Capturing the conditional covariances or correlations among the elements of a multivariate response vector based on covariates is important to various fields including neuroscience, epidemiology and biomedicine. We propose a new method called Covariance Regression with Random Forests (CovRegRF) to estimate the covariance matrix of a multivariate response given a set of covariates, using a random forest framework. Random forest trees are built with a splitting rule specially designed to maximize the difference between the sample covariance matrix estimates of the child nodes. We also propose a significance test for the partial effect of a subset of covariates. We evaluate the performance of the proposed method and significance test through a simulation study which shows that the proposed method provides accurate covariance matrix estimates and that the Type-1 error is well controlled. An application of the proposed method to thyroid disease data is also presented. CovRegRF is implemented in a freely available R package on CRAN.

Missingness and corruption are common problems for real-world traffic data. How to accurately perform imputation and prediction based on incomplete or even sparse traffic data becomes a critical research question in intelligent transportation systems. Low-rank matrix factorization (MF) is a common solution for the general missing value imputation problem. To better characterize and encode the strong spatial and temporal consistency in traffic data, existing work has introduced flexible spatial/temporal Gaussian process (GP) priors to model the latent factors in MF framework, which also allows us to perform kriging for unseen locations and virtual sensors. However, learning the hyperparameters in GP kernels remains a challenging task. In this paper, we present a Bayesian kernelized matrix factorization (BKMF) model with an efficient Markov chain Monte Carlo (MCMC) sampling algorithm for model inference. By learning the kernel hyperparameters from their marginal posteriors through a slice sampling treatment and updating the latent factors alternatively with Gibbs sampling, we achieve a fully Bayesian model for the spatiotemporally kernelized (i.e., GP prior regularized) MF framework. We apply BKMF on both imputation and kriging tasks, and our results demonstrate the superiority of BKMF compared with state-of-the-art spatiotemporal models. In addition, we also explore the effects of different GP kernels in characterizing networked spatiotemporal traffic state data.

Time series forecasting and spatiotemporal kriging are the two most important tasks in spatiotemporal data analysis. Recent research on graph neural networks has made substantial progress in time series forecasting, while little attention has been paid to the kriging problem---recovering signals for unsampled locations/sensors. Most existing scalable kriging methods (e.g., matrix/tensor completion) are transductive, and thus full retraining is required when we have a new sensor to interpolate. In this paper, we develop an Inductive Graph Neural Network Kriging (IGNNK) model to recover data for unsampled sensors on a network/graph structure. To generalize the effect of distance and reachability, we generate random subgraphs as samples and the corresponding adjacency matrix for each sample. By reconstructing all signals on each sample subgraph, IGNNK can effectively learn the spatial message passing mechanism. Empirical results on several real-world spatiotemporal datasets demonstrate the effectiveness of our model. In addition, we also find that the learned model can be successfully transferred to the same type of kriging tasks on an unseen dataset. Our results show that: 1) GNN is an efficient and effective tool for spatial kriging; 2) inductive GNNs can be trained using dynamic adjacency matrices; 3) a trained model can be transferred to new graph structures and 4) IGNNK can be used to generate virtual sensors.

MOTIVATION: Investigating the relationships between two sets of variables helps to understand their interactions and can be done with canonical correlation analysis (CCA). However, the correlation between the two sets can sometimes depend on a third set of covariates, often subject-related ones such as age, gender or other clinical measures. In this case, applying CCA to the whole population is not optimal and methods to estimate conditional CCA, given the covariates, can be useful. RESULTS: We propose a new method called Random Forest with Canonical Correlation Analysis (RFCCA) to estimate the conditional canonical correlations between two sets of variables given subject-related covariates. The individual trees in the forest are built with a splitting rule specifically designed to partition the data to maximize the canonical correlation heterogeneity between child nodes. We also propose a significance test to detect the global effect of the covariates on the relationship between two sets of variables. The performance of the proposed method and the global significance test is evaluated through simulation studies that show it provides accurate canonical correlation estimations and well-controlled Type-1 error. We also show an application of the proposed method with EEG data. AVAILABILITY AND IMPLEMENTATION: RFCCA is implemented in a freely available R package on CRAN (https://CRAN.R-project.org/package=RFCCA). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The human microbiota is the collection of microorganisms colonizing the human body, and plays an integral part in human health. A growing trend in microbiome analysis is to construct a network to estimate the co-occurrence patterns among taxa through precision matrices. Existing methods do not facilitate investigation into how these networks change with respect to covariates. RESULTS: We propose a new model called Microbiome Differential Network Estimation (MDiNE) to estimate network changes with respect to a binary covariate. The counts of individual taxa in the samples are modeled through a multinomial distribution whose probabilities depend on a latent Gaussian random variable. A sparse precision matrix over all the latent terms determines the co-occurrence network among taxa. The model fit is obtained and evaluated using Hamiltonian Monte Carlo methods. The performance of our model is evaluated through an extensive simulation study and is shown to outperform existing methods in terms of estimation of network parameters. We also demonstrate an application of the model to estimate changes in the intestinal microbial network topology with respect to Crohn's disease. AVAILABILITY AND IMPLEMENTATION: MDiNE is implemented in a freely available R package: https://github.com/kevinmcgregor/mdine. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Conventional phylogenetic clustering approaches rely on arbitrary cutpoints applied a posteriori to phylogenetic estimates. Although in practice, Bayesian and bootstrap-based clustering tend to lead to similar estimates, they often produce conflicting measures of confidence in clusters. The current study proposes a new Bayesian phylogenetic clustering algorithm, which we refer to as DM-PhyClus (Dirichlet-Multinomial Phylogenetic Clustering), that identifies sets of sequences resulting from quick transmission chains, thus yielding easily-interpretable clusters, without using any ad hoc distance or confidence requirement. RESULTS: Simulations reveal that DM-PhyClus can outperform conventional clustering methods, as well as the Gap procedure, a pure distance-based algorithm, in terms of mean cluster recovery. We apply DM-PhyClus to a sample of real HIV-1 sequences, producing a set of clusters whose inference is in line with the conclusions of a previous thorough analysis. CONCLUSIONS: DM-PhyClus, by eliminating the need for cutpoints and producing sensible inference for cluster configurations, can facilitate transmission cluster detection. Future efforts to reduce incidence of infectious diseases, like HIV-1, will need reliable estimates of transmission clusters. It follows that algorithms like DM-PhyClus could serve to better inform public health strategies.

MOTIVATION: DNA methylation patterns are well known to vary substantially across cell types or tissues. Hence, existing normalization methods may not be optimal if they do not take this into account. We therefore present a new R package for normalization of data from the Illumina Infinium Human Methylation450 BeadChip (Illumina 450 K) built on the concepts in the recently published funNorm method, and introducing cell-type or tissue-type flexibility. RESULTS: funtooNorm is relevant for data sets containing samples from two or more cell or tissue types. A visual display of cross-validated errors informs the choice of the optimal number of components in the normalization. Benefits of cell (tissue)-specific normalization are demonstrated in three data sets. Improvement can be substantial; it is strikingly better on chromosome X, where methylation patterns have unique inter-tissue variability. AVAILABILITY AND IMPLEMENTATION: An R package is available at https://github.com/GreenwoodLab/funtooNorm, and has been submitted to Bioconductor at http://bioconductor.org.

MOTIVATION: Recently, mapping studies of expression quantitative loci (eQTL) (where gene expression levels are viewed as quantitative traits) have provided insight into the biology of gene regulation. Bayesian methods provide natural modeling frameworks for analyzing eQTL studies, where information shared across markers and/or genes can increase the power to detect eQTLs. Bayesian approaches tend to be computationally demanding and require specialized software. As a result, most eQTL studies use univariate methods treating each gene independently, leading to suboptimal results. RESULTS: We present a powerful, computationally optimized and free open-source R package, iBMQ. Our package implements a joint hierarchical Bayesian model where all genes and SNPs are modeled concurrently. Model parameters are estimated using a Markov chain Monte Carlo algorithm. The free and widely used openMP parallel library speeds up computation. Using a mouse cardiac dataset, we show that iBMQ improves the detection of large trans-eQTL hotspots compared with other state-of-the-art packages for eQTL analysis. AVAILABILITY: The R-package iBMQ is available from the Bioconductor Web site at http://bioconductor.org and runs on Linux, Windows and MAC OS X. It is distributed under the Artistic Licence-2.0 terms. CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: In high density arrays, the identification of relevant genes for disease classification is complicated by not only the curse of dimensionality but also the highly correlated nature of the array data. In this paper, we are interested in the question of how many and which genes should be selected for a disease class prediction. Our work consists of a Bayesian supervised statistical learning approach to refine gene signatures with a regularization which penalizes for the correlation between the variables selected. RESULTS: Our simulation results show that we can most often recover the correct subset of genes that predict the class as compared to other methods, even when accuracy and subset size remain the same. On real microarray datasets, we show that our approach can refine gene signatures to obtain either the same or better predictive performance than other existing methods with a smaller number of genes. CONCLUSIONS: Our novel Bayesian approach includes a prior which penalizes highly correlated features in model selection and is able to extract key genes in the highly correlated context of microarray data. The methodology in the paper is described in the context of microarray data, but can be applied to any array data (such as micro RNA, for example) as a first step towards predictive modeling of cancer pathways. A user-friendly software implementation of the method is available.