Functional data analysis methods for genomics and financial data

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Many fields have recently seen a rapid increase in data volume and complexity. High-dimensional data have become pervasive in the sciences, in engineering, and in the modern industrial world. Effective data analysis and interpretation still represent the bottleneck in advancing knowledge in many areas of research, in both academia and industry. Hence, there is an urgency for novel statistically sound techniques, specifically tailored for the analysis of high-dimensional data. My research will address this need by developing statistical tools for functional data, i.e. data that vary over a continuum and can be represented as curves. Functional data analysis is often employed as a fully nonparametric approach for the modeling of data varying over time, such as time series and longitudinal data. A less popular but very promising application area is represented by the so-called "Omics" sciences (genomics, epigenomics.) - in which the modern high-throughput sequencing technologies produce high-dimensional data that can be represented as curves over the genome. The long-term objective of my research program is to develop novel statistical methods to analyze functional data and to provide computationally efficient implementations of such methods. In particular, my research over the next few years will focus on the problem of discovering functional motifs, i.e. typical "shapes" that may recur several times along and across a set of curves, capturing important local characteristics. I recently developed probabilistic K-mean with local alignment (probKMA), a clustering method able to identify K candidate functional motifs in a set of curves. My research program intends to build upon this recent development and will pursue several methodological and applied directions. My first focus will be to develop a new motif discovery technique based on biclustering. I will also extend these methods to detect motifs in a single curve as well as motifs whose instances have similar shapes but different lengths, and I will develop a rigorous assessment of the statistical significance of motifs found, that is critical to distinguish between real motifs and motifs that are randomly present in the background of curves. Afterward, I will apply the developed methods to the real-world problems that motivate them - in particular to the analysis of "Omics" data and time series of asset prices. The proposed research will result in user-friendly and fast software that will be freely available to the general public and will enable the extraction of relevant information from curves. The multidisciplinary nature of this research will translate into a broad training opportunity for students involved in my research. The training provided by my program, at the boundaries of several STEM disciplines, will contribute to the education of data scientists, who are becoming vital for both companies and universities.