Optimal Experimental Design in the Context of Objective-Based Uncertainty Quantification

In many real-world engineering applications, model uncertainty is inherent. Largescale dynamical systems cannot be perfectly modeled due to systems complexity, lack of enough training data, perturbation, or noise. Hence, it is often of interest to acquire more data through additional experiments to enhance system model. On the other hand, high cost of experiments and limited operational resources make it necessary to devise a cost-effective plan to conduct experiments. In this dissertation, we are concerned with the problem of prioritizing experiments, called experimental design, aimed at uncertainty reduction in dynamical systems. We take an objective-based view where both uncertainty and modeling objective are taken into account for experimental design. To do so, we utilize the concept of mean objective cost of uncertainty to quantify uncertainty. The first part of this dissertation is devoted to the experimental design for gene regulatory networks. Owing to the complexity of these networks, accurate inference is practically challenging. Moreover, from a translational perspective it is crucial that gene regulatory network uncertainty be quantified and reduced in a manner that pertains to the additional cost of network intervention that it induces. We propose a criterion to rank potential experiments based on the concept of mean objective cost of uncertainty. To lower the computational cost of the experimental design, we also propose a network reduction scheme by introducing a novel cost function that takes into account the disruption in the ranking of potential experiments caused by gene deletion. We investigate the performance of both the optimal and the approximate experimental design methods on synthetic and real gene regulatory networks. In the second part, we turn our attention to canonical expansions. Canonical expansions are convenient representations that can facilitate the study of random processes. We discuss objective-based experimental design in the context of canonical expansions for three major applications: filtering, signal detection, and signal compression. We present the general experimental design framework for linear filtering and specifically solve it for Wiener filtering. Then we focus on Karhunen-Loève expansion to study experimental design for signal detection and signal compression applications when the noise variance and the signal covariance matrix are unknown, respectively. In particular, we find the closed-form solution for the intrinsically Bayesian robust Karhunen-Loève compression which is required for the experimental design in the case of signal compression

Efficient experimental design for uncertainty reduction in gene regulatory networks

BACKGROUND: An 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. RESULTS: The 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. CONCLUSIONS: Simulation 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/

Evaluation and improvement of the regulatory inference for large co-expression networks with limited sample size

Abstract Background Co-expression has been widely used to identify novel regulatory relationships using high throughput measurements, such as microarray and RNA-seq data. Evaluation studies on co-expression network analysis methods mostly focus on networks of small or medium size of up to a few hundred nodes. For large networks, simulated expression data usually consist of hundreds or thousands of profiles with different perturbations or knock-outs, which is uncommon in real experiments due to their cost and the amount of work required. Thus, the performances of co-expression network analysis methods on large co-expression networks consisting of a few thousand nodes, with only a small number of profiles with a single perturbation, which more accurately reflect normal experimental conditions, are generally uncharacterized and unknown. Methods We proposed a novel network inference methods based on Relevance Low order Partial Correlation (RLowPC). RLowPC method uses a two-step approach to select on the high-confidence edges first by reducing the search space by only picking the top ranked genes from an intial partial correlation analysis and, then computes the partial correlations in the confined search space by only removing the linear dependencies from the shared neighbours, largely ignoring the genes showing lower association. Results We selected six co-expression-based methods with good performance in evaluation studies from the literature: Partial correlation, PCIT, ARACNE, MRNET, MRNETB and CLR. The evaluation of these methods was carried out on simulated time-series data with various network sizes ranging from 100 to 3000 nodes. Simulation results show low precision and recall for all of the above methods for large networks with a small number of expression profiles. We improved the inference significantly by refinement of the top weighted edges in the pre-inferred partial correlation networks using RLowPC. We found improved performance by partitioning large networks into smaller co-expressed modules when assessing the method performance within these modules. Conclusions The evaluation results show that current methods suffer from low precision and recall for large co-expression networks where only a small number of profiles are available. The proposed RLowPC method effectively reduces the indirect edges predicted as regulatory relationships and increases the precision of top ranked predictions. Partitioning large networks into smaller highly co-expressed modules also helps to improve the performance of network inference methods. The RLowPC R package for network construction, refinement and evaluation is available at GitHub: https://github.com/wyguo/RLowPC

Hypersonic phononic crystal structures for integrated nano-electromechanical/optomechanical devices

This dissertation embraces the study, design, and fabrication of integrated phononic devices on silicon chips for enabling new integrated radio frequency (RF)-photonics devices as well as new integrated nano/micro-electromechanical systems for on-chip sensing and RF signal processing. These integrated phononic devices are realized in fully CMOS-compatible platforms in the form of phononic crystal (PnC) structures (i.e., periodic structures supporting phononic bandgaps) and double-layer crystalline silicon (Si) structures. The designed phononic structures are compatible with integrated optics/electronics, and possess a higher efficiency and lower phononic/photonic losses. In particular, I developed a hypersonic pillar-based PnC platform with a wideband phononic bandgap at GHz frequencies on a thin film of aluminum nitride deposited on a Si substrate. This platform allows for designing low-loss integrated surface acoustic waveguides and resonators with piezoelectric excitation for filtering applications in wireless communication. In addition, I extended the application of PnC structures to design efficient on-chip stimulated Brillouin scattering (SBS) nano-devices for RF-photonics. These nanostructures are realized in silicon nitride membranes and therefore are fully compatible with integrated optics platforms. My studies on SBS in silicon nitride suggest further investigation of silicon nitride for enabling promising SBS-based systems. Moreover, in this dissertation, I studied and fabricated the integrated optomechanical resonators in the double-layer crystalline Si platform. The tiny air gap between the silicon layers of the structure allows for a highly-efficient optomechanical interaction. The applications of such double-layer optomechanical structures include on-chip RF oscillators (with no external electric feedback) and wide-band high-speed integrated optical switches for optical interconnects.Ph.D

The SpliZ generalizes ‘percent spliced in’ to reveal regulated splicing at single-cell resolution

Detecting single-cell-regulated splicing from droplet-based technologies is challenging. Here, we introduce the splicing Z score (SpliZ), an annotation-free statistical method to detect regulated splicing in single-cell RNA sequencing. We applied the SpliZ to human lung cells, discovering hundreds of genes with cell-type-specific splicing patterns including ones with potential implications for basic and translational biology

Publisher Correction: The SpliZ generalizes ‘percent spliced in’ to reveal regulated splicing at single-cell resolution (Nature Methods, (2022), 19, 3, (307-310), 10.1038/s41592-022-01400-x)

In the version of this article originally published, the corresponding author Julia Salzman was also listed as an equal contributor, in error. The error has been corrected in the HTML and PDF versions of the article

A Bayesian robust Kalman smoothing framework for state-space models with uncertain noise statistics

Abstract The classical Kalman smoother recursively estimates states over a finite time window using all observations in the window. In this paper, we assume that the parameters characterizing the second-order statistics of process and observation noise are unknown and propose an optimal Bayesian Kalman smoother (OBKS) to obtain smoothed estimates that are optimal relative to the posterior distribution of the unknown noise parameters. The method uses a Bayesian innovation process and a posterior-based Bayesian orthogonality principle. The optimal Bayesian Kalman smoother possesses the same forward-backward structure as that of the ordinary Kalman smoother with the ordinary noise statistics replaced by their effective counterparts. In the first step, the posterior effective noise statistics are computed. Then, using the obtained effective noise statistics, the optimal Bayesian Kalman filter is run in the forward direction over the window of observations. The Bayesian smoothed estimates are obtained in the backward step. We validate the performance of the proposed robust smoother in the target tracking and gene regulatory network inference problems