Daniel Marks

Daniel Marks, Dario Paccagnan, Mark van der Wilk

Variational inference (VI) is a central tool in modern machine learning, used to approximate an intractable target density by optimising over a tractable family of distributions. As the variational family cannot typically represent the target exactly, guarantees on the quality of the resulting approximation are crucial for understanding which of its properties VI can faithfully capture. Recent work has identified instances in which symmetries of the target and the variational family enable the recovery of certain statistics, even under model misspecification. However, these guarantees are inherently problem-specific and offer little insight into the fundamental mechanism by which symmetry forces statistic recovery. In this paper, we overcome this limitation by developing a general theory of symmetry-induced statistic recovery in variational inference. First, we characterise when variational minimisers inherit the symmetries of the target and establish conditions under which these pin down identifiable statistics. Second, we unify existing results by showing that previously known statistic recovery guarantees in location-scale families arise as special cases of our theory. Third, we apply our framework to distributions on the sphere to obtain novel guarantees for directional statistics in von Mises-Fisher families. Together, these results provide a modular blueprint for deriving new recovery guarantees for VI in a broad range of symmetry settings.

Ricardo Mokhtari, Azam Hamidinekoo, Daniel Sutton et al.

Crohn's Disease (CD) and Ulcerative Colitis (UC) are the two main Inflammatory Bowel Disease (IBD) types. We developed deep learning models to identify histological disease features for both CD and UC using only endoscopic labels. We explored fine-tuning and end-to-end training of two state-of-the-art self-supervised models for predicting three different endoscopic categories (i) CD vs UC (AUC=0.87), (ii) normal vs lesional (AUC=0.81), (iii) low vs high disease severity score (AUC=0.80). We produced visual attention maps to interpret what the models learned and validated them with the support of a pathologist, where we observed a strong association between the models' predictions and histopathological inflammatory features of the disease. Additionally, we identified several cases where the model incorrectly predicted normal samples as lesional but were correct on the microscopic level when reviewed by the pathologist. This tendency of histological presentation to be more severe than endoscopic presentation was previously published in the literature. In parallel, we utilised a model trained on the Colon Nuclei Identification and Counting (CoNIC) dataset to predict and explore 6 cell populations. We observed correlation between areas enriched with the predicted immune cells in biopsies and the pathologist's feedback on the attention maps. Finally, we identified several cell level features indicative of disease severity in CD and UC. These models can enhance our understanding about the pathology behind IBD and can shape our strategies for patient stratification in clinical trials.

Dario Paccagnan, Daniel Marks, Marco C. Campi et al.

Data-driven methods have become paramount in modern systems and control problems characterized by growing levels of complexity. In safety-critical environments, deploying these methods requires rigorous guarantees, a need that has motivated much recent work at the interface of statistical learning and control. However, many existing approaches achieve this goal at the cost of sacrificing valuable data for testing and calibration, or by constraining the choice of learning algorithm, thus leading to suboptimal performances. In this paper, we describe Pick-to-Learn (P2L) for Systems and Control, a framework that allows any data-driven control method to be equipped with state-of-the-art safety and performance guarantees. P2L enables the use of all available data to jointly synthesize and certify the design, eliminating the need to set aside data for calibration or validation purposes. In presenting a comprehensive version of P2L for systems and control, this paper demonstrates its effectiveness across a range of core problems, including optimal control, reachability analysis, safe synthesis, and robust control. In many of these applications, P2L delivers designs and certificates that outperform commonly employed methods, and shows strong potential for broad applicability in diverse practical settings.