DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets

One of the grand challenges of cell biology is inferring the gene regulatory network (GRN) which describes interactions between genes and their products that control gene expression and cellular function. We can treat this as a causal discovery problem but with two non-standard challenges: (1) regulatory networks are inherently cyclic so we should not model a GRN as a directed acyclic graph (DAG), and (2) observations have significant measurement noise, so for typical sample sizes there will always be a large equivalence class of graphs that are likely given the data, and we want methods that capture this uncertainty. Existing methods either focus on challenge (1), identifying cyclic structure from dynamics, or on challenge (2) learning complex Bayesian posteriors over DAGs, but not both. In this paper we leverage the fact that it is possible to estimate the "velocity" of gene expression with RNA velocity techniques to develop an approach that addresses both challenges. Because we have access to velocity information, we can treat the Bayesian structure learning problem as a problem of sparse identification of a dynamical system, capturing cyclic feedback loops through time. Since our objective is to model uncertainty over discrete structures, we leverage Generative Flow Networks (GFlowNets) to estimate the posterior distribution over the combinatorial space of possible sparse dependencies. Our results indicate that our method learns posteriors that better encapsulate the distributions of cyclic structures compared to counterpart state-of-the-art Bayesian structure learning approaches

Reverse engineering of genetic networks with Bayesian networks

This paper provides a brief introduction to learning Bayesian networks from gene-expression data. The method is contrasted with other approaches to the reverse engineering of biochemical networks, and the Bayesian learning paradigm is briefly described. The article demonstrates an application to a simple synthetic toy problem and evaluates the inference performance in terms of ROC (receiver operator characteristic) curves

Network estimation in State Space Model with L1-regularization constraint

Biological networks have arisen as an attractive paradigm of genomic science ever since the introduction of large scale genomic technologies which carried the promise of elucidating the relationship in functional genomics. Microarray technologies coupled with appropriate mathematical or statistical models have made it possible to identify dynamic regulatory networks or to measure time course of the expression level of many genes simultaneously. However one of the few limitations fall on the high-dimensional nature of such data coupled with the fact that these gene expression data are known to include some hidden process. In that regards, we are concerned with deriving a method for inferring a sparse dynamic network in a high dimensional data setting. We assume that the observations are noisy measurements of gene expression in the form of mRNAs, whose dynamics can be described by some unknown or hidden process. We build an input-dependent linear state space model from these hidden states and demonstrate how an incorporated $L_{1}$ regularization constraint in an Expectation-Maximization (EM) algorithm can be used to reverse engineer transcriptional networks from gene expression profiling data. This corresponds to estimating the model interaction parameters. The proposed method is illustrated on time-course microarray data obtained from a well established T-cell data. At the optimum tuning parameters we found genes TRAF5, JUND, CDK4, CASP4, CD69, and C3X1 to have higher number of inwards directed connections and FYB, CCNA2, AKT1 and CASP8 to be genes with higher number of outwards directed connections. We recommend these genes to be object for further investigation. Caspase 4 is also found to activate the expression of JunD which in turn represses the cell cycle regulator CDC2.Comment: arXiv admin note: substantial text overlap with arXiv:1308.359

Bayesian Orthogonal Least Squares (BOLS) algorithm for reverse engineering of gene regulatory networks

<p>Abstract</p> <p>Background</p> <p>A reverse engineering of gene regulatory network with large number of genes and limited number of experimental data points is a computationally challenging task. In particular, reverse engineering using linear systems is an underdetermined and ill conditioned problem, i.e. the amount of microarray data is limited and the solution is very sensitive to noise in the data. Therefore, the reverse engineering of gene regulatory networks with large number of genes and limited number of data points requires rigorous optimization algorithm.</p> <p>Results</p> <p>This study presents a novel algorithm for reverse engineering with linear systems. The proposed algorithm is a combination of the orthogonal least squares, second order derivative for network pruning, and Bayesian model comparison. In this study, the entire network is decomposed into a set of small networks that are defined as unit networks. The algorithm provides each unit network with P(D|H_i), which is used as confidence level. The unit network with higher P(D|H_i) has a higher confidence such that the unit network is correctly elucidated. Thus, the proposed algorithm is able to locate true positive interactions using P(D|H_i), which is a unique property of the proposed algorithm.</p> <p>The algorithm is evaluated with synthetic and <it>Saccharomyces cerevisiae </it>expression data using the dynamic Bayesian network. With synthetic data, it is shown that the performance of the algorithm depends on the number of genes, noise level, and the number of data points. With Yeast expression data, it is shown that there is remarkable number of known physical or genetic events among all interactions elucidated by the proposed algorithm.</p> <p>The performance of the algorithm is compared with Sparse Bayesian Learning algorithm using both synthetic and <it>Saccharomyces cerevisiae </it>expression data sets. The comparison experiments show that the algorithm produces sparser solutions with less false positives than Sparse Bayesian Learning algorithm.</p> <p>Conclusion</p> <p>From our evaluation experiments, we draw the conclusion as follows: 1) Simulation results show that the algorithm can be used to elucidate gene regulatory networks using limited number of experimental data points. 2) Simulation results also show that the algorithm is able to handle the problem with noisy data. 3) The experiment with Yeast expression data shows that the proposed algorithm reliably elucidates known physical or genetic events. 4) The comparison experiments show that the algorithm more efficiently performs than Sparse Bayesian Learning algorithm with noisy and limited number of data.</p

Stochastic dynamic modeling of short gene expression time-series data

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the expectation maximization (EM) algorithm is applied for modeling the gene regulatory network from gene time-series data. The gene regulatory network is viewed as a stochastic dynamic model, which consists of the noisy gene measurement from microarray and the gene regulation first-order autoregressive (AR) stochastic dynamic process. By using the EM algorithm, both the model parameters and the actual values of the gene expression levels can be identified simultaneously. Moreover, the algorithm can deal with the sparse parameter identification and the noisy data in an efficient way. It is also shown that the EM algorithm can handle the microarray gene expression data with large number of variables but a small number of observations. The gene expression stochastic dynamic models for four real-world gene expression data sets are constructed to demonstrate the advantages of the introduced algorithm. Several indices are proposed to evaluate the models of inferred gene regulatory networks, and the relevant biological properties are discussed