Representation learning and causality are fundamental research areas in machine learning and artificial intelligence. Identifiability is a critical concept in both fields: it determines whether underlying factors of variation can be uniquely reconstructed from data in representation learning, and specifies the conditions for answering causal queries unambiguously in causal inference. Causal Representation Learning (CRL) combines these two fields to seek latent representations that support causal reasoning. Recent theoretical advances in CRL have focused on the identifiability of a ground truth causal model. In this research proposal, I present two projects aimed at investigating previously unexplored aspects of CRL.

The first project aims to challenge the assumption of a unique ground truth causal model, by acknowledging that the same causal system can be described using different variables or levels of abstraction. To address this, we plan to investigate novel notions of identifiability, where the true model is reconstructed up to classes of causal abstractions consistently describing the system at different resolutions. We will also search for conditions under which these models can be learned based on available measurements. By doing so, we aim to clarify the conceptual foundations of CRL and inspire the development of new algorithms.

The second project aims to investigate latent causal modelling in targeted experiment, exploiting the rich experimental data and partial knowledge available in scientific domains to refine the CRL problem. Specifically, we will focus on neuroimaging experiments with treatment and control groups, with the objective of isolating the impact of covariates specific to the treatment group on functional brain data, disentangling it from responses elicited by the experimental protocol, shared across both groups. An additional difficulty stems from the variability in the coordinatizations of brain functional activities across different subjects due to anatomical differences. We plan to extend our previous work on group studies in neuroimaging to address these challenges. The outcome of this project could have a significant impact on scientific applications of machine learning, also beyond cognitive neuroscience.

In summary, my proposed research projects have the potential to advance the state-of-the-art in Causal Representation Learning, clarifying its conceptual foundations and enabling its application to real-world problems.