Constrained Identifiability of Causal Effects

We study the identification of causal effects in the presence of different types of constraints (e.g., logical constraints) in addition to the causal graph. These constraints impose restrictions on the models (parameterizations) induced by the causal graph, reducing the set of models considered by the identifiability problem. We formalize the notion of constrained identifiability, which takes a set of constraints as another input to the classical definition of identifiability. We then introduce a framework for testing constrained identifiability by employing tractable Arithmetic Circuits (ACs), which enables us to accommodate constraints systematically. We show that this AC-based approach is at least as complete as existing algorithms (e.g., do-calculus) for testing classical identifiability, which only assumes the constraint of strict positivity. We use examples to demonstrate the effectiveness of this AC-based approach by showing that unidentifiable causal effects may become identifiable under different types of constraints.

Modeling and Discovering Direct Causes for Predictive Models

We introduce a causal modeling framework that captures the input-output behavior of predictive models (e.g., machine learning models) by representing it using causal graphs. The framework enables us to define and identify features that directly cause the predictions, which has broad implications for data collection and model evaluation. We show two assumptions under which the direct causes can be discovered from data, one of which further simplifies the discovery process. In addition to providing sound and complete algorithms, we propose an optimization technique based on an independence rule that can be integrated with the algorithms to speed up the discovery process both theoretically and empirically.

Identifying Causal Effects Under Functional Dependencies

We study the identification of causal effects, motivated by two improvements to identifiability which can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Second, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure which removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects.

Tractable Bounding of Counterfactual Queries by Knowledge Compilation

We discuss the problem of bounding partially identifiable queries, such as counterfactuals, in Pearlian structural causal models. A recently proposed iterated EM scheme yields an inner approximation of those bounds by sampling the initialisation parameters. Such a method requires multiple (Bayesian network) queries over models sharing the same structural equations and topology, but different exogenous probabilities. This setup makes a compilation of the underlying model to an arithmetic circuit advantageous, thus inducing a sizeable inferential speed-up. We show how a single symbolic knowledge compilation allows us to obtain the circuit structure with symbolic parameters to be replaced by their actual values when computing the different queries. We also discuss parallelisation techniques to further speed up the bound computation. Experiments against standard Bayesian network inference show clear computational advantages with up to an order of magnitude of speed-up.

On the Complexity of Counterfactual Reasoning

We study the computational complexity of counterfactual reasoning in relation to the complexity of associational and interventional reasoning on structural causal models (SCMs). We show that counterfactual reasoning is no harder than associational or interventional reasoning on fully specified SCMs in the context of two computational frameworks. The first framework is based on the notion of treewidth and includes the classical variable elimination and jointree algorithms. The second framework is based on the more recent and refined notion of causal treewidth which is directed towards models with functional dependencies such as SCMs. Our results are constructive and based on bounding the (causal) treewidth of twin networks -- used in standard counterfactual reasoning that contemplates two worlds, real and imaginary -- to the (causal) treewidth of the underlying SCM structure. In particular, we show that the latter (causal) treewidth is no more than twice the former plus one. Hence, if associational or interventional reasoning is tractable on a fully specified SCM then counterfactual reasoning is tractable too. We extend our results to general counterfactual reasoning that requires contemplating more than two worlds and discuss applications of our results to counterfactual reasoning with a partially specified SCM that is coupled with data. We finally present empirical results that measure the gap between the complexities of counterfactual reasoning and associational/interventional reasoning on random SCMs.