Caveats for Causal Reasoning with Equilibrium Models

This thesis raises objections to the use of causal reasoning with equilibrium models. I consider two operators that are used to transform models: the {em Do} operator for modeling manipulation and the {em Equilibration} operator for modeling a system that has achieved equilibrium. I introduce a property of a causal model called the {em EMC Property} that is true iff the {em Do} operator commutes with the {em Equilibration} operator. I prove that not all models obey the EMC property, and I demonstrate empirically that when inferring a causal model from data, the learned model will not support causal reasoning if the EMC property is not obeyed. I find sufficient conditions for models to violate and not to violate the EMC property. In addition, I show that there exists a class of models that violate EMC and possess a set of variables whose manipulation will cause an instability in the system. All dynamic models in this class possess feedback, although I do not prove that feedback is a necessary or a sufficient condition for EMC violation. I define the {em Structural Stability Principle} which provides a necessary graphical criterion for stability in causal models. I will argue that the models in this class are quite common given typical assumptions about causal relations

Causal Consistency of Structural Equation Models

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.Comment: equal contribution between Rubenstein and Weichwald; accepted manuscrip

Intervening and Letting Go: Understanding Dynamic Causal Models

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

Intervening and Letting Go: On the Adequacy of Equilibrium Causal Models

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

Near-Decomposability and the Timescale Relativity of Causal Representations

A common strategy for simplifying complex systems involves partitioning them into subsystems whose behaviors are roughly independent of one another at shorter time-scales. Dynamic causal models (Iwasaki and Simon, 1994) explain how doing so reveals a system's non-equilibrium causal relationships. Here I use these models to elucidate the idealizations and abstractions involved in representing a system at a time-scale. The models reveal that key features of causal representations - such as which variables are exogenous - may vary with the time-scale at which a system is considered. This has implications for debates regarding which systems can be understood causally

A Constraint Optimization Approach to Causal Discovery from Subsampled Time Series Data

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