Incorporating graph information in Bayesian factor analysis with robust and adaptive shrinkage priors.

There has been an increasing interest in decomposing high-dimensional multi-omics data into a product of low-rank and sparse matrices for the purpose of dimension reduction and feature engineering. Bayesian factor models achieve such low-dimensional representation of the original data through different sparsity-inducing priors. However, few of these models can efficiently incorporate the information encoded by the biological graphs, which has been already proven to be useful in many analysis tasks. In this work, we propose a Bayesian factor model with novel hierarchical priors, which incorporate the biological graph knowledge as a tool of identifying a group of genes functioning collaboratively. The proposed model therefore enables sparsity within networks by allowing each factor loading to be shrunk adaptively and by considering additional layers to relate individual shrinkage parameters to the underlying graph information, both of which yield a more accurate structure recovery of factor loadings. Further, this new priors overcome the phase transition phenomenon, in contrast to existing graph-incorporated approaches, so that it is robust to noisy edges that are inconsistent with the actual sparsity structure of the factor loadings. Finally, our model can handle both continuous and discrete data types. The proposed method is shown to outperform several existing factor analysis methods through simulation experiments and real data analyses.

Robust knowledge-guided biclustering for multi-omics data.

Biclustering is a useful method for simultaneously grouping samples and features and has been applied across various biomedical data types. However, most existing biclustering methods lack the ability to integratively analyze multi-modal data such as multi-omics data such as genome, transcriptome and epigenome. Moreover, the potential of leveraging biological knowledge represented by graphs, which has been demonstrated to be beneficial in various statistical tasks such as variable selection and prediction, remains largely untapped in the context of biclustering. To address both, we propose a novel Bayesian biclustering method called Bayesian graph-guided biclustering (BGB). Specifically, we introduce a new hierarchical sparsity-inducing prior to effectively incorporate biological graph information and establish a unified framework to model multi-view data. We develop an efficient Markov chain Monte Carlo algorithm to conduct posterior sampling and inference. Extensive simulations and real data analysis show that BGB outperforms other popular biclustering methods. Notably, BGB is robust in terms of utilizing biological knowledge and has the capability to reveal biologically meaningful information from heterogeneous multi-modal data.

Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliability.

Bayesian neural network (BNN) allows for uncertainty quantification in prediction, offering an advantage over regular neural networks that has not been explored in the differential privacy (DP) framework. We fill this important gap by leveraging recent development in Bayesian deep learning and privacy accounting to offer a more precise analysis of the trade-off between privacy and accuracy in BNN. We propose three DP-BNNs that characterize the weight uncertainty for the same network architecture in distinct ways, namely DP-SGLD (via the noisy gradient method), DP-BBP (via changing the parameters of interest) and DP-MC Dropout (via the model architecture). Interestingly, we show a new equivalence between DP-SGD and DP-SGLD, implying that some non-Bayesian DP training naturally allows for uncertainty quantification. However, the hyperparameters such as learning rate and batch size, can have different or even opposite effects in DP-SGD and DP-SGLD. Extensive experiments are conducted to compare DP-BNNs, in terms of privacy guarantee, prediction accuracy, uncertainty quantification, calibration, computation speed, and generalizability to network architecture. As a result, we observe a new tradeoff between the privacy and the reliability. When compared to non-DP and non-Bayesian approaches, DP-SGLD is remarkably accurate under strong privacy guarantee, demonstrating the great potential of DP-BNN in real-world tasks.

Integrative analysis of multi-omics and imaging data with incorporation of biological information via structural Bayesian factor analysis.

MOTIVATION: With the rapid development of modern technologies, massive data are available for the systematic study of Alzheimer's disease (AD). Though many existing AD studies mainly focus on single-modality omics data, multi-omics datasets can provide a more comprehensive understanding of AD. To bridge this gap, we proposed a novel structural Bayesian factor analysis framework (SBFA) to extract the information shared by multi-omics data through the aggregation of genotyping data, gene expression data, neuroimaging phenotypes and prior biological network knowledge. Our approach can extract common information shared by different modalities and encourage biologically related features to be selected, guiding future AD research in a biologically meaningful way. METHOD: Our SBFA model decomposes the mean parameters of the data into a sparse factor loading matrix and a factor matrix, where the factor matrix represents the common information extracted from multi-omics and imaging data. Our framework is designed to incorporate prior biological network information. Our simulation study demonstrated that our proposed SBFA framework could achieve the best performance compared with the other state-of-the-art factor-analysis-based integrative analysis methods. RESULTS: We apply our proposed SBFA model together with several state-of-the-art factor analysis models to extract the latent common information from genotyping, gene expression and brain imaging data simultaneously from the ADNI biobank database. The latent information is then used to predict the functional activities questionnaire score, an important measurement for diagnosis of AD quantifying subjects' abilities in daily life. Our SBFA model shows the best prediction performance compared with the other factor analysis models. AVAILABILITY: Code are publicly available at https://github.com/JingxuanBao/SBFA. CONTACT: qlong@upenn.edu.