Consensus Monte Carlo for Random Subsets using Shared Anchors

A sparse factor model for clustering high-dimensional longitudinal data

Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and uncover underlying disease mechanisms. However, analyzing such kind of data can be difficult due to its high dimensionality, heterogeneity and computational challenges. In this article, we propose a Bayesian nonparametric mixture model for clustering high-dimensional mixed-type (eg, continuous, discrete and categorical) longitudinal features. We employ a sparse factor model on the joint distribution of random effects and the key idea is to induce clustering at the latent factor level instead of the original data to escape the curse of dimensionality. The number of clusters is estimated through a Dirichlet process prior. An efficient Gibbs sampler is developed to estimate the posterior distribution of the model parameters. Analysis of real and simulated data is presented and discussed. Our study demonstrates that the proposed model serves as a useful analytical tool for clustering high-dimensional longitudinal data.

Federated Learning for Sparse Bayesian Models with Applications to Electronic Health Records and Genomics

Federated learning is becoming increasingly more popular as the concern of privacy breaches rises across disciplines including the biological and biomedical fields. The main idea is to train models locally on each server using data that are only available to that server and aggregate the model (not data) information at the global level. While federated learning has made significant advancements for machine learning methods such as deep neural networks, to the best of our knowledge, its development in sparse Bayesian models is still lacking. Sparse Bayesian models are highly interpretable with natural uncertain quantification, a desirable property for many scientific problems. However, without a federated learning algorithm, their applicability to sensitive biological/biomedical data from multiple sources is limited. Therefore, to fill this gap in the literature, we propose a new Bayesian federated learning framework that is capable of pooling information from different data sources without breaching privacy. The proposed method is conceptually simple to understand and implement, accommodates sampling heterogeneity (i.e., non-iid observations) across data sources, and allows for principled uncertainty quantification. We illustrate the proposed framework with three concrete sparse Bayesian models, namely, sparse regression, Markov random field, and directed graphical models. The application of these three models is demonstrated through three real data examples including a multi-hospital COVID-19 study, breast cancer protein-protein interaction networks, and gene regulatory networks.

DNB: A Joint Learning Framework for Deep Bayesian Nonparametric Clustering

Clustering algorithms based on deep neural networks have been widely studied for image analysis. Most existing methods require partial knowledge of the true labels, namely, the number of clusters, which is usually not available in practice. In this article, we propose a Bayesian nonparametric framework, deep nonparametric Bayes (DNB), for jointly learning image clusters and deep representations in a doubly unsupervised manner. In doubly unsupervised learning, we are dealing with the problem of "unknown unknowns," where we estimate not only the unknown image labels but also the unknown number of labels as well. The proposed algorithm alternates between generating a potentially unbounded number of clusters in the forward pass and learning the deep networks in the backward pass. With the help of the Dirichlet process mixtures, the proposed method is able to partition the latent representations space without specifying the number of clusters a priori. An important feature of this work is that all the estimation is realized with an end-to-end solution, which is very different from the methods that rely on post hoc analysis to select the number of clusters. Another key idea in this article is to provide a principled solution to the problem of "trivial solution" for deep clustering, which has not been much studied in the current literature. With extensive experiments on benchmark datasets, we show that our doubly unsupervised method achieves good clustering performance and outperforms many other unsupervised image clustering methods.

Consensus clustering for Bayesian mixture models

BACKGROUND

Cluster analysis is an integral part of precision medicine and systems biology, used to define groups of patients or biomolecules. Consensus clustering is an ensemble approach that is widely used in these areas, which combines the output from multiple runs of a non-deterministic clustering algorithm. Here we consider the application of consensus clustering to a broad class of heuristic clustering algorithms that can be derived from Bayesian mixture models (and extensions thereof) by adopting an early stopping criterion when performing sampling-based inference for these models. While the resulting approach is non-Bayesian, it inherits the usual benefits of consensus clustering, particularly in terms of computational scalability and providing assessments of clustering stability/robustness.

RESULTS

In simulation studies, we show that our approach can successfully uncover the target clustering structure, while also exploring different plausible clusterings of the data. We show that, when a parallel computation environment is available, our approach offers significant reductions in runtime compared to performing sampling-based Bayesian inference for the underlying model, while retaining many of the practical benefits of the Bayesian approach, such as exploring different numbers of clusters. We propose a heuristic to decide upon ensemble size and the early stopping criterion, and then apply consensus clustering to a clustering algorithm derived from a Bayesian integrative clustering method. We use the resulting approach to perform an integrative analysis of three 'omics datasets for budding yeast and find clusters of co-expressed genes with shared regulatory proteins. We validate these clusters using data external to the analysis.

CONCLUSTIONS

Our approach can be used as a wrapper for essentially any existing sampling-based Bayesian clustering implementation, and enables meaningful clustering analyses to be performed using such implementations, even when computational Bayesian inference is not feasible, e.g. due to poor exploration of the target density (often as a result of increasing numbers of features) or a limited computational budget that does not along sufficient samples to drawn from a single chain. This enables researchers to straightforwardly extend the applicability of existing software to much larger datasets, including implementations of sophisticated models such as those that jointly model multiple datasets.