Several approaches to predictive uncertainty quantification have been introduced in recent years, considering uncertainty inaBayesian sense [2,7,18]aswell asfrom afrequentist'spoint ofview [15,5,34].

Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various fields. The halfspace depth was the first depth to aim at generalising the notion of quantile beyond the univariate case. Among the existing variety of depth definitions, it remains one of the most used notions of data depth. Taking a different angle from the quantile point of view, we show that the halfspace depth can also be regarded as the minimum loss of a set of classifiers for a specific labelling of the points. By changing the loss or the set of classifiers considered, this new angle naturally leads to a family of "loss depths", extending to well-studied classifiers such as, e.g., SVM or logistic regression, among others. This framework directly inherits computational efficiency of existing machine learning algorithms as well as their fast statistical convergence rates, and opens the data depth realm to the high-dimensional setting. Furthermore, the new loss depths highlight a connection between the dataset and the right amount of complexity or simplicity of the classifiers. The simplicity of classifiers as well as the interpretation as a risk makes our new kind of data depth easy to explain, yet efficient for anomaly detection, as is shown by experiments.

Deformable registration is a fundamental task in medical image processing, aiming to achieve precise alignment by establishing nonlinear correspondences between images. Traditional methods offer good adaptability and interpretability but are limited by computational efficiency. Although deep learning approaches have significantly improved registration speed and accuracy, they often lack flexibility and generalizability across different datasets and tasks. In recent years, foundation models have emerged as a promising direction, leveraging large and diverse datasets to learn universal features and transformation patterns for image registration, thus demonstrating strong cross-task transferability. However, these models still face challenges in generalization and robustness when encountering novel anatomical structures, varying imaging conditions, or unseen modalities. To address these limitations, this paper incorporates Sharpness-Aware Minimization (SAM) into foundation models to enhance their generalization and robustness in medical image registration. By optimizing the flatness of the loss landscape, SAM improves model stability across diverse data distributions and strengthens its ability to handle complex clinical scenarios. Experimental results show that foundation models integrated with SAM achieve significant improvements in cross-dataset registration performance, offering new insights for the advancement of medical image registration technology. Our code is available at https://github.com/Promise13/fm_sam}{https://github.com/Promise13/fm\_sam.

In stochastic optimal control and conditional generative modelling, a central computational task is to modify a reference diffusion process to maximise a given terminal-time reward. Most existing methods require this reward to be differentiable, using gradients to steer the diffusion towards favourable outcomes. However, in many practical settings, like diffusion bridges, the reward is singular, taking an infinite value if the target is hit and zero otherwise. We introduce a novel framework, based on Malliavin calculus and path-space integration by parts, that enables the development of methods robust to such singular rewards. This allows our approach to handle a broad range of applications, including classification, diffusion bridges, and conditioning without the need for artificial observational noise. We demonstrate that our approach offers stable and reliable training, outperforming existing techniques.

One-class anomaly detection aims to detect objects that do not belong to a predefined normal class. In practice training data lack those anomalous samples; hence state-of-the-art methods are trained to discriminate between normal and synthetically-generated pseudo-anomalous data. Most methods use data augmentation techniques on normal images to simulate anomalies. However the best-performing ones implicitly leverage a geometric bias present in the benchmarking datasets. This limits their usability in more general conditions. Others are relying on basic noising schemes that may be suboptimal in capturing the underlying structure of normal data. In addition most still favour the image domain to generate pseudo-anomalies training models end-to-end from only the normal class and overlooking richer representations of the information. To overcome these limitations we consider frozen yet rich feature spaces given by pretrained models and create pseudo-anomalous features with a novel adaptive linear feature perturbation technique. It adapts the noise distribution to each sample applies decaying linear perturbations to feature vectors and further guides the classification process using a contrastive learning objective. Experimental evaluation conducted on both standard and geometric bias-free datasets demonstrates the superiority of our approach with respect to comparable baselines. The codebase is accessible via our public repository.

Artificial intelligence (AI) has potential to revolutionize the field of oncology by enhancing the precision of cancer diagnosis, optimizing treatment strategies, and personalizing therapies for a variety of cancers. This review examines the limitations of conventional diagnostic techniques and explores the transformative role of AI in diagnosing and treating cancers such as lung, breast, colorectal, liver, stomach, esophageal, cervical, thyroid, prostate, and skin cancers. The primary objective of this paper is to highlight the significant advancements that AI algorithms have brought to oncology within the medical industry. By enabling early cancer detection, improving diagnostic accuracy, and facilitating targeted treatment delivery, AI contributes to substantial improvements in patient outcomes. The integration of AI in medical imaging, genomic analysis, and pathology enhances diagnostic precision and introduces a novel, less invasive approach to cancer screening. This not only boosts the effectiveness of medical facilities but also reduces operational costs. The study delves into the application of AI in radiomics for detailed cancer characterization, predictive analytics for identifying associated risks, and the development of algorithm-driven robots for immediate diagnosis. Furthermore, it investigates the impact of AI on addressing healthcare challenges, particularly in underserved and remote regions. The overarching goal of this platform is to support the development of expert recommendations and to provide universal, efficient diagnostic procedures. By reviewing existing research and clinical studies, this paper underscores the pivotal role of AI in improving the overall cancer care system. It emphasizes how AI-enabled systems can enhance clinical decision-making and expand treatment options, thereby underscoring the importance of AI in advancing precision oncology

Anomaly detection (AD) plays a pivotal role in AI applications, e.g., in classification, and intrusion/threat detection in cybersecurity. However, most existing methods face challenges of heterogeneity amongst feature subsets posed by non-independent and identically distributed (non-IID) data. We propose a novel neural network model called Multiple-Input Auto-Encoder for AD (MIAEAD) to address this. MIAEAD assigns an anomaly score to each feature subset of a data sample to indicate its likelihood of being an anomaly. This is done by using the reconstruction error of its sub-encoder as the anomaly score. All sub-encoders are then simultaneously trained using unsupervised learning to determine the anomaly scores of feature subsets. The final AUC of MIAEAD is calculated for each sub-dataset, and the maximum AUC obtained among the sub-datasets is selected. To leverage the modelling of the distribution of normal data to identify anomalies of the generative models, we develop a novel neural network architecture/model called Multiple-Input Variational Auto-Encoder (MIVAE). MIVAE can process feature subsets through its sub-encoders before learning distribution of normal data in the latent space. This allows MIVAE to identify anomalies that deviate from the learned distribution. We theoretically prove that the difference in the average anomaly score between normal samples and anomalies obtained by the proposed MIVAE is greater than that of the Variational Auto-Encoder (VAEAD), resulting in a higher AUC for MIVAE. Extensive experiments on eight real-world anomaly datasets demonstrate the superior performance of MIAEAD and MIVAE over conventional methods and the state-of-the-art unsupervised models, by up to 6% in terms of AUC score. Alternatively, MIAEAD and MIVAE have a high AUC when applied to feature subsets with low heterogeneity based on the coefficient of variation (CV) score.

In this paper, we propose a novel intrinsic wrapped Gaussian process regression model for response variable measured on Riemannian manifold. We apply the parallel transport operator to define an intrinsic covariance structure addressing a critical aspect of constructing a well defined Gaussian process regression model. We show that the posterior distribution of regression function is invariant to the choice of orthonormal frames for the coordinate representations of the covariance function. This method can be applied to data situated not only on Euclidean submanifolds but also on manifolds without a natural ambient space. The asymptotic properties for estimating the posterior distribution is established. Numerical studies, including simulation and real-world examples, indicate that the proposed method delivers strong performance.

Single-source domain generalization (SDG) aims to learn a model from a single source domain that can generalize well on unseen target domains. This is an important task in computer vision, particularly relevant to medical imaging where domain shifts are common. In this work, we consider a challenging yet practical setting: SDG for cross-modality medical image segmentation. We combine causality-inspired theoretical insights on learning domain-invariant representations with recent advancements in diffusion-based augmentation to improve generalization across diverse imaging modalities. Guided by the ``intervention-augmentation equivariant'' principle, we use controlled diffusion models (DMs) to simulate diverse imaging styles while preserving the content, leveraging rich generative priors in large-scale pretrained DMs to comprehensively perturb the multidimensional style variable. Extensive experiments on challenging cross-modality segmentation tasks demonstrate that our approach consistently outperforms state-of-the-art SDG methods across three distinct anatomies and imaging modalities. The source code is available at \href{https://github.com/ratschlab/ICMSeg}{https://github.com/ratschlab/ICMSeg}.