Kieran R. Campbell

Kieran R. Campbell, Christopher Yau

Standard models assign disease progression to discrete categories or stages based on well-characterized clinical markers. However, such a system is potentially at odds with our understanding of the underlying biology, which in highly complex systems may support a (near-)continuous evolution of disease from inception to terminal state. To learn such a continuous disease score one could infer a latent variable from dynamic "omics" data such as RNA-seq that correlates with an outcome of interest such as survival time. However, such analyses may be confounded by additional data such as clinical covariates measured in electronic health records (EHRs). As a solution to this we introduce covariate latent variable models, a novel type of latent variable model that learns a low-dimensional data representation in the presence of two (asymmetric) views of the same data source. We apply our model to TCGA colorectal cancer RNA-seq data and demonstrate how incorporating microsatellite-instability (MSI) status as an external covariate allows us to identify genes that stratify patients on an immune-response trajectory. Finally, we propose an extension termed Covariate Gaussian Process Latent Variable Models for learning nonparametric, nonlinear representations. An R package implementing variational inference for covariate latent variable models is available at http://github.com/kieranrcampbell/clvm.

MohammadReza Ebrahimi, Navona Calarco, Kieran Campbell et al.

Multi-subject fMRI studies are challenging due to the high variability of both brain anatomy and functional brain topographies across participants. An effective way of aggregating multi-subject fMRI data is to extract a shared representation that filters out unwanted variability among subjects. Some recent work has implemented probabilistic models to extract a shared representation in task fMRI. In the present work, we improve upon these models by incorporating temporal information in the common latent structures. We introduce a new model, Shared Gaussian Process Factor Analysis (S-GPFA), that discovers shared latent trajectories and subject-specific functional topographies, while modelling temporal correlation in fMRI data. We demonstrate the efficacy of our model in revealing ground truth latent structures using simulated data, and replicate experimental performance of time-segment matching and inter-subject similarity on the publicly available Raider and Sherlock datasets. We further test the utility of our model by analyzing its learned model parameters in the large multi-site SPINS dataset, on a social cognition task from participants with and without schizophrenia.

Kaspar Märtens, Kieran R. Campbell, Christopher Yau

The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to interpret the model in terms of the original features themselves. Our goal is to characterise how feature-level variation depends on latent low-dimensional representations, external covariates, and non-linear interactions between the two. In this paper, we propose to achieve this through a structured kernel decomposition in a hybrid Gaussian Process model which we call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We demonstrate the utility of our model on simulated examples and applications in disease progression modelling from high-dimensional gene expression data in the presence of additional phenotypes. In each setting we show how the c-GPLVM can extract low-dimensional structures from high-dimensional data sets whilst allowing a breakdown of feature-level variability that is not present in other commonly used dimensionality reduction approaches.