Roozbeh Dehghannasiri

Optimal experimental design for gene regulatory networks in the presence of uncertainty

Of major interest to translational genomics is the intervention in gene regulatory networks (GRNs) to affect cell behavior; in particular, to alter pathological phenotypes. Owing to the complexity of GRNs, accurate network inference is practically challenging and GRN models often contain considerable amounts of uncertainty. Considering the cost and time required for conducting biological experiments, it is desirable to have a systematic method for prioritizing potential experiments so that an experiment can be chosen to optimally reduce network uncertainty. Moreover, from a translational perspective it is crucial that GRN uncertainty be quantified and reduced in a manner that pertains to the operational cost that it induces, such as the cost of network intervention. In this work, we utilize the concept of mean objective cost of uncertainty (MOCU) to propose a novel framework for optimal experimental design. In the proposed framework, potential experiments are prioritized based on the MOCU expected to remain after conducting the experiment. Based on this prioritization, one can select an optimal experiment with the largest potential to reduce the pertinent uncertainty present in the current network model. We demonstrate the effectiveness of the proposed method via extensive simulations based on synthetic and real gene regulatory networks.

Efficient experimental design for uncertainty reduction in gene regulatory networks

BackgroundAn accurate understanding of interactions among genes plays a major role in developing therapeutic intervention methods. Gene regulatory networks often contain a significant amount of uncertainty. The process of prioritizing biological experiments to reduce the uncertainty of gene regulatory networks is called experimental design. Under such a strategy, the experiments with high priority are suggested to be conducted first.ResultsThe authors have already proposed an optimal experimental design method based upon the objective for modeling gene regulatory networks, such as deriving therapeutic interventions. The experimental design method utilizes the concept of mean objective cost of uncertainty (MOCU). MOCU quantifies the expected increase of cost resulting from uncertainty. The optimal experiment to be conducted first is the one which leads to the minimum expected remaining MOCU subsequent to the experiment. In the process, one must find the optimal intervention for every gene regulatory network compatible with the prior knowledge, which can be prohibitively expensive when the size of the network is large. In this paper, we propose a computationally efficient experimental design method. This method incorporates a network reduction scheme by introducing a novel cost function that takes into account the disruption in the ranking of potential experiments. We then estimate the approximate expected remaining MOCU at a lower computational cost using the reduced networks.ConclusionsSimulation results based on synthetic and real gene regulatory networks show that the proposed approximate method has close performance to that of the optimal method but at lower computational cost. The proposed approximate method also outperforms the random selection policy significantly. A MATLAB software implementing the proposed experimental design method is available at http://gsp.tamu.edu/Publications/supplementary/roozbeh15a/.

Intrinsically Bayesian Robust Kalman Filter: An Innovation Process Approach

In many contemporary engineering problems, model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability, time, or cost. The situation can be treated by assuming that the true model belongs to an uncertainty class of models. In this context, an intrinsically Bayesian robust (IBR) filter is one that is optimal relative to the cost function (in the classical sense) and the prior distribution over the uncertainty class (in the Bayesian sense). IBR filters have previously been found for both Wiener and granulometric morphological filtering. In this paper, we derive the IBR Kalman filter that performs optimally relative to an uncertainty class of state-space models. Introducing the notion of Bayesian innovation process and the Bayesian orthogonality principle, we show how the problem of designing an IBR Kalman filter can be reduced to a recursive system similar to the classical Kalman recursive equations, except with “effective” counterparts, such as the effective Kalman gain matrix. After deriving the recursive IBR Kalman equations for discrete time, we use the limiting method to obtain the IBR Kalman–Bucy equations for continuous time. Finally, we demonstrate the utility of the proposed framework for two real world problems: sensor networks and gene regulatory network inference.

Optimal Objective-Based Experimental Design for Uncertain Dynamical Gene Networks with Experimental Error

In systems biology, network models are often used to study interactions among cellular components, a salient aim being to develop drugs and therapeutic mechanisms to change the dynamical behavior of the network to avoid undesirable phenotypes. Owing to limited knowledge, model uncertainty is commonplace and network dynamics can be updated in different ways, thereby giving multiple dynamic trajectories, that is, dynamics uncertainty. In this manuscript, we propose an experimental design method that can effectively reduce the dynamics uncertainty and improve performance in an interaction-based network. Both dynamics uncertainty and experimental error are quantified with respect to the modeling objective, herein, therapeutic intervention. The aim of experimental design is to select among a set of candidate experiments the experiment whose outcome, when applied to the network model, maximally reduces the dynamics uncertainty pertinent to the intervention objective.

Optimal experimental design in canonical expansions with applications to signal compression

In this paper, we introduce an experimental design framework for Karhunen-Loeve compression. This method based on the concept of mean objective of uncertainty determines the best unknown parameter of the covariance matrix to be estimated first in order to improve the quality of the compressed signal. Moreover, we find the closed-form solution to the intrinsically Bayesian robust Karhunen-Loève compression that is required for experimental design and provides the optimal signal compression on average relative to the uncertainty class of covariance matrices. We verify the performance of the proposed experimental design method for the case in which the covariance matrix consists of disjoint blocks.

Frame rate up-conversion using nonparametric estimator

In some applications such as digital video broadcasting, video is transmitted over a low capacity channel with lower frame rates. The lower the frame rate, the jerkier or unevener the video motion would be noticed. To solve this problem, frame rate up conversion (FRUC) is employed to increase the frame rate. In this paper, we propose a new FRUC method using the nonlocal-means estimator. In this method, a pixel is reconstructed as a weighted linear combination of pixel pairs in its adjacent frames. The pixels of each pair are temporally symmetric from the view point of the pixel being interpolated. The weights are calculated based on the self-similarity assumption. To reduce the computational complexity, we calculate the weights of linear combination for each super-pixel. Experimental results show the superior performance of our proposed method in comparison to the existing methods.

A Bayesian framework for robust Kalman filtering under uncertain noise statistics

In this paper, we propose a Bayesian framework for robust Kalman filtering when noise statistics are unknown. The proposed intrinsically Bayesian robust Kalman filter is robust in the Bayesian sense meaning that it guarantees the best average performance relative to the prior distribution governing unknown noise parameters. The basics of Kalman filtering such as the projection theorem and the innovation process are revisited and extended to their Bayesian counterparts. These enable us to design the intrinsically Bayesian robust Kalman filter in a similar way that one can find the classical Kalman filter for a known model.

Intrinsically Bayesian Robust Karhunen-Loève Compression

Abstract Karhunen-Loeve (KL) compression is based on the canonical representation of a random process. When compressing to a finite sum, the optimal-MSE m -term summation consists of the KL terms possessing the m largest eigenvalues. This paper considers the situation in which an unknown covariance matrix belongs to an uncertainty class governed by a prior probability distribution. The intrinsically Bayesian robust (IBR) KL compression minimizes the expected MSE over the uncertainty class among all possible m -term KL expansions. We prove that the IBR KL compression is the KL expansion based on the expected covariance matrix over the uncertainty class. We then solve the following experimental design problem: among the unknown covariances, which should be determined to maximally reduce the mean objective cost of uncertainty (MOCU), which in the KL compression setting measures increased MSE resulting from our uncertainty. The IBR KL expansion and optimal experimental design are solved analytically for the Wishart distribution over the uncertainty class, a commonly employed distribution for covariance matrices in Bayesian settings.

Optimal experimental design in the context of canonical expansions

In a wide variety of engineering applications, the mathematical model cannot be fully identified. Therefore, one would like to construct robust operators (filters, classifiers, controllers etc.) that perform optimally relative to incomplete knowledge. Improving model identification through determining unknown parameters can enhance the performance of robust operators. One would like to perform the experiment that provides the most information relative to the engineering objective. The authors present an experimental design framework for parameter estimation in signal processing when the random process model is in the form of canonical expansions. The proposed experimental design is based on the concept of the mean objective cost of uncertainty, which quantifies model uncertainty by taking into account the performance degradation of the designed operator owing to the presence of uncertainty. They provide the general framework for experimental design in the context of canonical expansions and solve it for two major signal processing problems: optimal linear filtering and signal detection.

Erratum to: Efficient experimental design for uncertainty reduction in gene regulatory networks

The online version of the original article can be found under doi:10.1186/1471-2105-16-S13-S2.