous time. This is analogous to how Judea Pearl uses graphical information to identify causal effects in finite state Bayesian networks.

Correlation and Causation in the Study of Personality

Personality psychology aims to explain the causes and the consequences of variation in behavioural traits. Because of the observational nature of the pertinent data, this endeavour has provoked many controversies. In recent years, the computer scientist Judea Pearl has used a graphical approach to extend the innovations in causal inference developed by Ronald Fisher and Sewall Wright. Besides shedding much light on the philosophical notion of causality itself, this graphical framework now contains many powerful concepts of relevance to the controversies just mentioned. In this article, some of these concepts are applied to areas of personality research where questions of causation arise, including the analysis of observational data and the genetic sources of individual differences. Copyright © 2012 John Wiley & Sons, Ltd.

Identification of Natural Direct Effects When a Confounder of the Mediator Is Directly Affected by Exposure

Natural direct and indirect effects formalize traditional notions of mediation analysis into a rigorous causal framework and have recently received considerable attention in epidemiology and in social sciences. Sufficient conditions for the identification of natural direct effects were formulated by Judea Pearl under a nonparametric structural equations model, which assumes certain independencies between potential outcomes. A common situation in epidemiology is that a confounder of the mediator-outcome relationship is itself affected by the exposure, in which case natural direct effects fail to be nonparametrically identified without additional assumptions, even under Pearl's nonparametric structural equations model. In this article, we show that when a single binary confounder of the mediator is affected by the exposure, the natural direct effect is nonparametrically identified under the model, assuming monotonicity about the effect of the exposure on the confounder. A similar result is shown to hold for a vector of binary confounders of the mediator under a certain independence assumption about the confounders. Finally, we show that natural direct effects are more generally identified if there is no additive mean interaction between the mediator and the confounders of the mediator affected by exposure. When correct, this latter assumption is particularly appealing because it does not require monotonicity of effects of the exposure. In addition, it places no restriction on the nature of the confounders of the mediator, which can be continuous or polytomous.

Game changer

Judea Pearl's passionate advocacy of the importance of probability and causality helped revolutionize artificial intelligence.

Q&A: A sure thing

Artificial intelligence pioneer Judea Pearl discusses probability, causation, the calculus of intervention, and counterfactuals.

因果と実在, Judea Pearl, Causality, 第二版書評

因果と実在, Judea Pearl, Causality, 第二版書評

構造的因果モデルについて

This paper reviews basic ideas of Structural Causal Models (SCMs) proposed by Judea Pearl (1995, 2009a). SCMs are nonparametric structual equation models which express cause-effect relationship between variables, and justify matematical principles of both the potential outcome approach and the graphical model approach for statistical causal inference. In this paper, considering the difference/connection between SCMs and Rubin's Causal Models (RCMs) (Rubin, 1974, 1978, 2006), we state that (1) the expressive power of the potential outcome approach is higher than that of the graphical model approach, but (2) the graphical model approach. From these consderations, we conclude that we should discuss statistical causal inference based on both approaches.

Causal Diagrams for Treatment Effect Estimation with Application to Efficient Covariate Selection

Abstract Careful examination of the structure determining treatment choice and outcomes, as advocated by Heckman (2008), is central to the design of treatment effect estimators and, in particular, proper choice of covariates. Here, we demonstrate how causal diagrams developed in the machine learning literature by Judea Pearl and his colleagues, but not so well known to economists, can play a key role in this examination by using these methods to give a detailed analysis of the choice of efficient covariates identified by Hahn (2004).

Causality: Models, Reasoning and Inference, Second Edition by Judea Pearl

Causality: Models, Reasoning and Inference, Second Edition by Judea Pearl

Why the Causal View of Fitness Survives

We critically examine Denis Walsh's latest attack on the causalist view of fitness. Relying on Judea Pearl's Sure-Thing Principle and geneticist John Gillespie's model for fitness, Walsh has argued that the causal interpretation of fitness results in a reductio. We show that his conclusion only follows from misuse of the models, that is, (1) the disregard of the real biological bearing of the population-size parameter in Gillespie's model and (2) the confusion of the distinction between ordinary probability and Pearl's causal probability. Properly understood, the models used by Walsh do not threaten the causalist view of fitness.

Introduction to Special Section: Causality in Health Services Research

Introduction to Special Section: Causality in Health Services Research

Commentary on "Principal Stratification -- a Goal or a Tool?" by Judea Pearl

This commentary takes up Pearl's welcome challenge to clearly articulate the scientific value of principal stratification estimands that we and colleagues have investigated, in the area of randomized placebo-controlled preventive vaccine efficacy trials, especially trials of HIV vaccines. After briefly arguing that certain principal stratification estimands for studying vaccine effects on post-infection outcomes are of genuine scientific interest, the bulk of our commentary argues that the "causal effect predictiveness" (CEP) principal stratification estimand for evaluating immune biomarkers as surrogate endpoints is not of ultimate scientific interest, because it evaluates surrogacy restricted to the setting of a particular vaccine efficacy trial, but is nevertheless useful for guiding the selection of primary immune biomarker endpoints in Phase I/II vaccine trials and for facilitating assessment of transportability/bridging surrogacy.

Clarifying the role of principal stratification in the paired availability design.

The paired availability design for historical controls postulated four classes corresponding to the treatment (old or new) a participant would receive if arrival occurred during either of two time periods associated with different availabilities of treatment. These classes were later extended to other settings and called principal strata. Judea Pearl asks if principal stratification is a goal or a tool and lists four interpretations of principal stratification. In the case of the paired availability design, principal stratification is a tool that falls squarely into Pearl's interpretation of principal stratification as "an approximation to research questions concerning population averages." We describe the paired availability design and the important role played by principal stratification in estimating the effect of receipt of treatment in a population using data on changes in availability of treatment. We discuss the assumptions and their plausibility. We also introduce the extrapolated estimate to make the generalizability assumption more plausible. By showing why the assumptions are plausible we show why the paired availability design, which includes principal stratification as a key component, is useful for estimating the effect of receipt of treatment in a population. Thus, for our application, we answer Pearl's challenge to clearly demonstrate the value of principal stratification.

CMOL/CMOS Implementations of Bayesian Polytree Inference: Digital and Mixed-Signal Architectures and Performance/Price

In this paper, we focus on aspects of the hardware implementation of the Bayesian inference framework within the George and Hawkins' model. This framework is based on Judea Pearl's belief propagation. We then present a ?hardware design space exploration? methodology for implementing and analyzing the (digital and mixed-signal) hardware for the Bayesian (polytree) inference framework. This, particular, methodology involves: analyzing the computational/operational cost and the related microarchitecture, exploring candidate hardware components, proposing various custom architectures using both traditional CMOS and hybrid nanotechnology CMOS/nanowire/molecular hybrid (CMOL), and investigating the baseline performance/price of these hardware architectures. The results suggest that hybrid nanotechnology is a promising candidate to implement Bayesian inference. Such implementations utilize the very high density storage/computation benefits of these new nanoscale technologies much more efficiently, for example, the throughput per 858 mm2 obtained for CMOL-based architectures is 32-40 times better than the TPM for a CMOS based multiprocessor/multifield-programmable gate array system, and almost 2000 times better than the TPM for a single PC implementation. In general, the assessment of such hypothetical hardware architectures provides a baseline for large-scale implementations of Bayesian inference, and guidance for implementing the same using nanogrid structures.

Settable Systems: An Extension of Pearl's Causal Model with Optimization, Equilibrium, and Learning

Judea Pearl's Causal Model is a rich framework that provides deep insight into the nature of causal relations. As yet, however, the Pearl Causal Model (PCM) has had a lesser impact on economics or ...

Causal criteria and the problem of complex causation

Nancy Cartwright begins her recent book, Hunting Causes and Using Them, by noting that while a few years ago real causal claims were in dispute, nowadays "causality is back, and with a vengeance." In the case of the social sciences, Keith Morrison writes that "Social science asks 'why?'. Detecting causality or its corollary-prediction-is the jewel in the crown of social science research." With respect to the health sciences, Judea Pearl writes that the "research questions that motivate most studies in the health sciences are causal in nature." However, not all data used by people interested in making causal claims come from experiments that use random assignment to control and treatment groups. Indeed, much research in the social and health science depends on non-experimental, observational data. Thus, one of the most important problems in the social and health sciences concerns making warranted causal claims using non-experimental, observational data; viz., "Can observational data be used to make etiological inferences leading to warranted causal claims?" This paper examines one method of warranting causal claims that is especially widespread in epidemiology and the health sciences generally-the use of causal criteria. It is argued that cases of complex causation generally, and redundant causation-both causal overdetermination and causal preemption-specifically, undermine the use of such criteria to warrant causal claims.

A Comparison of Nine Counterfactual Theories of Causation Using Seven Examples.

The article compares and evaluates nine last-decade counterfactual theories of singular causation, which were either created or inspired by David Lewis, Joseph Y. Halpern and Judea Pearl and presented in the texts of six other authors. Some differences between those theories that have not yet been described in literature are shown in the article. It is argued that the majority of those theories analyze intuitively similar examples in different ways. In that respect, those theories impose distinctions which, according to the folk theory of causation, are (and should be) absent.