We developed a tool for detecting domain shifts, namely subtle differences in the probability distributions of datasets. We identify these shifts using an algorithm designed to detect localised density anomalies in high-dimensional feature spaces. If an anomaly is present, we then identify the feature subspace in which the anomaly is most pronounced. This allows us to trace the domain shift to a small set of features, making the shift interpretable. Moreover, we provide a protocol for compensating domain shifts by extracting, from two unlabelled datasets, subsets of samples with no detectable residual distributional difference. We validate the framework on controlled 20-dimensional benchmarks with known ground truth, recovering both broad and localized shifts together with their supporting feature subspaces. We then apply it to healthy electrocardiogram (ECG) recordings represented by 782 features. In age- and sex-matched cohort comparisons differing in measurement-device composition, the method detects device-induced shifts, extracts representative subsets enriched in the imbalanced device components, and identifies ECG features associated with the acquisition contrast. These results suggest that density-shift detection and subspace attribution provide a practical framework for uncovering hidden cohort biases before downstream modelling.

Consider the problem of improving the estimation of conditional average treatment effects (CATE) for a target domain of interest by leveraging related information from a source domain with a different feature space. This heterogeneous transfer learning problem for CATE estimation is ubiquitous in areas such as healthcare where we may wish to evaluate the effectiveness of a treatment for a new patient population for which different clinical covariates and limited data are available. In this paper, we address this problem by introducing several building blocks that use representation learning to handle the heterogeneous feature spaces and a flexible multi-task architecture with shared and private layers to transfer information between potential outcome functions across domains. Then, we show how these building blocks can be used to recover transfer learning equivalents of the standard CATE learners. On a new semi-synthetic data simulation benchmark for heterogeneous transfer learning we not only demonstrate performance improvements of our heterogeneous transfer causal effect learners across datasets, but also provide insights into the differences between these learners from a transfer perspective.

We introduce ParK, a new large-scale solver for kernel ridge regression. Our approach combines partitioning with random projections and iterative optimization to reduce space and time complexity while provably maintaining the same statistical accuracy. In particular, constructing suitable partitions directly in the feature space rather than in the input space, we promote orthogonality between the local estimators, thus ensuring that key quantities such as local effective dimension and bias remain under control. We characterize the statistical-computational tradeoff of our model, and demonstrate the effectiveness of our method by numerical experiments on large-scale datasets.