Papers by Naftali Weinberger
Philosophy of Science, Jan 12, 2022
Dynamical models of cognition have played a central role in recent cognitive science. In this pap... more Dynamical models of cognition have played a central role in recent cognitive science. In this paper, we consider a common strategy by which dynamical models describe their target systems neither as purely static nor as purely dynamic, but rather using a hybrid approach. This hybridity reveals how dynamical models involve representational choices that are important for understanding the relationship between dynamical and non-dynamical representations of a system.
Recently developed graphical causal modeling techniques significantly downplay the role of time i... more Recently developed graphical causal modeling techniques significantly downplay the role of time in causal inference. Time plays no role in the criteria specifying what it means for causal hypotheses to be observationally equivalent, and the probabilistic criteria used fail to distinguish among hypotheses that-given the assumption that causal variables precede effect variablesinvolve different time orderings among the variables. Additionally, the causal Markov condition-a central condition for choosing among causal hypotheses given a joint probability distribution-most straightforwardly applies to cases in which the variables are sampled from time-stationary distributions. Finally, it is commonplace to present models in which the variables are not explicitly indexed to times. The lack of emphasis on time in causal models may suggest that the models are neutral with respect to the temporal relationships among the causal variables. Here I propose that, in fact, the lack of reference to time in many causal models is a legacy of the fact that causal models were initially designed to model the relationships in simultaneous equations models. Simultaneous equations represent the stable long-term relationships among the modeled variables rather than the shorter-term dynamic of systems in which variables have not reached stable values. Rather than being neutral with respect to the temporal relations among the variables, many apparently atemporal causal models in fact apply only under specific temporal assumptions about the timescale at which the system is being modeled. After spelling out the interpretation of causal models as applying to systems that are treated as static, I consider ways that these models can be generalized to model the dynamics of systems that are away from equilibrium. First, I show how the dynamic causal models developed by Iwasaki and Simon (1994) generalize the causal ordering method from Simon (1977), which had been
Reintroducing Dynamics into Static Causal Models
Time and Causality across the Sciences
In this chapter I consider ways in which contemporary graphical causal models can be extended to ... more In this chapter I consider ways in which contemporary graphical causal models can be extended to model systems with complex temporal dynamics. I propose that the present limitations of many contemporary causal models in representing such dynamics are a legacy of their original application to simultaneous equations for long-term equilibrium relationships. Iwasaki and Simon (1994) provide a way of generalizing causal models to represent the dynamics of systems that are away from equilibrium. I clarify the temporal relationships among the variables in dynamic causal models, and illustrate how these relationships relate to those studied by time-series econometricians.
Causal representations are distinguished from non-causal ones by their ability to predict the res... more Causal representations are distinguished from non-causal ones by their ability to predict the results of interventions. This widely-accepted view suggests the following adequacy condition for causal models: a causal model is adequate only if it does not contain variables regarding which it makes systematically false predictions about the results of interventions. Here I argue that this condition should be rejected. For a class of equilibrium systems, there will be two incompatible causal models depending on whether one intervenes upon a certain variable to fix its value, or 'lets go' of the variable and allows it to vary. The latter model will fail to predict the result of interventions on the let-go-of variable. I argue that there is no basis for preferring one of these models to the other, and thus that models failing to predict interventions on particular variables can be just as adequate as those making no such false predictions. This undermines a key argument (Dash, 2003) against relying upon causal models inferred from equilibrium data. Dynamic causal models (Iwasaki and Simon, 1994; Voortman et al., 2012; Blom et al., 2020) provide graphical tools for representing and inferring the causal relationships in systems that are away from equilibrium. While standard causal modeling methods (Pearl, 2009; Spirtes et al., 2000) suffice for systems at equilibrium, dynamic causal models further employ time-derivatives and differential equations to represent the feedback loops by which dynamical systems maintain their equilibrium states. Dynamic causal models would initially appear to provide a generalization of causal models that, while important, could nevertheless be put to the side when studying systems at equilibrium. Yet Dash (2003) argues that, for a class of dynamical systems, the causal models one would infer from sampling their variables only at equilibrium will falsely represent the system's causal relationships, and dynamic causal models enable one to specify which these are. On this picture, rather that being a complement to equilibrium models, dynamic causal models serve as substitute, since for some systems only the dynamic model is adequate. In what follows, I will argue that Dash misdiagnoses the flaw with equilibrium models, and that correcting this misdiagnosis is crucial for understanding the adequacy conditions of causal models more generally. Causal representations are distinguished from non-causal ones by their ability to predict the results of interventions. Interventions are typically modeled using the do-operator, which, when applied to a variable, breaks all of (and only) the causal arrows going into it. While the do-operator is a formal operation, it can be used to predict the outcome of physical interventions meeting certain causal conditions about how the intervention influences 1 brought to you by CORE View metadata, citation and similar papers at core.ac.uk
Discussions of the causal status of race focus on the question of whether race itself can be expe... more Discussions of the causal status of race focus on the question of whether race itself can be experimentally manipulated. Yet many experiments testing for racial discrimination do not manipulate race, but rather a signal by which race influences an outcome. Such signal manipulations are easily formalized, though contexts of discrimination introduce an additional issue. Whether a signal counts as a signal for race is not merely a causal question, but depends on sociological and normative issues regarding discrimination. The notion of signal manipulation enables one to take these issues into account while still using causal counterfactual tests to detect discrimination.
Studies in History and Philosophy of Science Part A, 2020
Minds and Machines, 2017
Mechanist philosophers have examined several strategies scientists use for discovering causal mec... more Mechanist philosophers have examined several strategies scientists use for discovering causal mechanisms in neuroscience. Findings about the anatomical organization of the brain play a central role in several such strategies. Little attention has been paid, however, to the use of network analysis and causal modeling techniques for mechanism discovery. In particular, mechanist philosophers have not explored whether and how these strategies incorporate information about the anatomical organization of the brain. This paper clarifies these issues in the light of the distinction between structural, functional and effective connectivity. Specifically, we examine two quantitative strategies currently used for causal discovery from functional neuroimaging data: dynamic causal modeling and probabilistic graphical modeling. We show that dynamic causal modeling uses findings about the brain's anatomical organization to improve the statistical estimation of parameters in an already specified causal model of the target brain mechanism. Probabilistic graphical modeling, in contrast, makes no appeal to the brain's anatomical organization, but lays bare the conditions under which correlational data suffice to license reliable inferences about the causal organization of a target brain mechanism. The question of whether findings about the anatomical organization of the brain can and should constrain the inference of causal networks remains open, but we show how the tools supplied by graphical modeling methods help to address it.
The British Journal for the Philosophy of Science, 2016
Recent approaches to causal modeling rely upon the Causal Markov Condition, which specifies which... more Recent approaches to causal modeling rely upon the Causal Markov Condition, which specifies which probability distributions are compatible with a Directed Acyclic Graph (DAG). Further principles are required in order to choose among the large number of DAGs compatible with a given probability distribution. Here we present a principle that we call frugality. This principle tells one to choose the DAG with the fewest causal arrows. We argue that frugality has several desirable properties compared to the other principles that have been suggested, including the well-known Causal Faithfulness Condition.
If intelligence is a cause, it is a within-subjects cause
Theory & Psychology, 2015
Borsboom, Mellenbergh, and van Heerden argue that latent variables such as intelligence should be... more Borsboom, Mellenbergh, and van Heerden argue that latent variables such as intelligence should be given a between-subjects causal interpretation, but not a within-subjects causal interpretation. That is, while intelligence is a cause of one subject’s doing better than another on an IQ test, there is no non-comparative sense in which intelligence – as standardly measured – is a cause of an individual’s performance. Here I expand upon Pearl’s discussion of Simpson’s paradox to show that there cannot be a cause in a population that is not a cause in at least one of its members and that, consequently, causal variables cannot have an exclusively between-subjects interpretation. The illusion that they can results from not properly distinguishing between causal and non-causal models.
Erkenntnis, 2017
Within the causal modeling literature, debates about the Causal Faithfulness Condition (CFC) have... more Within the causal modeling literature, debates about the Causal Faithfulness Condition (CFC) have concerned whether it is probable that the parameters in causal models will have values such that distinct causal paths will cancel. As the parameters in a model are fixed by the probability distribution over its variables, it is initially puzzling what it means to assign probabilities to these parameters. I propose that to assign a probability to a parameter in a model is to treat that parameter as a function of a variable in an augmented model. By combining this proposal with widely adopted principles regarding which variables must be included in a model, I argue that the various proposed counterexamples to CFC involving coordinated parameters are not genuine counterexamples. I then consider the cases in which CFC fails due not to coordination, but by coincidence, and propose explanatory and predictive bases for ruling out such coincidences without presuming that they are improbable. The aim of the proposed defenses is not to show that CFC never fails, but rather to argue that its use in a particular context may be defended using general modeling assumptions rather than by relying on claims about how often it fails.
Philosophy of Science, 2020
A common strategy for simplifying complex systems involves partitioning them into subsystems whos... more A common strategy for simplifying complex systems involves partitioning them into subsystems whose behaviors are roughly independent of one another at shorter timescales. Dynamic causal models clarify how doing so reveals a system’s nonequilibrium causal relationships. Here I use these models to elucidate the idealizations and abstractions involved in representing a system at a timescale. The models reveal that key features of causal representations—such as which variables are exogenous—may vary with the timescale at which a system is considered. This has implications for debates regarding which systems can be represented causally.
Economics and Philosophy, 2022
Markus (2021) argues that the causal modelling frameworks of Pearl and Rubin are not ‘strongly eq... more Markus (2021) argues that the causal modelling frameworks of Pearl and Rubin are not ‘strongly equivalent’, in the sense of saying ‘the same thing in different ways’. Here I rebut Markus’ arguments against strong equivalence. The differences between the frameworks are best illuminated not by appeal to their causal semantics, but rather reflect pragmatic modelling choices.
Philosophy of Science, 2022
Dynamical models of cognition have played a central role in recent cognitive science. In this pap... more Dynamical models of cognition have played a central role in recent cognitive science. In this paper, we consider a common strategy by which dynamical models describe their target systems neither as purely static nor as purely dynamic, but rather using a hybrid approach. This hybridity reveals how dynamical models involve representational choices that are important for understanding the relationship between dynamical and non-dynamical representations of a system.
Synthese, 2017
Some recent accounts of constitutive relevance have identified mechanism components with entities... more Some recent accounts of constitutive relevance have identified mechanism components with entities that are causal intermediaries between the input and output of a mechanism. I argue that on such accounts there is no distinctive inter-level form of mechanistic explanation and that this highlights an absence in the literature of a compelling argument that there are such explanations. Nevertheless, the entities that these accounts call 'components' do play an explanatory role. Studying causal intermediaries linking variables X and Y provides knowledge of the counterfactual conditions under which X will continue to bring about Y . This explanatory role does not depend on whether intermediate variables count as components. The question of whether there are distinctively mechanistic explanations remains open.
The British Journal for the Philosophy of Science, 2017
A cause may influence its effect via multiple paths. Paradigmatically (Hesslow, 1974), taking bir... more A cause may influence its effect via multiple paths. Paradigmatically (Hesslow, 1974), taking birth control pills both decreases one's risk of thrombosis by preventing pregnancy and increases it by producing a blood chemical. Building on Pearl ( ), I explicate the notion of a path-specific effect. Roughly, a path-specific effect of C on E via path P is the degree to which a change in C would change E were they to be transmitted only via P. Facts about such effects may be gleaned from the structural equations commonly used to represent the causal relationships among variables. I contrast my analysis of the Hesslow case with those given by theorists of probabilistic causality, who mistakenly link it to issues of causal heterogeneity, token-causation and indeterminism. The reason probabilistic theories misdiagnose this case is that they pay inadequate attention to the structural relationships among variables.
Erkenntnis
Causal representations are distinguished from non-causal ones by their ability to predict the res... more Causal representations are distinguished from non-causal ones by their ability to predict the results of interventions. This widely-accepted view suggests the following adequacy condition for causal models: a causal model is adequate only if it does not contain variables regarding which it makes systematically false predictions about the results of interventions. Here I argue that this condition should be rejected. For a class of equilibrium systems, there will be two incompatible causal models depending on whether one intervenes upon a certain variable to fix its value, or ‘lets go’ of the variable and allows it to vary. The latter model will fail to predict the result of interventions on the let-go-of variable. I argue that there is no basis for preferring one of these models to the other, and thus that models failing to predict interventions on particular variables can be just as adequate as those making no such false predictions. This undermines a key argument (Dash in Caveats f...
Erkenntnis
Causal representations are distinguished from non-causal ones by their ability to predict the res... more Causal representations are distinguished from non-causal ones by their ability to predict the results of interventions. This widely-accepted view suggests the following adequacy condition for causal models: a causal model is adequate only if it does not contain variables regarding which it makes systematically false predictions about the results of interventions. Here I argue that this condition should be rejected. For a class of equilibrium systems, there will be two incompatible causal models depending on whether one intervenes upon a certain variable to fix its value, or 'lets go' of the variable and allows it to vary. The latter model will fail to predict the result of interventions on the let-go-of variable. I argue that there is no basis for preferring one of these models to the other, and thus that models failing to predict interventions on particular variables can be just as adequate as those making no such false predictions. This undermines a key argument (Dash, 2003) against relying upon causal models inferred from equilibrium data.
Simpson's Paradox
Stanford Encyclopedia of Philosophy, 2021
Simpson’s Paradox is a statistical phenomenon where an association between two variables in a pop... more Simpson’s Paradox is a statistical phenomenon where an association between two variables in a population emerges, disappears or reverses when the population is divided into subpopulations. For instance, two variables may be positively associated in a population, but be independent or even negatively associated in all subpopulations. Cases exhibiting the paradox are unproblematic from the perspective of mathematics and probability theory, but nevertheless strike many people as surprising. Additionally, the paradox has implications for a range of areas that rely on probabilities, including decision theory, causal inference, and evolutionary biology. Finally, there are many instances of the paradox, including in epidemiology and in studies of discrimination, where understanding the paradox is essential for drawing the correct conclusions from the data.
The following article provides a mathematical analysis of the paradox, explains its role in causal reasoning and inference, compares theories of what makes the paradox seem paradoxical, and surveys its applications in different domains.
Philosophy of Science
Dynamical models of cognition have played a central role in recent cog-nitive science. In this pa... more Dynamical models of cognition have played a central role in recent cog-nitive science. In this paper, we consider a common strategy by which dynamical models describe their target systems neither as purely static nor as purely dynamic, but rather using a hybrid approach. This hybrid-ity reveals how dynamical models involve representational choices that are important for understanding the relationship between dynamical and non-dynamical representations of a system.
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Papers by Naftali Weinberger
The following article provides a mathematical analysis of the paradox, explains its role in causal reasoning and inference, compares theories of what makes the paradox seem paradoxical, and surveys its applications in different domains.