Clinical research often focuses on complex traits in which many variables play a role in mechanisms driving, or curing, diseases. Clinical prediction is hard when data is high-dimensional, but additional information, like domain knowledge and previously published studies, may be helpful to improve predictions. Such complementary data, or co-data, provide information on the covariates, such as genomic location or p-values from external studies. Our method enables exploiting multiple and various co-data sources to improve predictions. We use discrete or continuous co-data to define possibly overlapping or hierarchically structured groups of covariates. These are then used to estimate adaptive multi-group ridge penalties for generalised linear and Cox models. We combine empirical Bayes estimation of group penalty hyperparameters with an extra level of shrinkage. This renders a uniquely flexible framework as any type of shrinkage can be used on the group level. The hyperparameter shrinkage learns how relevant a specific co-data source is, counters overfitting of hyperparameters for many groups, and accounts for structured co-data. We describe various types of co-data and propose suitable forms of hypershrinkage. The method is very versatile, as it allows for integration and weighting of multiple co-data sets, inclusion of unpenalised covariates and posterior variable selection. We demonstrate it on two cancer genomics applications and show that it may improve the performance of other dense and parsimonious prognostic models substantially, and stabilises variable selection.

In recent years, academics and investigative journalists have criticized certain commercial risk assessments for their black-box nature and failure to satisfy competing notions of fairness. Since then, the field of interpretable machine learning has created simple yet effective algorithms, while the field of fair machine learning has proposed various mathematical definitions of fairness. However, studies from these fields are largely independent, despite the fact that many applications of machine learning to social issues require both fairness and interpretability. We explore the intersection by revisiting the recidivism prediction problem using state-of-the-art tools from interpretable machine learning, and assessing the models for performance, interpretability, and fairness. Unlike previous works, we compare against two existing risk assessments (COMPAS and the Arnold Public Safety Assessment) and train models that output probabilities rather than binary predictions. We present multiple models that beat these risk assessments in performance, and provide a fairness analysis of these models. Our results imply that machine learning models should be trained separately for separate locations, and updated over time.

Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes, the surrogate models of choice in Bayesian optimisation, are often used with a constant prior mean function equal to the arithmetic mean of the observed function values. We show that the rate of convergence can depend sensitively on the choice of mean function. We empirically investigate 8 mean functions (constant functions equal to the arithmetic mean, minimum, median and maximum of the observed function evaluations, linear, quadratic polynomials, random forests and RBF networks), using 10 synthetic test problems and two real-world problems, and using the Expected Improvement and Upper Confidence Bound acquisition functions. We find that for design dimensions $\ge5$ using a constant mean function equal to the worst observed quality value is consistently the best choice on the synthetic problems considered. We argue that this worst-observed-quality function promotes exploitation leading to more rapid convergence. However, for the real-world tasks the more complex mean functions capable of modelling the fitness landscape may be effective, although there is no clearly optimum choice.

Precise and efficient automated identification of Gastrointestinal (GI) tract diseases can help doctors treat more patients and improve the rate of disease detection and identification. Currently, automatic analysis of diseases in the GI tract is a hot topic in both computer science and medical-related journals. Nevertheless, the evaluation of such an automatic analysis is often incomplete or simply wrong. Algorithms are often only tested on small and biased datasets, and cross-dataset evaluations are rarely performed. A clear understanding of evaluation metrics and machine learning models with cross datasets is crucial to bring research in the field to a new quality level. Towards this goal, we present comprehensive evaluations of five distinct machine learning models using Global Features and Deep Neural Networks that can classify 16 different key types of GI tract conditions, including pathological findings, anatomical landmarks, polyp removal conditions, and normal findings from images captured by common GI tract examination instruments. In our evaluation, we introduce performance hexagons using six performance metrics such as recall, precision, specificity, accuracy, F1-score, and Matthews Correlation Coefficient to demonstrate how to determine the real capabilities of models rather than evaluating them shallowly. Furthermore, we perform cross-dataset evaluations using different datasets for training and testing. With these cross-dataset evaluations, we demonstrate the challenge of actually building a generalizable model that could be used across different hospitals. Our experiments clearly show that more sophisticated performance metrics and evaluation methods need to be applied to get reliable models rather than depending on evaluations of the splits of the same dataset, i.e., the performance metrics should always be interpreted together rather than relying on a single metric.

Recent advances in biological research have seen the emergence of high-throughput technologies with numerous applications that allow the study of biological mechanisms at an unprecedented depth and scale. A large amount of genomic data is now distributed through consortia like The Cancer Genome Atlas (TCGA), where specific types of biological information on specific type of tissue or cell are available. In cancer research, the challenge is now to perform integrative analyses of high-dimensional multi-omic data with the goal to better understand genomic processes that correlate with cancer outcomes, e.g. elucidate gene networks that discriminate a specific cancer subgroups (cancer sub-typing) or discovering gene networks that overlap across different cancer types (pan-cancer studies). In this paper, we propose a novel mixed graphical model approach to analyze multi-omic data of different types (continuous, discrete and count) and perform model selection by extending the Birth-Death MCMC (BDMCMC) algorithm initially proposed by \citet{stephens2000bayesian} and later developed by \cite{mohammadi2015bayesian}. We compare the performance of our method to the LASSO method and the standard BDMCMC method using simulations and find that our method is superior in terms of both computational efficiency and the accuracy of the model selection results. Finally, an application to the TCGA breast cancer data shows that integrating genomic information at different levels (mutation and expression data) leads to better subtyping of breast cancers.

Motivation: It is known that the structure of transcription and protein interaction networks is informative of its biological function at multiple scales. However, thus far it has not been possible to systematically connect network topology to gene expression in a quantitative way. Results: We investigated whether there is a relationship between interaction networks and gene expression values by using a graph convolutional auto-encoder and two end-to-end learning approaches for three interaction networks and hundreds of experimental conditions in the model organism \textit{E.\ coli}. Graph neural networks use a message passing framework to learn an embedding of a graph in a continuous space, either using network topology alone, or including additional node features. We found that graph embeddings trained on transcription and PPI networks can explain more than 50 and 40 percent, respectively, of the variance in gene expression data, thus confirming the relationship between network structure and gene expression value. Additionally, for the task of predicting gene expression values using GNNs, with and without additional expression training data, we found that the message passing scheme of GNNs is able to obtain the lowest mean squared error between the tested models both in prediction of unseen test values, and in an auto-encoder scheme for reconstruction of the feature matrix of expression values.

Classification is a classic problem in data analytics and has been approached from many different angles, including machine learning. Traditionally, machine learning methods classify samples based solely on their features. This paradigm is evolving. Recent developments on Graph Convolutional Networks have shown that explicitly using information not directly present in the features to represent a type of relationship between samples can improve the classification performance by a significant margin. However, graphs are not often immediately present in data sets, thus limiting the applicability of Graph Convolutional Networks. In this paper, we explore if graphs extracted from the features themselves can aid classification performance. First, we show that constructing optimal geometric graphs directly from data features can aid classification tasks on both synthetic and real-world data sets from different domains. Second, we introduce two metrics to characterize optimal graphs: i) by measuring the alignment between the subspaces spanned by the features convolved with the graph and the ground truth; and ii) ratio of class separation in the output activations of Graph Convolutional Networks: this shows that the optimal graph maximally separates classes. Finally, we find that sparsifying the optimal graph can potentially improve classification performance.

Large-sample data became prevalent as data acquisition became cheaper and easier. While a large sample size has theoretical advantages for many statistical methods, it presents computational challenges. Sketching, or compression, is a well-studied approach to address these issues in regression settings, but considerably less is known about its performance in classification settings. Here we consider the computational issues due to large sample size within the discriminant analysis framework. We propose a new compression approach for reducing the number of training samples for linear and quadratic discriminant analysis, in contrast to existing compression methods which focus on reducing the number of features. We support our approach with a theoretical bound on the misclassification error rate compared to the Bayes classifier. Empirical studies confirm the significant computational gains of the proposed method and its superior predictive ability compared to random sub-sampling.

Distinguishing between misinformation and real information is one of the most challenging problems in today's interconnected world. The vast majority of the state-of-the-art in detecting misinformation is fully supervised, requiring a large number of high-quality human annotations. However, the availability of such annotations cannot be taken for granted, since it is very costly, time-consuming, and challenging to do so in a way that keeps up with the proliferation of misinformation. In this work, we are interested in exploring scenarios where the number of annotations is limited. In such scenarios, we investigate how tapping on a diverse number of resources that characterize a news article, henceforth referred to as "aspects" can compensate for the lack of labels. In particular, our contributions in this paper are twofold: 1) We propose the use of three different aspects: article content, context of social sharing behaviors, and host website/domain features, and 2) We introduce a principled tensor based embedding framework that combines all those aspects effectively. We propose HiJoD a 2-level decomposition pipeline which not only outperforms state-of-the-art methods with F1-scores of 74% and 81% on Twitter and Politifact datasets respectively but also is an order of magnitude faster than similar ensemble approaches.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of \textsc{Project and Forget} and prove that our algorithm converges to the global optimal solution and that the $L_2$ distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.