Graphical Causal Models Research Articles

Normality and actual causal strength

Existing research suggests that people’s judgments of actual causation can be influenced by the degree to which they regard certain events as normal. We develop an explanation for this phenomenon that draws on standard tools from the literature on graphical causal models and, in particular, on the idea of probabilistic sampling. Using these tools, we propose a new measure of actual causal strength. This measure accurately captures three effects of normality on causal judgment that have been observed in existing studies. More importantly, the measure predicts a new effect (“abnormal deflation”). Two studies show that people’s judgments do, in fact, show this new effect. Taken together, the patterns of people’s causal judgments thereby provide support for the proposed explanation.

Causal feature learning: an overview

Causal feature learning (CFL) (Chalupka et al., Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence. AUAI Press, Edinburgh, pp 181–190, 2015) is a causal inference framework rooted in the language of causal graphical models (Pearl J, Reasoning and inference. Cambridge University Press, Cambridge, 2009; Spirtes et al., Causation, Prediction, and Search. Massachusetts Institute of Technology, Massachusetts, 2000), and computational mechanics (Shalizi, PhD thesis, University of Wisconsin at Madison, 2001). CFL is aimed at discovering high-level causal relations from low-level data, and at reducing the experimental effort to understand confounding among the high-level variables. We first review the scientific motivation for CFL, then present a detailed introduction to the framework, laying out the definitions and algorithmic steps. A simple example illustrates the techniques involved in the learning steps and provides visual intuition. Finally, we discuss the limitations of the current framework and list a number of open problems.

Causal inference in cumulative risk assessment: The roles of directed acyclic graphs

Cumulative risk assessments (CRAs) address exposures to multiple chemical and nonchemical stressors and often focus on characterization of health risks in vulnerable populations. Evaluating complex exposure-response relationships in CRAs requires the use of formal and rigorous methods for causal inference. Directed acyclic graphs (DAGs) are graphical causal models used to organize and communicate knowledge about the underlying causal structure that generates observable data. Using existing graphical theories for causal inference with DAGs, risk analysts can identify confounders and effect measure modifiers to determine if the available data are both internally valid to obtain unbiased risk estimates and are generalizable to populations of interest. Conditional independencies implied by the structure of a DAG can be used to test assumptions used in a CRA against empirical data in a selected study and can contribute to the evidence evaluations related to specific causal pathways. This can facilitate quantitative use of these data, as well as help identify key research gaps, prioritize data collection activities, and evaluate risk management alternatives. DAGs also enable risk analysts to be explicit about sources of uncertainty and to determine whether a causal effect can be estimated from available data. Using a conceptual model and DAG for a hypothetical community located near a concentrated animal feeding operation (CAFO), we illustrate the advantages of using DAGs for evaluating causality in CRAs. DAGs also can be used in conjunction with weight of evidence (WOE) methodology to improve causal analysis for CRA, which could lead to more effective interventions to reduce population health risks.

A million variables and more: the Fast Greedy Equivalence Search algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance images.

We describe two modifications that parallelize and reorganize caching in the well-known Greedy Equivalence Search (GES) algorithm for discovering directed acyclic graphs on random variables from sample values. We apply one of these modifications, the Fast Greedy Search (FGS) assuming faithfulness, to an i.i.d. sample of 1,000 units to recover with high precision and good recall an average degree 2 directed acyclic graph (DAG) with one million Gaussian variables. We describe a modification of the algorithm to rapidly find the Markov Blanket of any variable in a high dimensional system. Using 51,000 voxels that parcellate an entire human cortex, we apply the FGS algorithm to Blood Oxygenation Level Dependent (BOLD) time series obtained from resting state fMRI.

Reasoning With Causal Cycles.

This article assesses how people reason with categories whose features are related in causal cycles. Whereas models based on causal graphical models (CGMs) have enjoyed success modeling category-based judgments as well as a number of other cognitive phenomena, CGMs are only able to represent causal structures that are acyclic. A number of new formalisms that allow cycles are introduced and evaluated. Dynamic Bayesian networks (DBNs) represent cycles by unfolding them over time. Chain graphs augment CGMs by allowing the presence of undirected links that model feedback relations between variables. Unfolded chain graphs are chain graphs that unfold over time. An existing model of causal cycles (alpha centrality) is also evaluated. Four experiments in which subjects reason about categories with cyclically related features provided evidence against DBNs and alpha centrality and for the two types of chain graphs. Chain graphs-a mechanism for representing the equilibrium distribution of a dynamic system-may thus be good candidates for modeling how people reason causally with complex systems. Applications of chain graphs to areas of cognition other than category-based judgments are discussed.

Causally Interpreting Intersectionality Theory

Social scientists report difficulties in drawing out testable predictions from the literature on intersectionality theory. We alleviate that difficulty by showing that some characteristic claims of the intersectionality literature can be interpreted causally. The formalism of graphical causal modeling allows claims about the causal effects of occupying intersecting identity categories to be clearly represented and submitted to empirical testing. After outlining this causal interpretation of intersectional theory, we address some concerns that have been expressed in the literature claiming that membership in demographic categories can have causal effects.

Econometric Identification of Causal Effects: A Graphical Approach with a Case Study

It is well known that causal inference relies on untestable a-priori causal assumptions. Identification refers to whether a causal relationship can be inferred from observed statistical associations; it requires an understanding of what statistical associations are induced by those causal assumptions. Since the assumptions are untestable, a transparent description of their statistical consequences helps the readers. However, the relation between causal assumptions and their induced statistical associations may not be obvious. In this paper I describe a technique known as Directed Acyclical Graphs or Graphical Bayesian Network or Graphical Causal Models. The technique was developed in the computer science literature in the 1980s (Pearl 2009) although it has antecedents in path analysis developed by Philip and Sewall Wright beginning in the 1920s (Wright 1921). In addition to describing the technique, I illustrate its application to a case study of a research issue in auditing.

Conditioning, intervening, and decision

Clark Glymour, together with his students Peter Spirtes and Richard Scheines, did pioneering work on graphical causal models (e.g. Spirtes et al., in Causation, prediction, and search, 2000). One of the central advances provided by these models is the ability to simply represent the effects of interventions. In an elegant paper (Meek and Glymour, in Br J Philos Sci 45: 1001–1021, 1994), Glymour and his student Christopher Meek applied these methods to problems in decision theory. One of the morals they drew was that causal decision theory should be understood in terms of interventions. I revisit their proposal, and extend the analysis by showing how graphical causal models might be used to address decision problems that arise in “exotic” situations, such as those involving crystal balls or time travelers.

Studying effective brain connectivity using multiregression dynamic models

A Multiregression Dynamic Model (MDM) is a class of multivariate time series that represents multiple dynamic causal processes in a graphical way. One of the advantages of this class is that, in contrast to many other Dynamic Bayesian Networks, the hypothesised relationships accommodate conditional conjugate inference. We demonstrate for the first time how it is straightforward to search over all possible connectivity networks with dynamically changing intensity of transmission to find the Maximum a Posteriori Probability (MAP) model within this class. This search method is made feasible by using a novel application of the integer programming algorithm. The search over all possible directed (acyclic or cyclic) graphical structures can be made especially fast by utilising the fact that, within this class of models, the joint likelihood factorizes. We proceed to show how diagnostic methods, analogous to those defined for static Bayesian Networks, can be used to suggest embellishment of the model class to extend the process of model selection. A typical goal of experimental neuroscience is to draw conclusions regarding the causal mechanisms that underpin neural communication. Often the main focus of interest in these experiments includes not only a search for the likely model of a specific individual, but an analysis of shared between-subject e↵ects. Currently, such features are analysed using rather coarse aggregation methods over shared time series. However, here we demonstrate that, using the estimation of multiple causal graphical models and Bayesian hyperclustering techniques, it is possible to use the full machinery of Bayesian methods to formally make inferences in a coherent way which contemplates hypotheses about shared dependences between such populations of subjects. Methods developed here are illustrated using simulated and real resting-state and steady-state task functional Magnetic Resonance Imaging (fMRI) data.

Causal learning in children.

How do children learn the causal structure of the environment? We first summarize a set of theories from the adult literature on causal learning, including associative models, parameter estimation theories, and causal structure learning accounts, as applicable to developmental science. We focus on causal graphical models as a description of children's causal knowledge, and the implications of this computational description for children's causal learning. We then examine the contributions of explanation and exploration to causal learning from a computational standpoint. Finally, we examine how children might learn causal knowledge from others and how computational and constructivist accounts of causal learning can be integrated. WIREs Cogn Sci 2014, 5:413-427. doi: 10.1002/wcs.1291 For further resources related to this article, please visit the WIREs website. The authors have declared no conflicts of interest for this article.

Independence and dependence in human causal reasoning

Causal graphical models (CGMs) are a popular formalism used to model human causal reasoning and learning. The key property of CGMs is the causal Markov condition, which stipulates patterns of independence and dependence among causally related variables. Five experiments found that while adult’s causal inferences exhibited aspects of veridical causal reasoning, they also exhibited a small but tenacious tendency to violate the Markov condition. They also failed to exhibit robust discounting in which the presence of one cause as an explanation of an effect makes the presence of another less likely. Instead, subjects often reasoned “associatively,” that is, assumed that the presence of one variable implied the presence of other, causally related variables, even those that were (according to the Markov condition) conditionally independent. This tendency was unaffected by manipulations (e.g., response deadlines) known to influence fast and intuitive reasoning processes, suggesting that an associative response to a causal reasoning question is sometimes the product of careful and deliberate thinking. That about 60% of the erroneous associative inferences were made by about a quarter of the subjects suggests the presence of substantial individual differences in this tendency. There was also evidence that inferences were influenced by subjects’ assumptions about factors that disable causal relations and their use of a conjunctive reasoning strategy. Theories that strive to provide high fidelity accounts of human causal reasoning will need to relax the independence constraints imposed by CGMs.

Chapter Seven - Edge Replacement and Minimality as Models of Causal Inference in Children

Recently, much research has focused on causal graphical models (CGMs) as a computational-level description of how children represent cause and effect. While this research program has shown promise, there are aspects of causal reasoning that CGMs have difficulty accommodating. We propose a new formalism that amends CGMs. This edge replacement grammar formalizes one existing and one novel theoretical commitment. The existing idea is that children are determinists, in the sense that they believe that apparent randomness comes from hidden complexity, rather than inherent nondeterminism in the world. The new idea is that children think of causation as a branching process: causal relations grow not directly from the cause, but from existing relations between the cause and other effects. We have shown elsewhere that these two commitments together, when formalized, can explain and quantitatively fit the otherwise puzzling effect of nonindependence observed in the adult causal reasoning literature. We then test the qualitative predictions of this new formalism on children in a series of three experiments.

Counterfactual Graphical Models for Longitudinal Mediation Analysis With Unobserved Confounding

Questions concerning mediated causal effects are of great interest in psychology, cognitive science, medicine, social science, public health, and many other disciplines. For instance, about 60% of recent papers published in leading journals in social psychology contain at least one mediation test (Rucker, Preacher, Tormala, & Petty, 2011). Standard parametric approaches to mediation analysis employ regression models, and either the "difference method" (Judd & Kenny, 1981), more common in epidemiology, or the "product method" (Baron & Kenny, 1986), more common in the social sciences. In this article, we first discuss a known, but perhaps often unappreciated, fact that these parametric approaches are a special case of a general counterfactual framework for reasoning about causality first described by Neyman (1923) and Rubin (1924) and linked to causal graphical models by Robins (1986) and Pearl (2006). We then show a number of advantages of this framework. First, it makes the strong assumptions underlying mediation analysis explicit. Second, it avoids a number of problems present in the product and difference methods, such as biased estimates of effects in certain cases. Finally, we show the generality of this framework by proving a novel result which allows mediation analysis to be applied to longitudinal settings with unobserved confounders.

Learning multivariate time series causal graphs based on conditional mutual information

Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis. This paper provides a method that employs both mutual information and conditional mutual information to identify the causal structure of multivariate time series causal graphical models. A three-step procedure is developed to learn the contemporaneous and the lagged causal relationships of time series causal graphs. Contrary to conventional constraint-based algorithm, the proposed algorithm does not involve any special kinds of distribution and is nonparametric. These properties are especially appealing for inference of time series causal graphs when the prior knowledge about the data model is not available. Simulations and case analysis demonstrate the effectiveness of the method.

Counterfactuals, graphical causal models and potential outcomes: Response to Lindquist and Sobel

Lindquist and Sobel claim that the graphical causal models they call "agnostic" do not imply any counterfactual conditionals. They doubt that "causal effects" can be discovered using graphical causal models typical of SEMs, DCMs, Bayes nets, Granger causal models, etc. Each of these claims is false or exaggerated. They recommend instead that investigators adopt the "potential outcomes" framework. The potential outcomes framework is an obstacle rather than an aid to discovering causal relations in fMRI contexts.

Quantitative Models for Causal Analysis in the Era of Genome Wide Association Studies

Causal inference in health research is a complex endeavor partly because the biomedical enterprise involves researchers from many disciplines including clinical medicine, epidemiology, genetics, basic sciences such as pathology and cell biology, and the behavioral sciences. A multidisciplinary approach is often needed to study health concerns and interpret findings, drawing upon expertise from epidemiologists, statisticians, physicians, nurses, geneticists, psychologists, and other practicing clinicians and researchers. In addition to the diversity of scientific disciplines and professions that are represented in many study groups, the range of health topics that can be studied is large and can include physical injuries such as traumatic brain injury; pain syndromes and other neurological conditions; chronic health conditions such as obesity, cancer, respiratory illnesses, and cardiovascular disease, gastrointestinal illnesses such as irritable bowel syndrome, infectious diseases such as H1N1 influenza and hepatitis C, psychiatric conditions such as post traumatic stress syndrome, depression, and suicide, adverse reproductive outcomes, and other health problems and concerns. Another feature of health research is that a range of study designs are employed by researchers including surveillance systems, observational studies with a case-control or cohort design, cross-sectional surveys, and randomized controlled trials. In recent years, observational studies include the large platforms of cases and controls that are identified for genome-wide association studies [1, 2]. In addition to statistical geneticists, the researchers who analyze data from genome-wide association studies and proteomics research often include persons with expertise in bioinformatics or machine learning techniques. These three features of health research (diversity of scientific disciplines, wide variety of health topics of interest, and alternative study designs) create both challenges and opportunities for researchers attempting to identify causal associations with possible etiologic agents and new therapeutic targets, so that research findings can be translated into targeted clinical interventions and evidence-based therapies. For example, in studies with an observational design, where assignment of exposures is not under control of the investigators, assessments of causality can be more challenging than in randomized trials [3, 4]. Investigations into the distribution and determinants of health conditions attempt to gain new knowledge through observation and inductive logic. Causal criteria commonly cited in epidemiology include temporal order of exposure and disease, biologic gradient or dose-response curve, biologic plausibility, biologic coherence, and consistency of findings, although some authors have recommended subsets of the criteria or refined definitions [5-7]. The strength of the observed association is also important in some assessments of causality. Criteria for causal criteria are widely used as a heuristic aid for assessing whether associations observed in epidemiologic research are causal although criteria-based methods provide only general guidelines for assessing the causality of associations rather than a strict checklist for identifying a causal relationship [3, 4]. The model of sufficient component causes [8] is widely used in epidemiology as a framework for teaching and understanding multicausality. A sufficient component cause is made up of a number of components, no one of which is sufficient for the disease or adverse health condition on its own [4, 8]. Diseases and adverse health conditions can be caused by more than one causal mechanism and each causal mechanism involves the combined action of several component causes. For example, both genetic factors and environmental exposures may have a role in the development of neurologic conditions such as amyotrophic lateral sclerosis. Other examples of diseases caused by interactions between genes and environment include complex, common diseases such as cancer, coronary heart disease, and diabetes [1]. A large and growing literature has dealt with statistical modeling approaches for estimating causal parameters or identifying causal associations using data from observational studies [9-13]. However, much of this important literature has not dealt directly with the special challenges that arise in causal assessments of data from genome-wide association studies including information about environmental exposures. Recent advances in genetics have challenged traditional frameworks for causal inference in observational research [14]. The goal of this article is to consider challenges that arise in causal assessments of data from genome-wide association studies, which utilize high throughput genotyping technologies to analyze biological specimens collected from large numbers of cases and controls for up to one million single nucleotide polymorphisms (SNPs) [1, 2]. Before considering those challenges, I briefly discuss key developments in quantitative models for causal analysis: counterfactual analysis and graphical causal models and structural equations modeling. I then provide a summary of quantitative techniques for analyzing data from genome-wide association studies and related gene expression and proteomic data, and offer some recommendations for causal assessments of results from such studies.

CAUSAL GRAPHICAL MODELS IN SYSTEMS GENETICS: A UNIFIED FRAMEWORK FOR JOINT INFERENCE OF CAUSAL NETWORK AND GENETIC ARCHITECTURE FOR CORRELATED PHENOTYPES.

Causal inference approaches in systems genetics exploit quantitative trait loci (QTL) genotypes to infer causal relationships among phenotypes. The genetic architecture of each phenotype may be complex, and poorly estimated genetic architectures may compromise the inference of causal relationships among phenotypes. Existing methods assume QTLs are known or inferred without regard to the phenotype network structure. In this paper we develop a QTL-driven phenotype network method (QTLnet) to jointly infer a causal phenotype network and associated genetic architecture for sets of correlated phenotypes. Randomization of alleles during meiosis and the unidirectional influence of genotype on phenotype allow the inference of QTLs causal to phenotypes. Causal relationships among phenotypes can be inferred using these QTL nodes, enabling us to distinguish among phenotype networks that would otherwise be distribution equivalent. We jointly model phenotypes and QTLs using homogeneous conditional Gaussian regression models, and we derive a graphical criterion for distribution equivalence. We validate the QTLnet approach in a simulation study. Finally, we illustrate with simulated data and a real example how QTLnet can be used to infer both direct and indirect effects of QTLs and phenotypes that co-map to a genomic region.

Detecting the presence and absence of causal relationships between expression of yeast genes with very few samples.

Inference of biological networks from high-throughput data is a central problem in bioinformatics. Particularly powerful for network reconstruction is data collected by recent studies that contain both genetic variation information and gene expression profiles from genetically distinct strains of an organism. Various statistical approaches have been applied to these data to tease out the underlying biological networks that govern how individual genetic variation mediates gene expression and how genes regulate and interact with each other. Extracting meaningful causal relationships from these networks remains a challenging but important problem. In this article, we use causal inference techniques to infer the presence or absence of causal relationships between yeast gene expressions in the framework of graphical causal models. We evaluate our method using a well studied dataset consisting of both genetic variations and gene expressions collected over randomly segregated yeast strains. Our predictions of causal regulators, genes that control the expression of a large number of target genes, are consistent with previously known experimental evidence. In addition, our method can detect the absence of causal relationships and can distinguish between direct and indirect effects of variation on a gene expression level.

Graphical Causal Modeling of Protein Structural and Dynamical Features

The causal relationship between protein structural features and conformational dynamics is difficult to isolate experimentally because even seemingly small perturbations, such as point mutations, can simultaneously alter many physical properties of proteins. Using molecular dynamics simulation trajectories for a series of point mutations at a single solvent-exposed position on the protein GB1, for which experimental NMR spin relaxation data also are available [1], effects of various types of inter-residue interactions are isolated via a graph-theory-based approach to causal modeling [2] previously applied in the biological sciences mainly to functional MRI studies [3] and genomics [4]. This approach produces directed acyclic graphs (DAGs) in which protein structural features such as hydrogen bonds, inter-residue contacts, and order parameters are encoded as nodes; the presence of an edge in the graph implies a causal relationship between features and the directionality of the edge implies the direction of causation.[1] Mayer, KL et al. (2003). Nat. Struct. Biol. 10: 962-965.[2] Pearl, J. (2000). Cambridge University Press, London; Pearl, J. (2009). Statistics Surveys. 3:96-146; Spirtes et al. (2000). MIT Press, Cambridge.[3] Eichler, M. (2005). Phil. Trans. R. Soc. B. 360(1457): 953-967.[4] Maathius, MH et al. (2009). Ann. Stat. 37(6A): 3133-3164.

Graphical causal models and VARs: an empirical assessment of the real business cycles hypothesis

This paper assesses the empirical plausibility of the real business cycle view that shocks to real variables are the dominant sources of economic fluctuations and that monetary policy shocks play an insignificant role in determining the behavior of real variables. I reconsider the vector autoregressive model of King et al. (Am Econ Rev 81:819–840, 1991), but propose an alternative identification method, based on graphical causal models. This method selects the contemporaneous causal structure using the information incorporated in the partial correlations among the residuals. The residuals orthogonalization which follows and the study of the impulse response functions confirm the results of King et al. (Am Econ Rev 81:819–840, 1991): permanent productivity shocks are not the dominant sources of aggregate fluctuations in US economy.