There is often a limited amount of omics data to design predictive models in biomedicine. Knowing that these omics data come from underlying processes that may share common pathways and disease mechanisms, it may be beneficial for designing a more accurate and reliable predictor in a target domain of interest, where there is a lack of labeled data to leverage available data in relevant source domains. Here, we focus on developing Bayesian transfer learning methods for analyzing next-generation sequencing (NGS) data to help improve predictions in the target domain. We formulate transfer learning in a fully Bayesian framework and define the relatedness by a joint prior distribution of the model parameters of the source and target domains. Defining joint priors acts as a bridge across domains, through which the related knowledge of source data is transferred to the target domain. We focus on RNA-seq discrete count data, which are often overdispersed. To appropriately model them, we consider the Negative Binomial model and propose an Optimal Bayesian Transfer Learning (OBTL) classifier that minimizes the expected classification error in the target domain. We evaluate the performance of the OBTL classifier via both synthetic and cancer data from The Cancer Genome Atlas (TCGA).

This paper studies classification of gene-expression trajectories coming from two classes, healthy and mutated (cancerous) using Boolean networks with perturbation (BNps) to model the dynamics of each class at the state level. Each class has its own BNp, which is partially known based on gene pathways. We employ a Gaussian model at the observation level to show the expression values of the genes given the hidden binary states at each time point. We use expectation maximization (EM) to learn the BNps and the unknown model parameters, derive closed-form updates for the parameters, and propose a learning algorithm. After learning, a plug-in Bayes classifier is used to classify unlabeled trajectories, which can have missing data. Measuring gene expressions at different times yields trajectories only when measurements come from a single cell. In multiple-cell scenarios, the expression values are averages over many cells with possibly different states. Via the central-limit theorem, we propose another model for expression data in multiple-cell scenarios. Simulations demonstrate that single-cell trajectory data can outperform multiple-cell average expression data relative to classification error, especially in high-noise situations. We also consider data generated via a mammalian cell-cycle network, both the wild-type and with a common mutation affecting p27.

Precision medicine aims for personalized prognosis and therapeutics by utilizing recent genome-scale high-throughput profiling techniques, including next-generation sequencing (NGS). However, translating NGS data faces several challenges. First, NGS count data are often overdispersed, requiring appropriate modeling. Second, compared to the number of involved molecules and system complexity, the number of available samples for studying complex disease, such as cancer, is often limited, especially considering disease heterogeneity. The key question is whether we may integrate available data from all different sources or domains to achieve reproducible disease prognosis based on NGS count data. In this paper, we develop a Bayesian Multi-Domain Learning (BMDL) model that derives domain-dependent latent representations of overdispersed count data based on hierarchical negative binomial factorization for accurate cancer subtyping even if the number of samples for a specific cancer type is small. Experimental results from both our simulated and NGS datasets from The Cancer Genome Atlas (TCGA) demonstrate the promising potential of BMDL for effective multi-domain learning without ``negative transfer'' effects often seen in existing multi-task learning and transfer learning methods.

Transfer learning studies effective ways to derive better predictors for a system of interest in atargetdomain, where there is lack of data, by utilizing data from other related systems assourcedomain(s). We define a Bayesian transfer learning framework for regression to integrate data between the domains through a joint prior distribution for the source and target parameters. We derive closed-form posteriors of the target parameters integrating both the source and target data, from which closed-form effective joint distributions in the target domain can be derived in terms of generalized hypergeometric functions of matrix argument to define the optimal Bayesian transfer regression (OBTR) operator. We show that the OBTR improves the mean squared error when the source and target domains are related on both synthetic and real-world data.

Gene-expression-based phenotype classification is used for disease diagnosis and prognosis relating to treatment strategies. The present paper considers classification based on sequential measurements of multiple genes using gene regulatory network (GRN) modeling. There are two networks, original and mutated, and observations consist of trajectories of network states. The problem is to classify an observation trajectory as coming from either the original or mutated network. GRNs are modeled via probabilistic Boolean networks, which incorporate stochasticity at both the gene and network levels. Mutation affects the regulatory logic. Classification is based upon observing a trajectory of states of some given length. We characterize the Bayes classifier and find the Bayes error for a general PBN and the special case of a single Boolean network affected by random perturbations (BNp). The Bayes error is related to network sensitivity, meaning the extent of alteration in the steady-state distribution of the original network owing to mutation. Using standard methods to calculate steady-state distributions is cumbersome and sometimes impossible, so we provide an efficient algorithm and approximations. Extensive simulations are performed to study the effects of various factors, including approximation accuracy. We apply the classification procedure to a p53 BNp and a mammalian cell cycle PBN.

This paper studies the classification of gene regulatory networks (GRNs) modeled by probabilistic Boolean networks (PBNs). After observing Gaussian expression values of n genes at m consecutive time points, with consideration of missing data, an algorithm based on expectation maximization (EM) is proposed to estimate the parameters and infer the unknown parts of the networks in the maximum likelihood (ML) sense. Then the estimated values are plugged in to the Bayes classifier, which is optimal, and the performance of the classifier is investigated through various simulations.

We propose a novel cooperative transmission scheme called Convolutional Network-Coded Cooperation (CNCC) for a network including N sources, one M-antenna relay, and one common destination. The source-relay (S-R) channels are assumed to be Nakagami-m fading, while the source-destination (S-D) and the relay-destination (R-D) channels are considered Rayleigh fading. The CNCC scheme exploits the generator matrix of a good (N + M', N,v) systematic convolutional code, with the free distance of dfreedesigned over GF(2), as the network coding matrix which is run by the network's nodes, such that the systematic symbols are directly transmitted from the sources, and the parity symbols are sent by the best antenna of the relay. An upper bound on the BER of the sources, and consequently, the achieved diversity orders are obtained. The numerical results indicate that the CNCC scheme outperforms the other cooperative schemes considered, in terms of the diversity order and the network throughput. The simulation results confirm the accuracy of the theoretical analysis.