Amina Noor

Inferring Gene Regulatory Networks via Nonlinear State-Space Models and Exploiting Sparsity

This paper considers the problem of learning the structure of gene regulatory networks from gene expression time series data. A more realistic scenario when the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter-based state estimation algorithm is considered instead of the contemporary linear approximation-based approaches. The parameters characterizing the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then subjected to a LASSO-based least squares regression operation which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with the extended Kalman filter (EKF) and Unscented Kalman Filter (UKF) employing the Mean Square Error (MSE) as the fidelity criterion in recovering the parameters of gene regulatory networks from synthetic data and real biological data. Extensive computer simulations illustrate that the proposed particle filter-based network inference algorithm outperforms EKF and UKF, and therefore, it can serve as a natural framework for modeling gene regulatory networks with nonlinear and sparse structure.

ROBNCA: robust network component analysis for recovering transcription factor activities

Network component analysis (NCA) is an efficient method of reconstructing the transcription factor activity (TFA), which makes use of the gene expression data and prior information available about transcription factor (TF) - gene regulations. We propose ROBust Network Component Analysis (ROBNCA), a novel iterative algorithm that explicitly models the possible outliers in the microarray data. ROBNCA algorithm provides a closed form solution for estimating the connectivity matrix, which was not available in prior contributions. The ROBNCA algorithm is compared to FastNCA and the Non-iterative NCA (NI-NCA) and is shown to estimate the TF activity profiles as well as the TF-gene control strength matrix with a much higher degree of accuracy than FastNCA and NI-NCA, irrespective of varying noise, and/or amount of outliers in case of synthetic data. The run time of the ROBNCA algorithm is comparable to that of FastNCA, and is hundreds of times faster than NI-NCA.

Reverse Engineering Sparse Gene Regulatory Networks Using Cubature Kalman Filter and Compressed Sensing

This paper proposes a novel algorithm for inferring gene regulatory networks which makes use of cubature Kalman filter (CKF) and Kalman filter (KF) techniques in conjunction with compressed sensing methods. The gene network is described using a state-space model. A nonlinear model for the evolution of gene expression is considered, while the gene expression data is assumed to follow a linear Gaussian model. The hidden states are estimated using CKF. The system parameters are modeled as a Gauss-Markov process and are estimated using compressed sensing-based KF. These parameters provide insight into the regulatory relations among the genes. The Cramér-Rao lower bound of the parameter estimates is calculated for the system model and used as a benchmark to assess the estimation accuracy. The proposed algorithm is evaluated rigorously using synthetic data in different scenarios which include different number of genes and varying number of sample points. In addition, the algorithm is tested on the DREAM4 in silico data sets as well as the in vivo data sets from IRMA network. The proposed algorithm shows superior performance in terms of accuracy, robustness, and scalability.

An Overview of the Statistical Methods Used for Inferring Gene Regulatory Networks and Protein-Protein Interaction Networks

The large influx of data from high-throughput genomic and proteomic technologies has encouraged the researchers to seek approaches for understanding the structure of gene regulatory networks and proteomic networks. This work reviews some of the most important statistical methods used for modeling of gene regulatory networks (GRNs) and protein-protein interaction (PPI) networks. The paper focuses on the recent advances in the statistical graphical modeling techniques, state-space representation models, and information theoretic methods that were proposed for inferring the topology of GRNs. It appears that the problem of inferring the structure of PPI networks is quite different from that of GRNs. Clustering and probabilistic graphical modeling techniques are of prime importance in the statistical inference of PPI networks, and some of the recent approaches using these techniques are also reviewed in this paper. Performance evaluation criteria for the approaches used for modeling GRNs and PPI networks are also discussed.

On Clock Offset Estimation in Wireless Sensor Networks with Weibull Distributed Network Delays

We consider the problem of Maximum Likelihood (ML) estimation of clock parameters in a two-way timing exchange scenario where the random delays assume a Weibull distribution, which represents a more generalized model. The ML estimate of the clock offset for the case of exponential distribution was obtained earlier. Moreover, it was reported that when the fixed delay is known, MLE is not unique. We determine the uniformly minimum variance unbiased (UMVU) estimators for exponential distribution under such a scenario and produce biased estimators having lower MSE than UMVU for all values of clock offset. We then consider the case when shape parameter is greater than one and reduce the corresponding optimization problems to their equivalent convex forms, thus guaranteeing convergence to a global minimum.

Information theoretic methods for modeling of gene regulatory networks

This paper reviews the information theoretic methods used for inferring gene regulatory networks. Mutual information has been widely used as a dependency measure to estimate the undirected interactions between genes using steady state data. However, employing time-series data results in a directed graph. Since two genes may be interacting with each other via an intermediate gene, their mutual information may show a direct dependency. To resolve this issue, data processing inequality and conditional mutual information have been employed. Mutual information, being a symmetric measure, is unable to predict directed edges using the steady-state data alone, while algorithms using time-series data can be computationally complex as more data is involved. Therefore, non-symmetric measures such as φ mixing coefficients have recently been proposed in the literature. The algorithms using these techniques are also discussed in this article. Estimation of information-theoretic metrics is explained which is a core component of all the methods. Performance metrics that are frequently used to test the robustness and accuracy of the algorithms are also described and some avenues of future research are proposed.

An Overview of NCA-Based Algorithms for Transcriptional Regulatory Network Inference

In systems biology, the regulation of gene expressions involves a complex network of regulators. Transcription factors (TFs) represent an important component of this network: they are proteins that control which genes are turned on or off in the genome by binding to specific DNA sequences. Transcription regulatory networks (TRNs) describe gene expressions as a function of regulatory inputs specified by interactions between proteins and DNA. A complete understanding of TRNs helps to predict a variety of biological processes and to diagnose, characterize and eventually develop more efficient therapies. Recent advances in biological high-throughput technologies, such as DNA microarray data and next-generation sequence (NGS) data, have made the inference of transcription factor activities (TFAs) and TF-gene regulations possible. Network component analysis (NCA) represents an efficient computational framework for TRN inference from the information provided by microarrays, ChIP-on-chip and the prior information about TF-gene regulation. However, NCA suffers from several shortcomings. Recently, several algorithms based on the NCA framework have been proposed to overcome these shortcomings. This paper first overviews the computational principles behind NCA, and then, it surveys the state-of-the-art NCA-based algorithms proposed in the literature for TRN reconstruction.

Joint clock offset and skew estimation for inactive nodes in Wireless Sensor Networks

We incorporate the clock skew in the message exchange mechanism of [3], without which the clock synchronization problem remains practically unsolved. For the offset-only case, we determine the ML estimators through a simple application of convex optimization, alleviating the need for the graphical search mentioned in [3]. We also propose estimators that outperform the ML estimators in terms of MSE. For the joint estimation of clock offset and skew, we show that the likelihood maximization can be equivalently represented as a linear program and can be solved efficiently by any gradient descent method.

Inferring gene regulatory networks with nonlinear models via exploiting sparsity

This paper considers the problem of inferring gene regulatory networks using time series data. A nonlinear model is assumed for the gene expression profiles, whereas the microarray data follows a linear Gaussian model. A particle filter based approach is proposed to estimate the gene expression profiles and the parameters are estimated online using Kalman filter. In order to capture the inherent sparsity of the gene networks, LASSO based least square optimization is performed. The performance of the proposed algorithm is compared with the extended Kalman filter (EKF) algorithm using Mean Square Error (MSE) as the fidelity criterion. The simulations are performed using the synthetic as well as real data and the proposed algorithm is observed to outperform the EKF in the scenarios considered.

A Closed-Form Solution for Transcription Factor Activity Estimation Using Network Component Analysis

Non-iterative network component analysis (NINCA), proposed by Jacklin at.al, employs convex optimization methods to estimate the transcription factor control strengths and transcription factor activities. While NINCA provides good estimation accuracy and higher consistency, the costly optimization routine used therein renders a high computational complexity. This correspondence presents a closed form solution to estimate the connectivity matrix which is tens of times faster, and provides similar accuracy and consistency, thus making the closed form NINCA (CFNINCA) algorithm useful for large data sets encountered in practice. The proposed solution is assessed for accuracy and consistency using synthetic and yeast cell cycle data sets by comparing with the existing state-of-the-art algorithms. The robustness of the algorithm to the possible inaccuracies in prior information is also analyzed and it is observed that CFNINCA and NINCA are much more robust to erroneous prior information as compared to FastNCA.