A Novel Gene Network Inference Algorithm Using Predictive Minimum Description Length Approach

Background: Reverse engineering of gene regulatory networks using information theory models has received much attention due to its simplicity, low computational cost, and capability of inferring large networks. One of the major problems with information theory models is to determine the threshold which defines the regulatory relationships between genes. The minimum description length (MDL) principle has been implemented to overcome this problem. The description length of the MDL principle is the sum of model length and data encoding length. A user-specified fine tuning parameter is used as control mechanism between model and data encoding, but it is difficult to find the optimal parameter. In this work, we proposed a new inference algorithm which incorporated mutual information (MI), conditional mutual information (CMI) and predictive minimum description length (PMDL) principle to infer gene regulatory networks from DNA microarray data. In this algorithm, the information theoretic quantities MI and CMI determine the regulatory relationships between genes and the PMDL principle method attempts to determine the best MI threshold without the need of a user-specified fine tuning parameter. Results: The performance of the proposed algorithm was evaluated using both synthetic time series data sets and a biological time series data set for the yeast Saccharomyces cerevisiae. The benchmark quantities precision and recall were used as performance measures. The results show that the proposed algorithm produced less false edges and significantly improved the precision, as compared to the existing algorithm. For further analysis the performance of the algorithms was observed over different sizes of data. Conclusions: We have proposed a new algorithm that implements the PMDL principle for inferring gene regulatory networks from time series DNA microarray data that eliminates the need of a fine tuning parameter. The evaluation results obtained from both synthetic and actual biological data sets show that the PMDL principle is effective in determining the MI threshold and the developed algorithm improves precision of gene regulatory network inference. Based on the sensitivity analysis of all tested cases, an optimal CMI threshold value has been identified. Finally it was observed that the performance of the algorithms saturates at a certain threshold of data size

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Time lagged information theoretic approaches to the reverse engineering of gene regulatory networks

Background: A number of models and algorithms have been proposed in the past for gene regulatory network (GRN) inference; however, none of them address the effects of the size of time-series microarray expression data in terms of the number of time-points. In this paper, we study this problem by analyzing the behaviour of three algorithms based on information theory and dynamic Bayesian network (DBN) models. These algorithms were implemented on different sizes of data generated by synthetic networks. Experiments show that the inference accuracy of these algorithms reaches a saturation point after a specific data size brought about by a saturation in the pair-wise mutual information (MI) metric; hence there is a theoretical limit on the inference accuracy of information theory based schemes that depends on the number of time points of micro-array data used to infer GRNs. This illustrates the fact that MI might not be the best metric to use for GRN inference algorithms. To circumvent the limitations of the MI metric, we introduce a new method of computing time lags between any pair of genes and present the pair-wise time lagged Mutual Information (TLMI) and time lagged Conditional Mutual Information (TLCMI) metrics. Next we use these new metrics to propose novel GRN inference schemes which provides higher inference accuracy based on the precision and recall parameters. Results: It was observed that beyond a certain number of time-points (i.e., a specific size) of micro-array data, the performance of the algorithms measured in terms of the recall-to-precision ratio saturated due to the saturation in the calculated pair-wise MI metric with increasing data size. The proposed algorithms were compared to existing approaches on four different biological networks. The resulting networks were evaluated based on the benchmark precision and recall metrics and the results favour our approach. Conclusions: To alleviate the effects of data size on information theory based GRN inference algorithms, novel time lag based information theoretic approaches to infer gene regulatory networks have been proposed. The results show that the time lags of regulatory effects between any pair of genes play an important role in GRN inference schemes

Structural Agnostic Modeling: Adversarial Learning of Causal Graphs

A new causal discovery method, Structural Agnostic Modeling (SAM), is presented in this paper. Leveraging both conditional independencies and distributional asymmetries in the data, SAM aims at recovering full causal models from continuous observational data along a multivariate non-parametric setting. The approach is based on a game between $d$ players estimating each variable distribution conditionally to the others as a neural net, and an adversary aimed at discriminating the overall joint conditional distribution, and that of the original data. An original learning criterion combining distribution estimation, sparsity and acyclicity constraints is used to enforce the end-to-end optimization of the graph structure and parameters through stochastic gradient descent. Besides the theoretical analysis of the approach in the large sample limit, SAM is extensively experimentally validated on synthetic and real data

Generating probabilistic Boolean networks from a prescribed stationary distribution

Modeling gene regulation is an important problem in genomic research. Boolean networks (BN) and its generalization probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. BN is a deterministic model while PBN is a stochastic model. In a PBN, on one hand, its stationary distribution gives important information about the long-run behavior of the network. On the other hand, one may be interested in system synthesis which requires the construction of networks from the observed stationary distribution. This results in an inverse problem which is ill-posed and challenging. Because there may be many networks or no network having the given properties and the size of the inverse problem is huge. In this paper, we consider the problem of constructing PBNs from a given stationary distribution and a set of given Boolean Networks (BNs). We first formulate the inverse problem as a constrained least squares problem. We then propose a heuristic method based on Conjugate Gradient (CG) algorithm, an iterative method, to solve the resulting least squares problem. We also introduce an estimation method for the parameters of the PBNs. Numerical examples are then given to demonstrate the effectiveness of the proposed methods. © 2010 Elsevier Inc. All rights reserved.postprin