The Kernelized Taylor Diagram

This paper presents the kernelized Taylor diagram, a graphical framework for visualizing similarities between data populations. The kernelized Taylor diagram builds on the widely used Taylor diagram, which is used to visualize similarities between populations. However, the Taylor diagram has several limitations such as not capturing non-linear relationships and sensitivity to outliers. To address such limitations, we propose the kernelized Taylor diagram. Our proposed kernelized Taylor diagram is capable of visualizing similarities between populations with minimal assumptions of the data distributions. The kernelized Taylor diagram relates the maximum mean discrepancy and the kernel mean embedding in a single diagram, a construction that, to the best of our knowledge, have not been devised prior to this work. We believe that the kernelized Taylor diagram can be a valuable tool in data visualization.

Mixing Up Contrastive Learning: Self-Supervised Representation Learning for Time Series

The lack of labeled data is a key challenge for learning useful representation from time series data. However, an unsupervised representation framework that is capable of producing high quality representations could be of great value. It is key to enabling transfer learning, which is especially beneficial for medical applications, where there is an abundance of data but labeling is costly and time consuming. We propose an unsupervised contrastive learning framework that is motivated from the perspective of label smoothing. The proposed approach uses a novel contrastive loss that naturally exploits a data augmentation scheme in which new samples are generated by mixing two data samples with a mixing component. The task in the proposed framework is to predict the mixing component, which is utilized as soft targets in the loss function. Experiments demonstrate the framework's superior performance compared to other representation learning approaches on both univariate and multivariate time series and illustrate its benefits for transfer learning for clinical time series.

Uncertainty-Aware Deep Ensembles for Reliable and Explainable Predictions of Clinical Time Series

Deep learning-based support systems have demonstrated encouraging results in numerous clinical applications involving the processing of time series data. While such systems often are very accurate, they have no inherent mechanism for explaining what influenced the predictions, which is critical for clinical tasks. However, existing explainability techniques lack an important component for trustworthy and reliable decision support, namely a notion of uncertainty. In this paper, we address this lack of uncertainty by proposing a deep ensemble approach where a collection of DNNs are trained independently. A measure of uncertainty in the relevance scores is computed by taking the standard deviation across the relevance scores produced by each model in the ensemble, which in turn is used to make the explanations more reliable. The class activation mapping method is used to assign a relevance score for each time step in the time series. Results demonstrate that the proposed ensemble is more accurate in locating relevant time steps and is more consistent across random initializations, thus making the model more trustworthy. The proposed methodology paves the way for constructing trustworthy and dependable support systems for processing clinical time series for healthcare related tasks.

Information Plane Analysis of Deep Neural Networks via Matrix-Based Renyi's Entropy and Tensor Kernels

Analyzing deep neural networks (DNNs) via information plane (IP) theory has gained tremendous attention recently as a tool to gain insight into, among others, their generalization ability. However, it is by no means obvious how to estimate mutual information (MI) between each hidden layer and the input/desired output, to construct the IP. For instance, hidden layers with many neurons require MI estimators with robustness towards the high dimensionality associated with such layers. MI estimators should also be able to naturally handle convolutional layers, while at the same time being computationally tractable to scale to large networks. None of the existing IP methods to date have been able to study truly deep Convolutional Neural Networks (CNNs), such as the e.g.\ VGG-16. In this paper, we propose an IP analysis using the new matrix--based R\'enyi's entropy coupled with tensor kernels over convolutional layers, leveraging the power of kernel methods to represent properties of the probability distribution independently of the dimensionality of the data. The obtained results shed new light on the previous literature concerning small-scale DNNs, however using a completely new approach. Importantly, the new framework enables us to provide the first comprehensive IP analysis of contemporary large-scale DNNs and CNNs, investigating the different training phases and providing new insights into the training dynamics of large-scale neural networks.

Understanding Convolutional Neural Network Training with Information Theory

Using information theoretic concepts to understand and explore the inner organization of deep neural networks (DNNs) remains a big challenge. Recently, the concept of an information plane (coupled with the famed information bottleneck principle) began to shed light on the analysis of multilayer perceptrons (MLPs). We provided an in-depth insight into stacked autoencoders (SAEs) using a novel matrix-based Renyi's {\alpha}-entropy functional, enabling for the first time the analysis of the dynamics of learning using information flow in the real-world scenario involving complex network architecture and large data. Despite the great potential of these past works, there are several open questions when it comes to applying information theoretic concepts to understand convolutional neural networks (CNNs). These include for instance the accurate estimation of information quantities among multiple variables, and the many different training methodologies. By extending the novel matrix-based Renyi's {\alpha}-entropy functional to a multivariate scenario and introducing the partial information decomposition (PID) framework, this paper presents a systematic method to analyze CNNs training using information theory. Our results validate two fundamental data processing inequalities in CNNs, and also reveals some fundamental issues embedded in the training phase of CNNs.

Uncertainty and Interpretability in Convolutional Neural Networks for Semantic Segmentation of Colorectal Polyps

Convolutional Neural Networks (CNNs) are propelling advances in a range of different computer vision tasks such as object detection and object segmentation. Their success has motivated research in applications of such models for medical image analysis. If CNN-based models are to be helpful in a medical context, they need to be precise, interpretable, and uncertainty in predictions must be well understood. In this paper, we develop and evaluate recent advances in uncertainty estimation and model interpretability in the context of semantic segmentation of polyps from colonoscopy images. We evaluate and enhance several architectures of Fully Convolutional Networks (FCNs) for semantic segmentation of colorectal polyps and provide a comparison between these models. Our highest performing model achieves a 76.06\% mean IOU accuracy on the EndoScene dataset, a considerable improvement over the previous state-of-the-art.