Network component analysis (NCA) is an important method for inferring transcriptional regulatory networks (TRNs) and recovering transcription factor activities (TFAs) using gene expression data, and the prior information about the connectivity matrix. The algorithms currently available crucially depend on the completeness of this prior information. However, inaccuracies in the measurement process may render incompleteness in the available knowledge about the connectivity matrix. Hence, computationally efficient algorithms are needed to overcome the possible incompleteness in the available data. We present a sparse network component analysis algorithm (sparseNCA), which incorporates the effect of incompleteness in the estimation of TRNs by imposing an additional sparsity constraint using the norm, which results in a greater estimation accuracy. In order to improve the computational efficiency, an iterative re-weighted method is proposed for the NCA problem which not only promotes sparsity but is hundreds of times faster than the norm based solution. The performance of sparseNCA is rigorously compared to that of FastNCA and NINCA using synthetic data as well as real data. It is shown that sparseNCA outperforms the existing state-of-the-art algorithms both in terms of estimation accuracy and consistency with the added advantage of low computational complexity. The performance of sparseNCA compared to its predecessors is particularly pronounced in case of incomplete prior information about the sparsity of the network. Subnetwork analysis is performed on the E.coli data which reiterates the superior consistency of the proposed algorithm.

The problems of node localization and clock synchronization in wireless sensor networks are naturally tied from a statistical signal processing perspective. In this work, we consider the joint estimation of an unknown node's location and clock parameters by incorporating the effect of imperfections in node oscillators, which render a time varying nature to the clock parameters. In order to alleviate the computational complexity associated with the optimal maximum a-posteriori estimator, a simpler approach based on the Expectation-Maximization (EM) algorithm is proposed which iteratively estimates the clock parameters using a Kalman smoother in the E-step, and the location of the unknown node in the M-step. The convergence and the mean square error (MSE) performance of the proposed algorithm are evaluated using simulation studies which demonstrate the high fidelity of the proposed joint estimation approach.

MOTIVATION: 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. Most of the contemporary algorithms either exhibit the drawback of inconsistency and poor reliability, or suffer from prohibitive computational complexity. In addition, the existing algorithms do not possess the ability to counteract the presence of outliers in the microarray data. Hence, robust and computationally efficient algorithms are needed to enable practical applications. RESULTS: We propose ROBust Network Component Analysis (ROBNCA), a novel iterative algorithm that explicitly models the possible outliers in the microarray data. An attractive feature of the ROBNCA algorithm is the derivation of a closed form solution for estimating the connectivity matrix, which was not available in prior contributions. The ROBNCA algorithm is compared with FastNCA and the non-iterative NCA (NI-NCA). ROBNCA estimates 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, correlation and/or amount of outliers in case of synthetic data. The ROBNCA algorithm is also tested on Saccharomyces cerevisiae data and Escherichia coli data, and it is observed to outperform the existing algorithms. The run time of the ROBNCA algorithm is comparable with that of FastNCA, and is hundreds of times faster than NI-NCA. AVAILABILITY: The ROBNCA software is available at http://people.tamu.edu/∼amina/ROBNCA

Clock synchronization has become an indispensable requirement in wireless sensor networks due to its central importance in vital network operations such as data fusion and duty cycling, and has attracted considerable research interest recently. Assuming exponentially distributed random delays in a two-way message exchange mechanism, this work proposes a network-wide clock synchronization algorithm using a factor graph representation of the network. Message passing using the max-product algorithm is adopted to derive the update rules for the proposed iterative procedure. A closed form solution is obtained for each node's belief about its clock offset at each iteration. Simulation results show that the application of the proposed message passing-based network-wide clock synchronization algorithm provides convergent estimates for both regular cycle-free and random topologies. Moreover, the mean square error (MSE) performance of the proposed algorithm is also compared with the Cramer-Rao bound (CRB) for small example networks, which further highlights the effectiveness of the proposed algorithm.

The problems of node localization and clock synchronization in wireless sensor networks are naturally tied from a statistical signal processing perspective. In this work, we consider the joint estimation of an unknown node's location and clock parameters by incorporating the effect of imperfections in node oscillators, which render a time varying nature to the clock parameters. The data exchange mechanism is based on a two-way message exchange with anchor nodes. In order to alleviate the computational complexity associated with the optimal maximum a-posteriori estimator, two iterative approaches are proposed as simpler alternatives. The first approach utilizes an Expectation-Maximization (EM) based algorithm which iteratively estimates the clock parameters and the location of the unknown node. The EM algorithm is further simplified by a non-linear processing of the data to obtain a closed form solution of the location estimation problem using least squares (LS). The performance of the estimation algorithms is benchmarked by deriving the Hybrid Cramer-Rao lower bound (HCRB) on the mean square error (MSE) of the estimators. The theoretical findings are corroborated by simulation studies which reveal that the LS estimator closely matches the performance of the EM algorithm for small time of arrival measurement noise, and is well suited for implementation in low cost sensor networks.

The problem of clock offset estimation in a two-way timing exchange regime is considered when the likelihood function of the observation time stamps is exponentially distributed. In order to capture the imperfections in node oscillators, which render a time-varying nature to the clock offset, a novel Bayesian approach to the clock offset estimation is proposed using a factor graph representation of the posterior density. Message passing using the max-product algorithm yields a closed form expression for the Bayesian inference problem.

Multi-user downlink MIMO communication has the potential to increase throughput using efficient beamforming. However, the precoding criteria assume perfect knowledge of the beamforming matrices at the base station (BS). This requires a user to transmit its complete channel information to the BS, a task that entails significant overhead. Limited feedback precoding, a part of LTE standardization now, needs only limited information be fed back to the BS. This paper studies the capacity loss incurred by using LTE codebooks, under different power allocation schemes with varying degrees of optimality. The sub-optimal power allocation schemes also ensure a better throughput-fairness trade-off. It is observed that using LTE codebooks results in a significant loss and that there is a need to develop codebooks which offer better adaptation to channel variations.

The problem of clock offset estimation in a two-way timing message exchange regime is considered when the likelihood function of the observation time stamps is Gaussian, exponential, or log-normally distributed. A parameterized solution to the maximum likelihood (ML) estimation of clock offset is analytically obtained, which differs from the earlier approaches where the likelihood function is maximized graphically. In order to capture the imperfections in node oscillators, which may render a time-varying nature to the clock offset, a novel Bayesian approach to the clock offset estimation is proposed by using a factor graph representation of the posterior density. Message passing using the max-product algorithm yields an exact expression for the Bayesian inference problem. Several lower bounds on the variance of an estimator are derived for arbitrary exponential family distributed likelihood functions which, while serving as stepping stones to benchmark the performance of the proposed clock offset estimators, can be useful in their own right in classical as well Bayesian parameter estimation theory. To corroborate the theoretical findings, extensive simulation results are discussed for classical as well as Bayesian estimators in various scenarios. It is observed that the performance of the proposed estimators is fairly close to the fundamental limits established by the lower bounds.

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.