| dc.description.abstract | In engineering and life science applications, designing reliable and reproducible predictors is of utmost importance and interest. On one hand, the amount of available data for the application and problem of interest may be limited due to the costs associated with collecting or generating data in these domains. Limited relevant data can prohibit the effective design of such predictors. On the other hand, some form of prior knowledge is usually available even before observing any data, but is often neglected in predictor design. Bayesian approaches that are naturally equipped with uncertainty quantification are ideal candidates for these applications. In this dissertation, we develop methods and frameworks to leverage such prior knowledge, and data from other domains, if available, to improve the design of Bayesian predictors for the domain and application of interest.
We first propose a new prior construction methodology based on a general framework of constraints in the form of conditional probability statements. The new constraint framework is flexible as it naturally handles the potential inconsistency in archived relationships between the variables and conditioning can be augmented by other knowledge, such as population statistics. We demonstrate the effectiveness of our approach using pathway information and available knowledge of gene regulating functions for phenotypic classification. We then extend the method to mixture models which are useful in the presence of data heterogeneity.
Next, we focus on utilizing data from other domains to improve prediction accuracy in the target domain of interest. We develop a new generative model for optimal Bayesian supervised domain adaptation that can integrate next-generation sequencing data from different domains along with their labels, in addition to leveraging prior interactome knowledge. We show the superior performance of the proposed method, in terms of accuracy in identifying cancer subtypes by taking advantage of data from different domains and the available prior knowledge.
We then turn our attention to physical systems. First, we explain the concept of optimal experiment design under model uncertainty for autonomously collecting data and learning physical models. We discuss how prior construction fits in the overall design loop for an operator. We then show how an efficient experiment design framework can accelerate exploration of the design space for a materials discovery application under model uncertainty.
Finally, we propose a novel framework of Bayesian reduced-order models for complex systems with high-dimensional systems dynamics or fields. In particular, we develop learnable Bayesian proper orthogonal decomposition that predicts the high-dimensional quantities of interest with reliable uncertainty estimates, in addition to embedding prior knowledge in terms of physics constraints. We showcase the proposed approach on predicting temperature and pressure fields. | en |
