Geometric Characterisation and Structured Trajectory Surrogates for Clinical Dataset Condensation

Given a dataset of finitely many elements $\mathcal{T} = \{\mathbf{x}_i\}_{i = 1}^N$, the goal of dataset condensation (DC) is to construct a synthetic dataset $\mathcal{S} = \{\tilde{\mathbf{x}}_j\}_{j = 1}^M$ which is significantly smaller ($M \ll N$) such that a model trained from scratch on $\mathcal{S}$ achieves comparable or even superior generalization performance to a model trained on $\mathcal{T}$. Recent advances in DC reveal a close connection to the problem of approximating the data distribution represented by $\mathcal{T}$ with a reduced set of points. In this work, we present a unified framework that encompasses existing DC methods and extend the task-specific notion of DC to a more general and formal definition using notions of discrepancy, which quantify the distance between probability distribution in different regimes. Our framework broadens the objective of DC beyond generalization, accommodating additional objectives such as robustness, privacy, and other desirable properties.

Access to clinical data is essential for developing reliable healthcare machine learning systems, but direct use of electronic health records is constrained by privacy regulation, institutional review, data-use agreements, and the risk of re-identification. Synthetic data promises a practical alternative: it can preserve useful statistical and clinical structure while reducing exposure of sensitive patient records. Prior studies often evaluate a single generator, one dataset, or a narrow downstream task, making it difficult to know when synthetic data can support model development and when it fails to preserve task-critical signal. We introduce CoMedBench, a reproducible benchmark that evaluates a family of generators under a common clinical-validity framework and one shared training and evaluation engine, spanning static tabular and temporal downstream tasks on established critical-care datasets. In total the benchmark spans 37 dataset-task pairs across two modalities consists of 20 static tabular and 17 temporal ICU time-series-drawn from seven public data sources: three intensive-care databases (MIMIC-III, MIMIC-IV, and eICU) together with the UCI Machine Learning Repository, the CDC BRFSS diabetes cohort (2015), NHANES (1999-2014), and the pycox survival datasets (GBSG and METABRIC). The benchmark evaluates both statistical fidelity and task utility by comparing models trained and tested across real and synthetic data. In these settings, synthetic training data preserves most of the downstream signal: on tabular tasks the reference generator CoMed-CTGAN retains a mean AUROC utility (the synthetic-to-real performance ratio) of 90.6%, rising to 97.3% for the strongest generator, CoMed-TVAE. Temporal ICU tasks are harder and more generator-sensitive: CoMed-CTGAN retains 81.6% (AUROC) and only 64.0% under the imbalance-sensitive AUPRC, whereas CoMed-TVAE still retains ~95% (AUROC).

Trajectory inference is a fundamental problem in many scientific domains: given a collection of unpaired snapshots of observations at discrete time points, the goal is to generate smooth trajectories that best resemble and interpolate the data. Existing algorithms exhibit computational challenges: they either rely on preprocessing subroutines to enforce smoothness or on simulation-based training objectives, both of which can be expensive. In order to overcome these limitations, we propose a new algorithm called Acceleration Matching (\texttt{AM}). Our approach consists of lifting the original interpolation problem to phase space and then regressing onto an explicit conditional acceleration field that induces random, smooth trajectories that agree with the prescribed marginals. Importantly, our resulting training algorithm only requires positional data, avoids trajectory simulation during training, and is devoid of expensive preprocessing. We provide ample numerical evidence suggesting that \texttt{AM} is competitive with or superior to existing algorithms on several benchmark problems from the existing literature.