Causal Representation Learning

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data, such as image pixels. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as identifiability. A recent breakthrough explores identifiability by leveraging the change of causal influences among latent causal variables across multiple environments.

Identifiable Latent Polynomial Causal Models Through the Lens of Change

The task of causal representation learning aims to uncover latent higher-level causal representations that affect lower-level observations. Identifying true latent causal representations from observed data, while allowing instantaneous causal relations among latent variables, remains a challenge. In this work, we introduce a novel identifiability condition where the underlying latent causal model satisfies a polynomial model and noise distributions conform to the exponential family. Under some mild assumptions, we can show that the latent causal representations can be identified up to trivial permutation and scaling. Additionally, we investigate the necessity of imposing changes on all causal parameters and present partial identifiability results when part of them remains unchanged. Further, we propose a novel empirical estimation method, grounded in our theoretical finding, that enables learning consistent latent causal representations. [pdf]

Identifiable Latent Neural Causal Models

Causal representation learning seeks to uncover latent, high-level causal representations from low-level observed data. It is particularly good at predictions under unseen distribution shifts, because these shifts can generally be interpreted as consequences of interventions. Hence leveraging seen distribution shifts becomes a natural strategy to help identify causal representations, which in turn benefits predictions where distributions are previously unseen. Determining the types (or conditions) of such distribution shifts that do contribute to the identifiability of causal representations is critical. This work establishes a sufficient and necessary condition characterizing the types of distribution shifts for identifiability in the context of latent additive noise models. Furthermore, we present partial identifiability results when only a portion of distribution shifts meets the condition. In addition, we extend our findings to latent post-nonlinear causal models. [pdf]

Identification of Nonlinear Latent Hierarchical Models

In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of both causal structure and latent variables can be achieved under mild assumptions: on causal structures, we allow for the existence of multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we do not make parametric assumptions, thus permitting general nonlinearity and multi-dimensional continuous variables. Specifically, we first develop a basic identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. [pdf]