Peter Spirtes, Clark Glymour and Richard Scheines. Causality From Probability.

Barry Schein proposes combining a second-order treatment of plurals with DonaldDavidson's suggestion that there are positions for reference to events in ordinary predicates inorder to account for several of the more puzzling features of ...

For nearly as long as the word “correlation” has been part of statistical parlance, students have been warned that correlation does not prove causation, and that only experimental studies, e.g., randomized clinical trials, can establish the existence of a causal relationship. Over the last few decades, somewhat of a consensus has emerged between statisticians, computer scientists, and philosophers on how to represent causal claims and connect them to probabilistic relations. One strand of this work studies the conditions under which evidence (...) accumulated from non-experimental (observational) studies can be used to infer a causal relationship. In this paper, I compare the typical conditions required to infer that one variable is a direct cause of another in observational and experimental studies. I argue that they are essentially the same. (shrink)

Richard Scheines and Wilfred Sieg. Computer Environments for Proof Construction.

In Causation, Prediction, and Search, we undertook a three part project. First, we characterized when causal models are indistinguishable by population conditional independence relations under several different assumptions relating causality to probability. Second, we proposed a number of algorithms that take sample data and optional background knowledge as input, and output a class of causal models compatible with the data and the background knowledge; the algorithms were accompanied by proofs of their correctness given assumptions that were clearly stated in CPS, (...) and that we will restate below. Finally, we offered a theory of how to predict the effects of interventions in causal structures, given only partial knowledge of causal structure. Freedman's objections are all directed against the causal inference algorithms we proposed. We do not have room here to discuss all of his criticisms, but we have answered his major points. With regard to the points we do not have room to discuss, the reader should be warned that Freedman is an unreliable interpreter of what we have written. For convenience, we have divided Freedman's objections into the following categories. 1.) Freedman questions some of the assumptions on which our correctness theorems are based. Some of his criticisms are based on covariance matrices that he constructed. None of the examples he constructed in sections 11.2, 11.3, or 12.3 are counterexamples to any theorem that we stated, nor are they even germane to the question of how probable are the assumptions we make. His examples only illustrate points discussed in detail in our book, in which we give similar examples. 2.) The most serious charge that Freedman makes is that the algorithms do not compute what we say they do. (shrink)

Clark Glymour, Richard Scheines, Peter Spirtes and Kevin Kelly. Discovering Causal Structure: Artifical Intelligence, Philosophy of Science and Statistical Modeling.

Richard Scheines, Gaea Leinhardt, Joel Smith, and Kwangsu Cho. Teaching and Learning with Online Courses.

Horror movies have discovered an easy recipe for making people creepy: alter their eyes. Instead of normal eyes, zombies’ eyes are vacantly white, vampires’ eyes glow with the color of blood, and those possessed by demons are cavernously black. In the Academy Award winning Pan’s Labyrinth, director Guillermo del Toro created the creepiest of all creatures by entirely removing its eyes from its face, placing them instead in the palms of its hands. The unease induced by altering eyes may help (...) to explain the uncanny valley, which is the eeriness of robots that are almost—but not quite—human. Much research has explored the uncanny valley, including the research reported by MacDorman & Entezari, which focuses on individual differences that might predict the eeriness of humanlike robots. In their paper, they suggest that a full understanding of this phenomenon needs to synthesize individual differences with features of the robot. One theory that links these two concepts is mind perception, which past research highlights as essential to the uncanny valley. Mind perception is linked to both individual differences—autism—and to features of the robot—the eyes—and can provide a deeper understanding of this arresting phenomenon. In this paper, we present original data that links uncanniness to the eyes through aberrant perceptions of mind. (shrink)

S There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934 ). Spirtes ( 1994), Spirtes et al. ( 1993) and Pearl & Verma ( 1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These results (...) are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables. We resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures. We show that the asymptotically consistent procedures are ‘pointwise consistent’, but ‘uniformly consistent’ tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results. We also show the nonexistence of valid, consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators. Our results make no assumption about the form of the tests or estimators. In particular, the tests could be classical independence tests, they could be Bayes tests or they could be tests based on scoring methods such as  or . The implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper. The results hinge on the following fact: it is possible to find, for each sample size n, distributions P and Q such that P and Q are empirically indistinguishable and yet P and Q correspond to different causal effects. (shrink)

The statistical community has brought logical rigor and mathematical precision to the problem of using data to make inferences about a model’s parameter values. The TETRAD project, and related work in computer science and statistics, aims to apply those standards to the problem of using data and background knowledge to make inferences about a model’s specification. We begin by drawing the analogy between parameter estimation and model specification search. We then describe how the specification of a structural equation model entails (...) familiar constraints on the covariance matrix for all admissible values of its parameters; we survey results on the equivalence of structural equation models, and we discuss search strategies for model specification. We end by presenting several algorithms that are implemented in the TETRAD II program. (shrink)

Richard Scheines and Joe Ramsey. Simulating Genetic Regulartory Networks.

The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those (...) based on the maximum likelihood solution, e.g., output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters of underidentified models, as we illustrate on a simple errors-in-variables model. (shrink)

: "In this paper we compare computerized environments in which students complete proof construction exercises in formal logic. Afterbeing given a pretest for logical aptitude, three matched groups were presented identical course material on logic for approximately five weeks by a computer. During the treatment, all students were required to complete several hundred proof construction exercises. The three groups did the exercises and the midterm in different environments. The group with a more sophisticated interface performed better on the midterm. Nearly (...) all the difference in performance showed up in the harder problems. In a follow up experiment in which flexible strategic problem solving help was added to the environment, performance improved slightly, but the data are inconclusive.". (shrink)

In a series of 5 experiments in 2000 and 2001, several hundred students at two different universities with three different professors and six different teaching assistants took a semester long course on causal and statistical reasoning in either traditional lecture/recitation or online/recitation format. In this paper we compare the pre-post test gains of these students, we identify features of the online experience that were helpful and features that were not, and we identify student learning strategies that were effective and those (...) that were not. Students who entirely replaced going to lecture with doing online modules did as well and usually better than those who went to lecture. Simple strategies like incorporating frequent interactive comprehension checks into the online material proved effective, but online students attended face-to-face recitations less often than lecture students and suffered because of it. Supporting the idea that small, interactive recitations are more effective than large, passive lectures, recitation attendance was three times as important as lecture attendance for predicting pre-test to post-test gains. For the online student, embracing the online environment as opposed to trying to convert it into a traditional print-based one was an important strategy, but simple diligence in attempting “voluntary” exercises was by far the most important factor in student success. (shrink)

Extension of the logical language to deliver plural reference and the logical relations that constitute knowledge of the singular and plural acquires empirical bite just in case it conforms with increasing precision to the syntax of the natural language and affords explanation of what speakers know about the distribution and meaning of plural expressions in their language. As for the syntax of natural language, this discussion, being none too precise, is guided throughout by just two considerations and their immediate consequences, (...) which is discussed at greater length in this article. The first, morpheme univocality, is that a morpheme despite its various syntactic and morphological contexts has a single meaning that supports all its occurrences. (shrink)

There is now substantial agreement about the representational component of a normative theory of causal reasoning: Causal Bayes Nets. There is less agreement about a normative theory of causal discovery from data, either computationally or cognitively, and almost no work investigating how teaching the Causal Bayes Nets representational apparatus might help individuals faced with a causal learning task. Psychologists working to describe how naïve participants represent and learn causal structure from data have focused primarily on learning from single trials under (...) a variety of conditions. In contrast, one component of the normative theory focuses on learning from a sample drawn from a population under some experimental or observational study regime. Through a virtual Causality Lab that embodies the normative theory of causal reasoning and which allows us to record student behavior, we have begun to systematically explore how best to teach the normative theory. In this paper we explain the overall project and report on pilot studies which suggest that students can quickly be taught to (appear to) be quite rational. (shrink)

We present an algorithm to infer causal relations between a set of measured variables on the basis of experiments on these variables. The algorithm assumes that the causal relations are linear, but is otherwise completely general: It provides consistent estimates when the true causal structure contains feedback loops and latent variables, while the experiments can involve surgical or `soft' interventions on one or multiple variables at a time. The algorithm is `online' in the sense that it combines the results from (...) any set of available experiments, can incorporate background knowledge and resolves conflicts that arise from combining results from different experiments. In addition we provide a necessary and sufficient condition that determines when the algorithm can uniquely return the true graph, and can be used to select the next best experiment until this condition is satisfied. We demonstrate the method by applying it to simulated data and the flow cytometry data of Sachs et al. (shrink)

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (shrink)

The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an intervention. We provide an account of ‘hard' and ‘soft' interventions and discuss what they can contribute to causal discovery. We also describe how the choice of the optimal intervention(s) depends heavily on the (...) particular experimental setup and the assumptions that can be made. ‡The first author is funded by the Causal Learning Collaborative Initiative supported by the James S. McDonnell Foundation. Many aspects of this paper were inspired by discussions with members of the collaborative. †To contact the authors, please write to: Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213; e-mail: [email protected] and scheines@cmu.edu. (shrink)

Practically, causation matters. Juries must decide, for example, whether a pregnant mother’s refusal to give birth by caesarean section was the cause of one of her twins death. Policy makers must decide whether violence on TV causes violence in life. Neither question can be coherently debated without some theory of causation. Fortunately (or not, depending on where one sits), a virtual plethora of theories of causation have been championed in the third of a century between 1970 and 2004.

Cruelty is such a ubiquitous and at the same time disturbing phenomenon that we take for granted that we understand what it is, and how it impacts the ways in which we think about our humanity as a moral condition—how we understand our moral significance. Cruelty: A Book About Us offers an accessible interrogation of cruelty and humanity, and, most critically, it provides a groundwork for us to raise questions collectively; it is an invitation for us all to join in (...) the dialogue. Through academic studies, literary works, and’ personal stories and observations, this book provokes deeper insights into why cruel acts trouble our usual ways of articulating and addressing wrongness. Mining interdisciplinary sources, it excavates what we may not know we don't know and guides us in conversations about this profoundly evocative and often uneasy subject. (shrink)

Previous research on the use of diagrams for argumentation instruction has highlighted, but not conclusively demonstrated, their potential benefits. We examine the relative benefits of using diagrams and diagramming tools to teach causal reasoning about public policy. Sixty-three Carnegie Mellon University students were asked to analyze short policy texts using either: 1) text only, 2) text and a pre-made, correct diagram representing the causal claims in the text, or 3) text and a diagramming tool with which to construct their own (...) causal diagram. After a pretest and training, we tested student performance on a new policy text and found that students given a correct diagram significantly outperformed the other groups. Finally, we compared learning by testing students on a third policy problem in which we removed all diagram or tool aids and found that students who constructed their own diagrams learned the most. We describe these results and interpret them in a way that foreshadows work we now plan for a cognitive-tutor on causal diagram construction. (shrink)

In Causation, Prediction, and Search (CPS hereafter), Peter Spirtes, Clark Glymour and I developed a theory of statistical causal inference. In his presentation at the Notre Dame conference (and in his paper, this volume), Glymour discussed the assumptions on which this theory is built, traced some of the mathematical consequences of the assumptions, and pointed to situations in which the assumptions might fail. Nevertheless, many at Notre Dame found the theory difficult to understand and/or assess. As a result I was (...) asked to write this paper to provide a more intuitive introduction to the theory. In what follows I shun almost all formality and avoid the numerous and complicated qualifiers that typically accompany definitions or important philosophical concepts. They can be all be found in Glymour's paper or in CPS, which are clear although sometimes dense. Here I attempt to fix intuitions by highlighting a few of the essential ideas and by providing extremely simple examples throughout. (shrink)

Researchers routinely face the problem of inferring causal relationships from large amounts of data, sometimes involving hundreds of variables. Often, it is the causal relationships between "latent" (unmeasured) variables that are of primary interest. The problem is how causal relationships between unmeasured variables can be inferred from measured data. For example, naval manpower researchers have been asked to infer the causal relations among psychological traits such as job satisfaction and job challenge from a data base in which neither trait is (...) measured directly, but in which answers to interview questions are plausibly associated with each trait. By combining background knowledge with an algorithm that searches for causal structure among the unobserved variables, we have created a tool that can reliably extract useful causal information about latent variables from large data bases. In what follows we describe the class of causal models to which our.. (shrink)

The statistical evidence for the detrimental effect of exposure to low levels of lead on the cognitive capacities of children has been debated for several decades. In this paper I describe how two techniques from artificial intelligence and statistics help make the statistical evidence for the accepted epidemiological conclusion seem decisive. The first is a variable-selection routine in TETRAD III for finding causes, and the second a Bayesian estimation of the parameter reflecting the causal influence of Actual Lead Exposure, a (...) latent variable, on the measured IQ score of middle class suburban children. (shrink)

The past two decades have seen a dramatic growth in the use of statisticians and economists for the presentation of expert testimony in legal proceedings. In this paper, we describe a hypothetical case modeled on real ones and involving statistical testimony regarding the causal effect of lead on lowering the IQs of children who ingest lead paint chips. The data we use come from a well-known pioneering study on the topic and the analyses we describe as the expert testimony are (...) similar to ones that can be found in major scientific journals. The battle of the experts in this hypothetical case resembles that which many encounter as expert witnesses. The paper concludes with some observations and advice. (shrink)

Dept. of Philosophy Center for Biomedical Center for Biomedical Dept. of Philosophy Carnegie Mellon Univ.

Linear structural equation models with latent (unmeasured) variables are used widely in sociology, psychometrics, and political science. When such models have a unidimensional..

Students can use an educational system’s help in unexpected ways. For example, they may bypass abstract hints in search of a concrete solution. This behavior has traditionally been labeled as a form of gaming or help abuse. We propose that some examples of this behavior are not abusive and that bottom-out hints can act as worked examples. We create a model for distinguishing good student use of bottom-out hints from bad student use of bottom-out hints by means of logged response (...) times. We show that this model not only predicts learning, but captures behaviors related to self-explanation. (shrink)

We present an algorithm to infer causal relations between a set of measured variables on the basis of experiments on these variables. The algorithm assumes that the causal relations are linear, but is otherwise completely general: It provides consistent estimates when the true causal structure contains feedback loops and latent variables, while the experiments can involve surgical or ‘soft’ interventions on one or multiple variables at a time. The algorithm is ‘online’ in the sense that it combines the results from (...) any set of available experiments, can incorporate background knowledge and resolves con- flicts that arise from combining results from different experiments. In addition we provide a necessary and sufficient condition that (i) determines when the algorithm can uniquely return the true graph, and (ii) can be used to select the next best experiment until this condition is satisfied. We demonstrate the method by applying it to simulated data and the flow cytometry data of Sachs et al (2005). (shrink)

Peter Spirtes, Clark Glymour, Richard Scheines, Christopher Meek, S. Fineberg, E. Slate. Prediction and Experimental Design with Graphical Causal Models.

Speaking of dental floss contaminated with bacteria, I may separate the dental floss that is sterile from the dental floss that isn’t sterile. The definite description “the dental floss that isn’t sterile” contracts its reference to just the dental floss near bacteria, although it, the dental floss whole, isn’t sterile. To accommodate the definite descriptions that contract their reference, received definitions for ⌜the Φ⌝ are amended from to read as in : ⌜the Φ⌝ refers to that which any Φ is (...) part of and is the least such. ⌜the Φ⌝ refers to that which any Φ overlaps and is the least such. If definite description is to be based on a purely logical notion of plural and mass predication, it is further amended. Like overt demonstratives—⌜this/these Φ⌝, ⌜that/those Φ⌝—any definite description in natural language is also perspectival, scanning everywhere the description Φ is satisfied:⌜the Φ⌝ refers to the least Φ that overlap Φ anywhere there is Φ. (shrink)

By combining experimental interventions with search procedures for graphical causal models we show that under familiar assumptions, with perfect data, N - 1 experiments suffice to determine the causal relations among N > 2 variables when each experiment randomizes at most one variable. We show the same bound holds for adaptive learners, but does not hold for N > 4 when each experiment can simultaneously randomize more than one variable. This bound provides a type of ideal for the measure of (...) success of heuristic approached in active learning methods of casual discovery, which currently use less informative measures. (shrink)

Horror movies have discovered an easy recipe for making people creepy: alter their eyes. Instead of normal eyes, zombies’ eyes are vacantly white, vampires’ eyes glow with the color of blood, and those possessed by demons are cavernously black. In the Academy Award winning Pan’s Labyrinth, director Guillermo del Toro created the creepiest of all creatures by entirely removing its eyes from its face, placing them instead in the palms of its hands. The unease induced by altering eyes may help (...) to explain the uncanny valley, which is the eeriness of robots that are almost—but not quite—human. Much research has explored the uncanny valley, including the research reported by MacDorman & Entezari, which focuses on individual differences that might predict the eeriness of humanlike robots. In their paper, they suggest that a full understanding of this phenomenon needs to synthesize individual differences with features of the robot. One theory that links these two concepts is mind perception, which past research highlights as essential to the uncanny valley. Mind perception is linked to both individual differences—autism—and to features of the robot—the eyes—and can provide a deeper understanding of this arresting phenomenon. In this paper, we present original data that links uncanniness to the eyes through aberrant perceptions of mind. (shrink)

Horror movies have discovered an easy recipe for making people creepy: alter their eyes. Instead of normal eyes, zombies’ eyes are vacantly white, vampires’ eyes glow with the color of blood, and those possessed by demons are cavernously black. In the Academy Award winning Pan’s Labyrinth, director Guillermo del Toro created the creepiest of all creatures by entirely removing its eyes from its face, placing them instead in the palms of its hands. The unease induced by altering eyes may help (...) to explain the uncanny valley, which is the eeriness of robots that are almost—but not quite—human. Much research has explored the uncanny valley, including the research reported by MacDorman & Entezari, which focuses on individual differences that might predict the eeriness of humanlike robots. In their paper, they suggest that a full understanding of this phenomenon needs to synthesize individual differences with features of the robot. One theory that links these two concepts is mind perception, which past research highlights as essential to the uncanny valley. Mind perception is linked to both individual differences—autism—and to features of the robot—the eyes—and can provide a deeper understanding of this arresting phenomenon. In this paper, we present original data that links uncanniness to the eyes through aberrant perceptions of mind. (shrink)

Shane Harwood and Richard Scheines. Genetic Algorithm Search Over Causal Models.

We have examined only a few of the basic questions about causal inference that result from Reichenbach's two principles. We have not considered what happens when the probability distribution is a mixture of distributions from different causal structures, or how unmeasured common causes can be detected, or what inferences can reliably be drawn about causal relations among unmeasured variables, or the exact advantages that experimental control offers. A good deal is known about these questions, and there is a good deal (...) more to find out. (shrink)

Since Fodor 1970, negation has worn a Homogeneity Condition to the effect that homogeneous predicates, ) denote homogeneously—all or nothing —to characterize the meaning of – when uttered out-of-the blue, in contrast to –:The mirrors are smooth. The mirrors are not smooth. The mirrors circle the telescope’s reflector. The mirrors do not circle the telescope’s reflector. It has been a problem for philosophical logic and for the semantics of natural language that – appear to defy the Principle of Excluded Middle (...) while – do not—Smooth ¬Smooth Circle ¬Circle. An impoverished logical form – has been the occasion to embellish all else—Boolean algebra, lexical presuppositions, Strongest Meaning Hypothesis, trivalence, supervaluation, double strengthening, etc., enriching the semantics and pragmatics with what remains a special theory of negation, which may be dismissed when the logical syntax and semantics of negation reflects that negated sentences are also tensed sentences. (shrink)

Over the last two decades, a fundamental outline of a theory of causal inference has emerged. However, this theory does not consider the following problem. Sometimes two or more measured variables are deterministic functions of one another, not deliberately, but because of redundant measurements. In these cases, manipulation of an observed defined variable may actually be an ambiguous description of a manipulation of some underlying variables, although the manipulator does not know that this is the case. In this article we (...) revisit the question of precisely characterizing conditions and assumptions under which reliable inference about the effects of manipulations is possible, even when the possibility of “ambiguous manipulations” is allowed. (shrink)

James M. Robins, Richard Scheines, Peter Spirtes, and Larry Wasserman. The Limits of Causal Knowledge.

The Carnegie Mellon Proof Tutor project was motivated by pedagogical concerns: we wanted to use a "mechanical" (i.e. computerized) tutor for teaching students..

Clark Glymour, Richard Scheines, Peter Spirtes, and Christopher Meek. Regression and Causation.

Although learning from multiple representations has been shown to be effective in a variety of domains, little is known about the mechanisms by which it occurs. We analyzed log data on error-rate, hint-use, and time-spent obtained from two experiments with a Cognitive Tutor for fractions. The goal of the experiments was to compare learning from multiple graphical representations of fractions to learning from a single graphical representation. Finding that a simple statistical model did not fit data from either experiment, we (...) searched over all possible mediation models consistent with background knowledge, finding several that fit the data well. We also searched over alternative measures of student error-rate, hint-use, and time-spent to see if our data were better modeled with simple monotonic or u-shaped non-monotonic relationships. We found no evidence for non-monotonicity. No matter what measures we used, time-spent was irrelevant, and hint-use was only occasionally relevant. Although the total effect of multiple representations on learning was positive, they also had a negative effect on learning, mediated by a higher error-rate. Our evidence suggests that multiple representations increase error-rate, which in turn inhibits learning. The mechanisms by which multiple representations improve learning are as yet unmodeled. (shrink)