Manual for mcclust.ext R package

This R package provides post-processing tools for MCMC samples of partitions to summarize the posterior in Bayesian clustering models. Functions for point estimation are provided, giving a single representative clustering of the posterior. And, to characterize uncertainty in the point estimate, credible balls can be computed

Shared Differential Clustering across Single-cell RNA Sequencing Datasets with the Hierarchical Dirichlet Process

Single-cell RNA sequencing (scRNA-seq) is powerful technology that allows researchers to understand gene expression patterns at the single-cell level. However, analysing scRNA-seq data is challenging due to issues and biases in data collection. In this work, we construct an integrated Bayesian model that simultaneously addresses normalization, imputation and batch effects and also nonparametrically clusters cells into groups across multiple datasets. A Gibbs sampler based on a finite-dimensional approximation of the HDP is developed for posterior inference

Shared Differential Clustering across Single-cell RNA Sequencing Datasets with the Hierarchical Dirichlet Process

Single-cell RNA sequencing (scRNA-seq) is powerful technology that allows researchers to understand gene expression patterns at the single-cell level. However, analysing scRNA-seq data is challenging due to issues and biases in data collection. In this work, we construct an integrated Bayesian model that simultaneously addresses normalization, imputation and batch effects and also nonparametrically clusters cells into groups across multiple datasets. A Gibbs sampler based on a finite-dimensional approximation of the HDP is developed for posterior inference

Ultra-fast Deep Mixtures of Gaussian Process Experts

Mixtures of experts have become an indispensable tool for flexible modelling in a supervised learning context, and sparse Gaussian processes (GP) have shown promise as a leading candidate for the experts in such models. In the present article, we propose to design the gating network for selecting the experts from such mixtures of sparse GPs using a deep neural network (DNN). This combination provides a flexible, robust, and efficient model which is able to significantly outperform competing models. We furthermore consider efficient approaches to computing maximum a posteriori (MAP) estimators of these models by iteratively maximizing the distribution of experts given allocations and allocations given experts. We also show that a recently introduced method called Cluster-Classify-Regress (CCR) is capable of providing a good approximation of the optimal solution extremely quickly. This approximation can then be further refined with the iterative algorithm

Leveraging variational autoencoders for multiple data imputation

Missing data persists as a major barrier to data analysis across numerous applications. Recently, deep generative models have been used for imputation of missing data, motivated by their ability to capture highly non-linear and complex relationships in the data. In this work, we investigate the ability of deep models, namely variational autoencoders (VAEs), to account for uncertainty in missing data through multiple imputation strategies. We find that VAEs provide poor empirical coverage of missing data, with underestimation and overconfident imputations, particularly for more extreme missing data values. To overcome this, we employ $\beta$-VAEs, which viewed from a generalized Bayes framework, provide robustness to model misspecification. Assigning a good value of $\beta$ is critical for uncertainty calibration and we demonstrate how this can be achieved using cross-validation. In downstream tasks, we show how multiple imputation with $\beta$-VAEs can avoid false discoveries that arise as artefacts of imputation.Comment: 17 pages, 3 main figures, 6 supplementary figure

Pseudo-marginal Bayesian inference for Gaussian process latent variable models

A Bayesian inference framework for supervised Gaussian process latent variable models is introduced. The framework overcomes the high correlations between latent variables and hyperparameters by collapsing the statistical model through approximate integration of the latent variables. Using an unbiased pseudo estimate for the marginal likelihood, the exact hyperparameter posterior can then be explored using collapsed Gibbs sampling and, conditional on these samples, the exact latent posterior can be explored through elliptical slice sampling. The framework is tested on both simulated and real examples. When compared with the standard approach based on variational inference, this approach leads to significant improvements in the predictive accuracy and quantification of uncertainty, as well as a deeper insight into the challenges of performing inference in this class of models