The accelerated exploration of the materials space in order to identify configurations with optimal properties is an ongoing challenge. Current paradigms are typically centered around the idea of performing this exploration through high-throughput experimentation/computation. Such approaches, however, do not account for-the always present-constraints in resources available. Recently, this problem has been addressed by framing materials discovery as an optimal experiment design. This work augments earlier efforts by putting forward a framework that efficiently explores the materials design space not only accounting for resource constraints but also incorporating the notion of model uncertainty. The resulting approach combines Bayesian Model Averaging within Bayesian Optimization in order to realize a system capable of autonomously and adaptively learning not only the most promising regions in the materials space but also the models that most efficiently guide such exploration. The framework is demonstrated by efficiently exploring the MAX ternary carbide/nitride space through Density Functional Theory (DFT) calculations.

In this study, a framework for the multi-objective materials discovery based on Bayesian approaches is developed. The capabilities of the framework are demonstrated on an example case related to the discovery of precipitation strengthened NiTi shape memory alloys with up to three desired properties. In the presented case the framework is used to carry out an efficient search of the shape memory alloys with desired properties while minimizing the required number of computational experiments. The developed scheme features a Bayesian optimal experimental design process that operates in a closed loop. A Gaussian process regression model is utilized in the framework to emulate the response and uncertainty of the physical/computational data while the sequential exploration of the materials design space is carried out by using an optimal policy based on the expected hyper-volume improvement acquisition function. This scalar metric provides a measure of the utility of querying the materials design space at different locations, irrespective of the number of objectives in the performed task. The framework is deployed for the determination of the composition and microstructure of precipitation-strengthened NiTi shape memory alloys with desired properties, while the materials response as a function of microstructure is determined through a thermodynamically-consistent micromechanical model.

BackgroundPhenotypic classification is problematic because small samples are ubiquitous; and, for these, use of prior knowledge is critical. If knowledge concerning the feature-label distribution – for instance, genetic pathways – is available, then it can be used in learning. Optimal Bayesian classification provides optimal classification under model uncertainty. It differs from classical Bayesian methods in which a classification model is assumed and prior distributions are placed on model parameters. With optimal Bayesian classification, uncertainty is treated directly on the feature-label distribution, which assures full utilization of prior knowledge and is guaranteed to outperform classical methods.ResultsThe salient problem confronting optimal Bayesian classification is prior construction. In this paper, we propose a new prior construction methodology based on a general framework of constraints in the form of conditional probability statements. We call this prior the maximal knowledge-driven information prior (MKDIP). The new constraint framework is more flexible than our previous methods as it naturally handles the potential inconsistency in archived regulatory relationships and conditioning can be augmented by other knowledge, such as population statistics. We also extend the application of prior construction to a multinomial mixture model when labels are unknown, which often occurs in practice. The performance of the proposed methods is examined on two important pathway families, the mammalian cell-cycle and a set of p53-related pathways, and also on a publicly available gene expression dataset of non-small cell lung cancer when combined with the existing prior knowledge on relevant signaling pathways.ConclusionThe new proposed general prior construction framework extends the prior construction methodology to a more flexible framework that results in better inference when proper prior knowledge exists. Moreover, the extension of optimal Bayesian classification to multinomial mixtures where data sets are both small and unlabeled, enables superior classifier design using small, unstructured data sets. We have demonstrated the effectiveness of our approach using pathway information and available knowledge of gene regulating functions; however, the underlying theory can be applied to a wide variety of knowledge types, and other applications when there are small samples.

Gene-expression-based classification and regression are major concerns in translational genomics. If the feature-label distribution is known, then an optimal classifier can be derived. If the regressor-target distribution is known, then an optimal regression function can be derived. In practice, neither is known, data must be employed, and, for small samples, prior knowledge concerning the feature-label or regressor-target distribution can be used in the learning process. Optimal Bayesian classification and optimal Bayesian regression provide optimality under uncertainty. With optimal Bayesian classification (or regression), uncertainty is treated directly on the feature-label (or regressor-target) distribution. The fundamental engineering problem is prior construction. The Regularized Expected Mean Log-Likelihood Prior (REML) utilizes pathway information and provides viable priors for the feature-label distribution, assuming that the training data contain labels. In practice, the labels may not be observed. This paper extends the REML methodology to a Gaussian mixture model (GMM) when the labels are unknown. Prior construction bundled with prior update via Bayesian sampling results in Monte Carlo approximations to the optimal Bayesian regression function and optimal Bayesian classifier. Simulations demonstrate that the GMM REML prior yields better performance than the EM algorithm for small data sets. We apply it to phenotype classification when the prior knowledge consists of colon cancer pathways.

Background Missing values frequently arise in modern biomedical studies due to various reasons, including missing tests or complex profiling technologies for different omics measurements. Missing values can complicate the application of clustering algorithms, whose goals are to group points based on some similarity criterion. A common practice for dealing with missing values in the context of clustering is to first impute the missing values, and then apply the clustering algorithm on the completed data. Results We consider missing values in the context of optimal clustering, which finds an optimal clustering operator with reference to an underlying random labeled point process (RLPP). We show how the missing-value problem fits neatly into the overall framework of optimal clustering by incorporating the missing value mechanism into the random labeled point process and then marginalizing out the missing-value process. In particular, we demonstrate the proposed framework for the Gaussian model with arbitrary covariance structures. Comprehensive experimental studies on both synthetic and real-world RNA-seq data show the superior performance of the proposed optimal clustering with missing values when compared to various clustering approaches. Conclusion Optimal clustering with missing values obviates the need for imputation-based pre-processing of the data, while at the same time possessing smaller clustering errors. Electronic supplementary material The online version of this article (10.1186/s12859-019-2832-3) contains supplementary material, which is available to authorized users.