Paul D. W. Kirk

Jackie Rao, Paul D. W. Kirk

Effective clustering of biomedical data is crucial in precision medicine, enabling accurate stratifiction of patients or samples. However, the growth in availability of high-dimensional categorical data, including `omics data, necessitates computationally efficient clustering algorithms. We present VICatMix, a variational Bayesian finite mixture model designed for the clustering of categorical data. The use of variational inference (VI) in its training allows the model to outperform competitors in term of efficiency, while maintaining high accuracy. VICatMix furthermore performs variable selection, enhancing its performance on high-dimensional, noisy data. The proposed model incorporates summarisation and model averaging to mitigate poor local optima in VI, allowing for improved estimation of the true number of clusters simultaneously with feature saliency. We demonstrate the performance of VICatMix with both simulated and real-world data, including applications to datasets from The Cancer Genome Atlas (TCGA), showing its use in cancer subtyping and driver gene discovery. We demonstrate VICatMix's utility in integrative cluster analysis with different `omics datasets, enabling the discovery of novel subtypes. \textbf{Availability:} VICatMix is freely available as an R package, incorporating C++ for faster computation, at https://github.com/j-ackierao/VICatMix.

Alessandra Cabassi, Sylvia Richardson, Paul D. W. Kirk

When using Markov chain Monte Carlo (MCMC) algorithms to perform inference for Bayesian clustering models, such as mixture models, the output is typically a sample of clusterings (partitions) drawn from the posterior distribution. In practice, a key challenge is how to summarise this output. Here we build upon the notion of the posterior similarity matrix (PSM) in order to suggest new approaches for summarising the output of MCMC algorithms for Bayesian clustering models. A key contribution of our work is the observation that PSMs are positive semi-definite, and hence can be used to define probabilistically-motivated kernel matrices that capture the clustering structure present in the data. This observation enables us to employ a range of kernel methods to obtain summary clusterings, and otherwise exploit the information summarised by PSMs. For example, if we have multiple PSMs, each corresponding to a different dataset on a common set of statistical units, we may use standard methods for combining kernels in order to perform integrative clustering. We may moreover embed PSMs within predictive kernel models in order to perform outcome-guided data integration. We demonstrate the performances of the proposed methods through a range of simulation studies as well as two real data applications. R code is available at https://github.com/acabassi/combine-psms.

Alessandra Cabassi, Denis Seyres, Mattia Frontini et al.

Building classification models that predict a binary class label on the basis of high dimensional multi-omics datasets poses several challenges, due to the typically widely differing characteristics of the data layers in terms of number of predictors, type of data, and levels of noise. Previous research has shown that applying classical logistic regression with elastic-net penalty to these datasets can lead to poor results (Liu et al., 2018). We implement a two-step approach to multi-omic logistic regression in which variable selection is performed on each layer separately and a predictive model is then built using the variables selected in the first step. Here, our approach is compared to other methods that have been developed for the same purpose, and we adapt existing software for multi-omic linear regression (Zhao and Zucknick, 2020) to the logistic regression setting. Extensive simulation studies show that our approach should be preferred if the goal is to select as many relevant predictors as possible, as well as achieving prediction performances comparable to those of the best competitors. Our motivating example is a cardiometabolic syndrome dataset comprising eight 'omic data types for 2 extreme phenotype groups (10 obese and 10 lipodystrophy individuals) and 185 blood donors. Our proposed approach allows us to identify features that characterise cardiometabolic syndrome at the molecular level. R code is available at https://github.com/acabassi/logistic-regression-for-multi-omic-data.

Jackie Rao, Francesca L. Crowe, Tom Marshall et al.

We present a federated learning approach for Bayesian model-based clustering of large-scale binary and categorical datasets. We introduce a principled 'divide and conquer' inference procedure using variational inference with local merge and delete moves within batches of the data in parallel, followed by 'global' merge moves across batches to find global clustering structures. We show that these merge moves require only summaries of the data in each batch, enabling federated learning across local nodes without requiring the full dataset to be shared. Empirical results on simulated and benchmark datasets demonstrate that our method performs well in comparison to existing clustering algorithms. We validate the practical utility of the method by applying it to large scale electronic health record (EHR) data.

Leiv Rønneberg, Vidhi Lalchand, Paul D. W. Kirk

Dose-response prediction in cancer is an active application field in machine learning. Using large libraries of \textit{in-vitro} drug sensitivity screens, the goal is to develop accurate predictive models that can be used to guide experimental design or inform treatment decisions. Building on previous work that makes use of permutation invariant multi-output Gaussian Processes in the context of dose-response prediction for drug combinations, we develop a variational approximation to these models. The variational approximation enables a more scalable model that provides uncertainty quantification and naturally handles missing data. Furthermore, we propose using a deep generative model to encode the chemical space in a continuous manner, enabling prediction for new drugs and new combinations. We demonstrate the performance of our model in a simple setting using a high-throughput dataset and show that the model is able to efficiently borrow information across outputs.

Alessandra Cabassi, Paul D. W. Kirk

Diverse applications - particularly in tumour subtyping - have demonstrated the importance of integrative clustering techniques for combining information from multiple data sources. Cluster-Of-Clusters Analysis (COCA) is one such approach that has been widely applied in the context of tumour subtyping. However, the properties of COCA have never been systematically explored, and its robustness to the inclusion of noisy datasets, or datasets that define conflicting clustering structures, is unclear. We rigorously benchmark COCA, and present Kernel Learning Integrative Clustering (KLIC) as an alternative strategy. KLIC frames the challenge of combining clustering structures as a multiple kernel learning problem, in which different datasets each provide a weighted contribution to the final clustering. This allows the contribution of noisy datasets to be down-weighted relative to more informative datasets. We compare the performances of KLIC and COCA in a variety of situations through simulation studies. We also present the output of KLIC and COCA in real data applications to cancer subtyping and transcriptional module discovery. R packages "klic" and "coca" are available on the Comprehensive R Archive Network.