Deconfounding and Causal Regularisation for Stability and External Validity

Distributional anchor regression

Prediction models often fail if train and test data do not stem from the same distribution. Out-of-distribution (OOD) generalization to unseen, perturbed test data is a desirable but difficult-to-achieve property for prediction models and in general requires strong assumptions on the data generating process (DGP). In a causally inspired perspective on OOD generalization, the test data arise from a specific class of interventions on exogenous random variables of the DGP, called anchors. Anchor regression models, introduced by Rothenhäusler et al. (J R Stat Soc Ser B 83(2):215-246, 2021. 10.1111/rssb.12398), protect against distributional shifts in the test data by employing causal regularization. However, so far anchor regression has only been used with a squared-error loss which is inapplicable to common responses such as censored continuous or ordinal data. Here, we propose a distributional version of anchor regression which generalizes the method to potentially censored responses with at least an ordered sample space. To this end, we combine a flexible class of parametric transformation models for distributional regression with an appropriate causal regularizer under a more general notion of residuals. In an exemplary application and several simulation scenarios we demonstrate the extent to which OOD generalization is possible.

Ridge Penalization in High-Dimensional Testing With Applications to Imaging Genetics

High-dimensionality is ubiquitous in various scientific fields such as imaging genetics, where a deluge of functional and structural data on brain-relevant genetic polymorphisms are investigated. It is crucial to identify which genetic variations are consequential in identifying neurological features of brain connectivity compared to merely random noise. Statistical inference in high-dimensional settings poses multiple challenges involving analytical and computational complexity. A widely implemented strategy in addressing inference goals is penalized inference. In particular, the role of the ridge penalty in high-dimensional prediction and estimation has been actively studied in the past several years. This study focuses on ridge-penalized tests in high-dimensional hypothesis testing problems by proposing and examining a class of methods for choosing the optimal ridge penalty. We present our findings on strategies to improve the statistical power of ridge-penalized tests and what determines the optimal ridge penalty for hypothesis testing. The application of our work to an imaging genetics study and biological research will be presented.