Grant: Discovery Grants Program - Individual

Nowadays, multivariate data originating for instance from biostatistics, meteorological, engineering or astronomical studies are becoming more challenging to data mine in light of their increasing complexity and size. Efficient methodologies that are principally based on joint sample moments and are independent of the sample size are advocated in this research proposal as they are ideally suited for analyzing `Big Data'. As well, such techniques mitigate the curse of dimensionality. The distributional representations resulting from generalizations of widely utilized models are expressed in functional forms that allow for interpretability, lend themselves to algebraic manipulations and give rise to highly flexible copulae, which describe the dependence between variables of interest. Being remarkably versatile, such models should find applications in reliability theory and quality assurance testing. The results will be adapted to the context of regression with a view to discarding uninformative variables and eliciting relevant patterns and relationships between the significant ones. As well, both novel and established multivariate methodologies such as hierarchical clustering analysis and data visualization techniques such as scatterplot matrices will be brought to bear to great advantage in the fields of neuroimaging - for assessing the dissimilarities between vectors of responses associated with certain stimuli - and environmetrics - for detecting trends in the face of climatic changes. As well, they should enhance the understanding of the underlying processes and, for instance, lead to advances in predictive analytics in connection with the occurrence of catastrophic events such as floods and earthquakes. The software documentation and source code to be developed for implementing the planned distributional breakthroughs shall be made available. Various approaches will be devised to extract pertinent distributional information from relatively small subsets of large-scale data sets. Once utilized in conjunction with innovative data reduction and variable selection techniques, the modeling methodologies being herein advocated will permit to process more rapidly massive spatio-temporal and higher-dimensional data sets that frequently arrive in streams as in the cases of high throughput cancer screening and DNA sequencing, the burgeoning blockchain technologies, metadata analyses, and the fast expanding field of artificial intelligence, which is at the core of autonomous and interactive systems such as self-driving vehicles. By addressing both volume and velocity in connection with the analysis of massive and complex streaming data, the proposed generalized models and innovative moment-based methodologies herald a paradigmatic shift in the processing of large-scale multivariate observations.