A Continuous-time Stochastic Gradient Descent Method for Continuous Data

Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target functions - integrated with respect to a probability measure. Such problems can often be solved by stochastic optimization methods: performing optimization steps with respect to the indexed target function with randomly switched indices. In this work, we study a continuous-time variant of the stochastic gradient descent algorithm for optimization problems with continuous data. This so-called stochastic gradient process consists in a gradient flow minimizing an indexed target function that is coupled with a continuous-time index process determining the index. Index processes are, e.g., reflected diffusions, pure jump processes, or other L\'evy processes on compact spaces. Thus, we study multiple sampling patterns for the continuous data space and allow for data simulated or streamed at runtime of the algorithm. We analyze the approximation properties of the stochastic gradient process and study its longtime behavior and ergodicity under constant and decreasing learning rates. We end with illustrating the applicability of the stochastic gradient process in a polynomial regression problem with noisy functional data, as well as in a physics-informed neural network.

Conditional Image Generation with Score-Based Diffusion Models

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling. In this work we conduct a systematic comparison and theoretical analysis of different approaches to learning conditional probability distributions with score-based diffusion models. In particular, we prove results which provide a theoretical justification for one of the most successful estimators of the conditional score. Moreover, we introduce a multi-speed diffusion framework, which leads to a new estimator for the conditional score, performing on par with previous state-of-the-art approaches. Our theoretical and experimental findings are accompanied by an open source library MSDiff which allows for application and further research of multi-speed diffusion models.

Advancing COVID-19 Diagnosis with Privacy-Preserving Collaboration in Artificial Intelligence

Artificial intelligence (AI) provides a promising substitution for streamlining COVID-19 diagnoses. However, concerns surrounding security and trustworthiness impede the collection of large-scale representative medical data, posing a considerable challenge for training a well-generalised model in clinical practices. To address this, we launch the Unified CT-COVID AI Diagnostic Initiative (UCADI), where the AI model can be distributedly trained and independently executed at each host institution under a federated learning framework (FL) without data sharing. Here we show that our FL model outperformed all the local models by a large yield (test sensitivity /specificity in China: 0.973/0.951, in the UK: 0.730/0.942), achieving comparable performance with a panel of professional radiologists. We further evaluated the model on the hold-out (collected from another two hospitals leaving out the FL) and heterogeneous (acquired with contrast materials) data, provided visual explanations for decisions made by the model, and analysed the trade-offs between the model performance and the communication costs in the federated training process. Our study is based on 9,573 chest computed tomography scans (CTs) from 3,336 patients collected from 23 hospitals located in China and the UK. Collectively, our work advanced the prospects of utilising federated learning for privacy-preserving AI in digital health.

Focal Attention Networks: optimising attention for biomedical image segmentation

In recent years, there has been increasing interest to incorporate attention into deep learning architectures for biomedical image segmentation. The modular design of attention mechanisms enables flexible integration into convolutional neural network architectures, such as the U-Net. Whether attention is appropriate to use, what type of attention to use, and where in the network to incorporate attention modules, are all important considerations that are currently overlooked. In this paper, we investigate the role of the Focal parameter in modulating attention, revealing a link between attention in loss functions and networks. By incorporating a Focal distance penalty term, we extend the Unified Focal loss framework to include boundary-based losses. Furthermore, we develop a simple and interpretable, dataset and model-specific heuristic to integrate the Focal parameter into the Squeeze-and-Excitation block and Attention Gate, achieving optimal performance with fewer number of attention modules on three well-validated biomedical imaging datasets, suggesting judicious use of attention modules results in better performance and efficiency.

Incorporating Boundary Uncertainty into loss functions for biomedical image segmentation

Manual segmentation is used as the gold-standard for evaluating neural networks on automated image segmentation tasks. Due to considerable heterogeneity in shapes, colours and textures, demarcating object boundaries is particularly difficult in biomedical images, resulting in significant inter and intra-rater variability. Approaches, such as soft labelling and distance penalty term, apply a global transformation to the ground truth, redefining the loss function with respect to uncertainty. However, global operations are computationally expensive, and neither approach accurately reflects the uncertainty underlying manual annotation. In this paper, we propose the Boundary Uncertainty, which uses morphological operations to restrict soft labelling to object boundaries, providing an appropriate representation of uncertainty in ground truth labels, and may be adapted to enable robust model training where systematic manual segmentation errors are present. We incorporate Boundary Uncertainty with the Dice loss, achieving consistently improved performance across three well-validated biomedical imaging datasets compared to soft labelling and distance-weighted penalty. Boundary Uncertainty not only more accurately reflects the segmentation process, but it is also efficient, robust to segmentation errors and exhibits better generalisation.

Calibrating the Dice loss to handle neural network overconfidence for biomedical image segmentation

The Dice similarity coefficient (DSC) is both a widely used metric and loss function for biomedical image segmentation due to its robustness to class imbalance. However, it is well known that the DSC loss is poorly calibrated, resulting in overconfident predictions that cannot be usefully interpreted in biomedical and clinical practice. Performance is often the only metric used to evaluate segmentations produced by deep neural networks, and calibration is often neglected. However, calibration is important for translation into biomedical and clinical practice, providing crucial contextual information to model predictions for interpretation by scientists and clinicians. In this study, we identify poor calibration as an emerging challenge of deep learning based biomedical image segmentation. We provide a simple yet effective extension of the DSC loss, named the DSC++ loss, that selectively modulates the penalty associated with overconfident, incorrect predictions. As a standalone loss function, the DSC++ loss achieves significantly improved calibration over the conventional DSC loss across five well-validated open-source biomedical imaging datasets. Similarly, we observe significantly improved when integrating the DSC++ loss into four DSC-based loss functions. Finally, we use softmax thresholding to illustrate that well calibrated outputs enable tailoring of precision-recall bias, an important post-processing technique to adapt the model predictions to suit the biomedical or clinical task. The DSC++ loss overcomes the major limitation of the DSC, providing a suitable loss function for training deep learning segmentation models for use in biomedical and clinical practice.

Learning convex regularizers satisfying the variational source condition for inverse problems

Variational regularization has remained one of the most successful approaches for reconstruction in imaging inverse problems for several decades. With the emergence and astonishing success of deep learning in recent years, a considerable amount of research has gone into data-driven modeling of the regularizer in the variational setting. Our work extends a recently proposed method, referred to as adversarial convex regularization (ACR), that seeks to learn data-driven convex regularizers via adversarial training in an attempt to combine the power of data with the classical convex regularization theory. Specifically, we leverage the variational source condition (SC) during training to enforce that the ground-truth images minimize the variational loss corresponding to the learned convex regularizer. This is achieved by adding an appropriate penalty term to the ACR training objective. The resulting regularizer (abbreviated as ACR-SC) performs on par with the ACR, but unlike ACR, comes with a quantitative convergence rate estimate.

StyleGAN-induced data-driven regularization for inverse problems

Recent advances in generative adversarial networks (GANs) have opened up the possibility of generating high-resolution photo-realistic images that were impossible to produce previously. The ability of GANs to sample from high-dimensional distributions has naturally motivated researchers to leverage their power for modeling the image prior in inverse problems. We extend this line of research by developing a Bayesian image reconstruction framework that utilizes the full potential of a pre-trained StyleGAN2 generator, which is the currently dominant GAN architecture, for constructing the prior distribution on the underlying image. Our proposed approach, which we refer to as learned Bayesian reconstruction with generative models (L-BRGM), entails joint optimization over the style-code and the input latent code, and enhances the expressive power of a pre-trained StyleGAN2 generator by allowing the style-codes to be different for different generator layers. Considering the inverse problems of image inpainting and super-resolution, we demonstrate that the proposed approach is competitive with, and sometimes superior to, state-of-the-art GAN-based image reconstruction methods.

Predicting isocitrate dehydrogenase mutation status in glioma using structural brain networks and graph neural networks

Glioma is a common malignant brain tumor with distinct survival among patients. The isocitrate dehydrogenase (IDH) gene mutation provides critical diagnostic and prognostic value for glioma. It is of crucial significance to non-invasively predict IDH mutation based on pre-treatment MRI. Machine learning/deep learning models show reasonable performance in predicting IDH mutation using MRI. However, most models neglect the systematic brain alterations caused by tumor invasion, where widespread infiltration along white matter tracts is a hallmark of glioma. Structural brain network provides an effective tool to characterize brain organisation, which could be captured by the graph neural networks (GNN) to more accurately predict IDH mutation. Here we propose a method to predict IDH mutation using GNN, based on the structural brain network of patients. Specifically, we firstly construct a network template of healthy subjects, consisting of atlases of edges (white matter tracts) and nodes (cortical/subcortical brain regions) to provide regions of interest (ROIs). Next, we employ autoencoders to extract the latent multi-modal MRI features from the ROIs of edges and nodes in patients, to train a GNN architecture for predicting IDH mutation. The results show that the proposed method outperforms the baseline models using the 3D-CNN and 3D-DenseNet. In addition, model interpretation suggests its ability to identify the tracts infiltrated by tumor, corresponding to clinical prior knowledge. In conclusion, integrating brain networks with GNN offers a new avenue to study brain lesions using computational neuroscience and computer vision approaches.

Adaptive unsupervised learning with enhanced feature representation for intra-tumor partitioning and survival prediction for glioblastoma

Glioblastoma is profoundly heterogeneous in regional microstructure and vasculature. Characterizing the spatial heterogeneity of glioblastoma could lead to more precise treatment. With unsupervised learning techniques, glioblastoma MRI-derived radiomic features have been widely utilized for tumor sub-region segmentation and survival prediction. However, the reliability of algorithm outcomes is often challenged by both ambiguous intermediate process and instability introduced by the randomness of clustering algorithms, especially for data from heterogeneous patients. In this paper, we propose an adaptive unsupervised learning approach for efficient MRI intra-tumor partitioning and glioblastoma survival prediction. A novel and problem-specific Feature-enhanced Auto-Encoder (FAE) is developed to enhance the representation of pairwise clinical modalities and therefore improve clustering stability of unsupervised learning algorithms such as K-means. Moreover, the entire process is modelled by the Bayesian optimization (BO) technique with a custom loss function that the hyper-parameters can be adaptively optimized in a reasonably few steps. The results demonstrate that the proposed approach can produce robust and clinically relevant MRI sub-regions and statistically significant survival predictions.