Conditionally-additive-noise Models for Structure Learning
This work addresses the challenge of causal structure learning in complex systems, offering a more flexible and assumption-free approach for researchers in causal inference and machine learning.
The paper tackles the problem of inferring causal direction between variables in multivariate systems by extending additive-noise models to conditionally-additive-noise models, introducing regression-free independence tests based on conditional variances, and deriving a criterion that works without assumptions on equation forms or hidden variables.
Constraint-based structure learning algorithms infer the causal structure of multivariate systems from observational data by determining an equivalent class of causal structures compatible with the conditional independencies in the data. Methods based on additive-noise (AN) models have been proposed to further discriminate between causal structures that are equivalent in terms of conditional independencies. These methods rely on a particular form of the generative functional equations, with an additive noise structure, which allows inferring the directionality of causation by testing the independence between the residuals of a nonlinear regression and the predictors (nrr-independencies). Full causal structure identifiability has been proven for systems that contain only additive-noise equations and have no hidden variables. We extend the AN framework in several ways. We introduce alternative regression-free tests of independence based on conditional variances (cv-independencies). We consider conditionally-additive-noise (CAN) models, in which the equations may have the AN form only after conditioning. We exploit asymmetries in nrr-independencies or cv-independencies resulting from the CAN form to derive a criterion that infers the causal relation between a pair of variables in a multivariate system without any assumption about the form of the equations or the presence of hidden variables.