Statistical Learning With Expert Knowledge and Complex Data

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Making sense of data is one of the great challenges of our century. A decade ago, the major issue in many applications was to obtain relevant data and properly store it to be used in statistical modeling, inference and prediction. Today, it is much easier to collect all kinds of data. However, creating interpretable knowledge from this data, developing new learning algorithms and constructing accurate predictive models are becoming more challenging tasks. Current approaches to statistical learning provide solutions to these problems by using and/or developing specific learning models (or a committee of them) that work with the data in hand. Often researchers have access to primary assessments of area specific experts, results of earlier surveys, or inexpensive measurements related to the problem of interest. An efficient strategy is to first examine a small number of randomly selected sets of samples from the underlying population (sometimes very massive) to either identify more representative (rank-based) data for the study or assign ranks to already observed data. The extra rank information can work in tandem with the usual learning methods to design more effective learning strategies and create an interactive learning harmony between the learning algorithms and expert knowledge. Straightforward applications of available methods in the literature on rank-based data force stringent assumptions that are not often appropriate. My proposed research program is focused on the development of new methodologies, learning algorithms and computational tools to actively imbed the rank information of rank-based data into the learning process and produce highly accurate statistical learning techniques for data centric problems. Rank-based predictive models, deep neural networks, support vector machines and finite mixture models will be developed for efficient prediction, classification, and clustering purposes. The developed methods will be computationally intensive in their implementation and involve complex modeling. Rigorous mathematical analysis of such models will provide insight into the process of inference from rank-based data, as well as the value of the rank information and how this information may be used to construct more reliable and highly accurate estimation and prediction models. The developed techniques will be used in real applications such as diagnosis studies in medical research (e.g., osteoporosis diagnosis using image data and radiologists' primary assessments) and/or industry (e.g., partial discharge classification in high voltage insulators). The development of rank-based statistical learning techniques will have a high degree of potential for technology transfer and opportunities for revenue generation for Canada. The team of 10 HQP trainees of this research will have advanced multidisciplinary training to meet the growing need for multidisciplinary Canadian experts in the area of Data Science.