Bayesian Optimization Objective-Based Experimental Design

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/.

The need for efficient computational screening of molecular candidates that possess desired properties frequently arises in various scientific and engineering problems, including drug discovery and materials design. However, the large size of the search space containing the candidates and the substantial computational cost of high-fidelity property prediction models makes screening practically challenging. In this work, we propose a general framework for constructing and optimizing a virtual screening (HTVS) pipeline that consists of multi-fidelity models. The central idea is to optimally allocate the computational resources to models with varying costs and accuracy to optimize the return-on-computational-investment (ROCI). Based on both simulated as well as real data, we demonstrate that the proposed optimal HTVS framework can significantly accelerate screening virtually without any degradation in terms of accuracy. Furthermore, it enables an adaptive operational strategy for HTVS, where one can trade accuracy for efficiency.

Optimal experimental design for materials discovery

BackgroundA salient purpose for studying gene regulatory networks is to derive intervention strategies, the goals being to identify potential drug targets and design gene-based therapeutic intervention. Optimal stochastic control based on the transition probability matrix of the underlying Markov chain has been studied extensively for probabilistic Boolean networks. Optimization is based on minimization of a cost function and a key goal of control is to reduce the steady-state probability mass of undesirable network states. Owing to computational complexity, it is difficult to apply optimal control for large networks.ResultsIn this paper, we propose three new greedy stationary control policies by directly investigating the effects on the network long-run behavior. Similar to the recently proposed mean-first-passage-time (MFPT) control policy, these policies do not depend on minimization of a cost function and avoid the computational burden of dynamic programming. They can be used to design stationary control policies that avoid the need for a user-defined cost function because they are based directly on long-run network behavior; they can be used as an alternative to dynamic programming algorithms when the latter are computationally prohibitive; and they can be used to predict the best control gene with reduced computational complexity, even when one is employing dynamic programming to derive the final control policy. We compare the performance of these three greedy control policies and the MFPT policy using randomly generated probabilistic Boolean networks and give a preliminary example for intervening in a mammalian cell cycle network.ConclusionThe newly proposed control policies have better performance in general than the MFPT policy and, as indicated by the results on the mammalian cell cycle network, they can potentially serve as future gene therapeutic intervention strategies.

The concept of design space, as described in the ICH Harmonized Tripartite Guideline Q8 for Pharmaceutical Development (Q8 Pharmaceutical development, ICH harmonized tripartite guidelines, in International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use, 2005), was introduced to justify regulatory flexibility in pharmaceutical manufacturing operations. The basis for this concept is that advanced understanding of variables affecting product quality, obtained either through historical operation or demonstrated through process modeling, justifies replacement of traditional process targets with acceptable operational ranges. Process adjustments that allow operation within the region defined by the design space do not require regulatory oversight. Whereas there are many advantages to having the flexibility to operate within such ranges, the concept is only valid when the design space has been adequately described by appropriate experimentation. Given the complexity of pharmaceutical processes and the number of variables to consider in developing operational ranges, only a well-executed program of experiments, supported by appropriate statistical analyses, could provide the necessary information to truly capture a design space. Thus, the risk of employing a design space is that the model will be applied to a region outside of the approved design space, either through a false statistical inference or by omitting some important factor effects. This article presents a review of the experimental strategies typically employed to develop pharmaceutical processes with special emphasis on the assumptions and limitations of the approaches. An alternative strategy that provides an opportunity to build on previous information efficiently without requiring extraordinary skill in statistics, Bayesian optimal design, is introduced as an alternative to the classical approaches.

In this chapter, we provide a general overview on the Bayesian experimental design of various statistical models in the recent years. The Bayesian optimal designs incorporate the prior information and uncertainties of the models by using various utility functions, which describe various aims of the experiments. Although there are difficulties in obtaining the analytical expression of the expected utilities and their corresponding numerical approximations under Bayesian framework, the development of fast computational algorithms will bring wider applications of Bayesian experimental design to more complicated models.

BackgroundIn a gene regulatory network (GRN), gene expressions are affected by noise, and stochastic fluctuations exist in the interactions among genes. These stochastic interactions are context dependent, thus it becomes important to consider noise in a context-sensitive manner in a network model. As a logical model, context-sensitive probabilistic Boolean networks (CSPBNs) account for molecular and genetic noise in the temporal context of gene functions. In a CSPBN with n genes and k contexts, however, a computational complexity of O(nk222n ) (or O(nk2 n )) is required for an accurate (or approximate) computation of the state transition matrix (STM) of the size (2 n ∙ k) × (2 n ∙ k) (or 2 n × 2 n ). The evaluation of a steady state distribution (SSD) is more challenging. Recently, stochastic Boolean networks (SBNs) have been proposed as an efficient implementation of an instantaneous PBN.ResultsThe notion of stochastic Boolean networks (SBNs) is extended for the general model of PBNs, i.e., CSPBNs. This yields a novel structure of context-sensitive SBNs (CSSBNs) for modeling the stochasticity in a GRN. A CSSBN enables an efficient simulation of a CSPBN with a complexity of O(nLk2 n ) for computing the state transition matrix, where L is a factor related to the required sequence length in CSSBN for achieving a desired accuracy. A time-frame expanded CSSBN can further efficiently simulate the stationary behavior of a CSPBN and allow for a tunable tradeoff between accuracy and efficiency. The CSSBN approach is more efficient than an analytical method and more accurate than an approximate analysis.ConclusionsContext-sensitive stochastic Boolean networks (CSSBNs) are proposed as an efficient approach to modeling the effects of gene perturbation and intervention in gene regulatory networks. A CSSBN analysis provides biologically meaningful insights into the oscillatory dynamics of the p53-Mdm2 network in a context-switching environment. It is shown that random gene perturbation has a greater effect on the final distribution of the steady state of a network compared to context switching activities. The CSSBN approach can further predict the steady state distribution of a glioma network under gene intervention. Ultimately, this will help drug discovery and develop effective drug intervention strategies.

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the scenario where we can sequentially update our beliefs about the model parameters through data gathered in the experiment. A class of models of particular interest for the natural and medical sciences are implicit models, where the data generating distribution is intractable, but sampling from it is possible. Even though there has been a lot of work on static BED for implicit models in the past few years, the notoriously difficult problem of sequential BED for implicit models has barely been touched upon. We address this gap in the literature by devising a novel sequential design framework for parameter estimation that uses the Mutual Information (MI) between model parameters and simulated data as a utility function to find optimal experimental designs, which has not been done before for implicit models. Our approach uses likelihood-free inference by ratio estimation to simultaneously estimate posterior distributions and the MI. During the sequential BED procedure we utilise Bayesian optimisation to help us optimise the MI utility. We find that our framework is efficient for the various implicit models tested, yielding accurate parameter estimates after only a few iterations.

The intervention in gene regulatory networks has been modelled as the Markov decision process problem. However, this approach only allows one external control, which is inadequate in many situations such as drug and gene therapies. In this paper, we propose the non-cooperative stochastic game model for intervention in the genetic regulatory networks as the generalization of the Markov decision process approach and formulate the intervention problem into solving the Nash equilibrium. The definition of equilibrium has been proposed and the existences for both infinite and finite horizon cases have been proven. We provide the numerical example for using non-cooperative stochastic game model on the mammalian cell cycle network. We also compare the results under the Nash equilibrium and independent Markov decision process approach.

A prime objective of modeling genetic regulatory networks is the identification of potential targets for therapeutic intervention. To date, optimal stochastic intervention has been studied in the context of probabilistic Boolean networks, with the control policy based on the transition probability matrix of the associated Markov chain and dynamic programming used to find optimal control policies. Dynamical programming algorithms are problematic owing to their high computational complexity. Two additional computationally burdensome issues that arise are the potential for controlling the network and identifying the best gene for intervention. This paper proposes an algorithm based on mean first-passage time that assigns a stationary control policy for each gene candidate. It serves as an approximation to an optimal control policy and, owing to its reduced computational complexity, can be used to predict the best control gene. Once the best control gene is identified, one can derive an optimal policy or simply utilize the approximate policy for this gene when the network size precludes a direct application of dynamic programming algorithms. A salient point is that the proposed algorithm can be model-free. It can be directly designed from time-course data without having to infer the transition probability matrix of the network.

Optimal experimental design is an important methodology for most efficiently allocating resources in an experiment to best achieve some goal. Bayesian experimental design considers the potential impact that various choices of the controllable variables has on the posterior distribution of the unknowns. Optimal Bayesian design involves optimising an expected utility function, which is an analytically intractable integral over the prior predictive distribution. These integrals are typically estimated via standard Monte Carlo methods. In this paper, we demonstrate that the use of randomised quasi-Monte Carlo can bring significant reductions to the variance of the estimated expected utility. This variance reduction will then lead to a more efficient optimisation algorithm for maximising the expected utility.

We are honored to be guest editors for this special issue of Applied Stochastic Models in Business and Industry, dedicated to Kathryn Chaloner's life and achievements. Contributions from her colleagues and friends in this volume are devoted to Kathryn's early research interest in Bayesian optimal design. She was a pioneer in this field and had a broad impact on the subsequent literature on experimental design. Kathryn was internationally known for her research in Bayesian Statistics, which included design of experiments, outlier detection, prior elicitation, and clinical trials, and for her advancements in the study of HIV/AIDS. She was an accomplished researcher, teacher, and mentor. She actively encouraged women and under-represented minority students to join the field of biostatistics and provided mentorship, support, and encouragement. The special issue contains seven papers. The first three papers present some of the recent work in Bayesian optimal designs for nonlinear models, binary responses, and experiments with adversarial components. This is followed by two articles on Bayesian designs in clinical trials. The last two articles of the special issue involve engineering design problems. The paper by Giovagnoli considers the binary response models of Chaloner and Larntz (1989, Journal of Statistical Planning and Inference, 21:191–208) and develops an adaptive version of A-optimal Bayesian designs that are revised as additional data become available during the experiment. Adaptive Bayesian compound designs is also discussed as another extension. Konstantinou and Dette develop approximate Bayesian D-optimal designs for nonlinear regression models that involve covariates that cannot be observed directly. Applications to specific nonlinear models including the exponential regression model are considered and characterizations of the D-optimal saturated designs are presented. Optimal sample size selection for experiments is considered by De Santis and Gubbiotti in an adversarial setting where the decision makers have different prior opinions while having common utility functions and data. Using a Bayesian decision approach with a quadratic loss function, the authors present results for the one-parameter exponential family and investigate effect of the priors on the optimal sample size. Müller, Xu, and Thall discuss advantages and limitations of Bayesian decision theoretic approach in design of clinical trials. In doing so, the authors present a specific case study and point out the limitations such as the computational difficulties involved in solving sequential problems as well as selection of utility functions capturing different stakeholder interests. The article by Ventz, Parmigiani, and Trippa also consider limitations of the Bayesian framework in design of clinical trials and propose a strategy to alleviate these. The proposed strategy involves combining Bayesian designs with frequentist metrics such as error rates, confidence intervals, etc. that are commonly used by medical community and regulatory agencies. The authors show that this can be achieved by an inclusion of frequentist constraints into the Bayesian formulation. The constrained decision theoretic framework is illustrated via several applications and computational algorithms are presented for implementing the proposed approach. Nakamura, Seepaul, Kadane, and Reeja-Jayan discuss design of experiments in materials science. The authors consider use of a batch-sequential experiment and a regression model to determine optimal levels of input variables for synthesis of ceramic materials. It is illustrated that the optimal settings produce more reliable results than other experiments. The final article by Polson and Soyer considers Bayesian design of accelerated life tests for reliability assessment. An augmented probability simulation (APS) approach using Lindley's (1976, Annals of Statistics, 4:1–10) conjugate utility functions is proposed to compute optimal designs in an efficient manner. The proposed approach is illustrated using single and multiple point designs. Use of particle based methods for APS is also discussed as an alternative to Markov chain Monte Carlo methods.

Surrogate-based sequential Bayesian experimental design using non-stationary Gaussian Processes

Brain tumor is one of the most aggressive diseases nowadays, resulting in a very short life span if it is diagnosed at an advanced stage. The treatment planning phase is thus essential for enhancing the quality of life for patients. The use of Magnetic Resonance Imaging (MRI) in the diagnosis of brain tumors is extremely widespread, but the manual interpretation of large amounts of images requires considerable effort and is prone to human errors. Hence, an automated method is necessary to identify the most common brain tumors. Convolutional Neural Network (CNN) architectures are successful in image classification due to their high layer count, which enables them to conceive the features effectively on their own. The tuning of CNN hyperparameters is critical in every dataset since it has a significant impact on the efficiency of the training model. Given the high dimensionality and complexity of the data, manual hyperparameter tuning would take an inordinate amount of time, with the possibility of failing to identify the optimal hyperparameters. In this paper, we proposed a Bayesian Optimization-based efficient hyperparameter optimization technique for CNN. This method was evaluated by classifying 3064 T-1-weighted CE-MRI images into three types of brain tumors (Glioma, Meningioma, and Pituitary). Based on Transfer Learning, the performance of five well-recognized deep pre-trained models is compared with that of the optimized CNN. After using Bayesian Optimization, our CNN was able to attain 98.70% validation accuracy at best without data augmentation or cropping lesion techniques, while VGG16, VGG19, ResNet50, InceptionV3, and DenseNet201 achieved 97.08%, 96.43%, 89.29%, 92.86%, and 94.81% validation accuracy, respectively. Moreover, the proposed model outperforms state-of-the-art methods on the CE-MRI dataset, demonstrating the feasibility of automating hyperparameter optimization.

Aim/Purpose: Traditional hyperparameter tuning methods’ inefficiency and low accuracy in diabetes prediction. Application and evaluation of Bayesian optimization aim to increase the accuracy of diabetes prediction models. Background: Bayesian optimization (BO) has emerged as a powerful technique for hyperparameter tuning in machine learning models with its methodical approach for optimizing complex functions with expensive evaluations. Selecting the optimal hyperparameters for models can significantly increase prediction accuracy in the healthcare sector, particularly for diabetes prediction, hence improving patient outcomes and resource management. Methodology: Among the well-known diabetes databases used in the study is the Pima Indian Diabetes Database. Among the machine learning models developed and whose hyperparameters are modified via Bayesian optimization are Support Vector Machines (SVM), Random Forest, and Gradient Boosting Machines (GBM). The optimization process is compared with traditional tuning methods to assess improvements in model performance. Contribution: Problems include the increasing prevalence of diabetes worldwide and the role vital function prediction models play in early diagnosis and therapy. Especially when dealing with enormous datasets common in healthcare, grid search, and random search are sometimes computationally taxing and inefficient. However, Bayesian optimization promises a more practical and economical approach by selecting hyperparameters iteratively based on earlier evaluations. Findings: Bayesian optimization not only yields faster calculation times but also outperforms traditional methods. More precisely, models adapted by Bayesian optimization show greater sensitivity and specificity, which are crucial for accurate and prompt diabetes diagnosis. Recommendation for Researchers: By highlighting the specific elements and network characteristics that are behind the anomalies it discovers, on a real-time or large scale dataset. Future Research: This work can be improvised using several recent artificial intelligence algorithms with the integration of IoT on real-time datasets.