Kernels and ensembles for horizontal and vertical information selection

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Exemplified by the support vector machine and the AdaBoost algorithm, kernel methods and ensemble methods constituted much of the new research in statistical machine learning during the last decade. My proposed research will focus on the development of these two classes of methods for two very general data-analytic problems, which I call horizontal and vertical information selection. Suppose we are given a data matrix, where the rows are observations and the columns are variables. By "vertical" selection, I mean the selection of important rows. In applications, these rows can be "bad guys" (e.g., fraudulent financial transactions) or "good guys" (e.g., chemical molecules with potential to inhibit a certain virus). By "horizontal" selection, I mean the selection of important columns. In applications, these columns are the most important factors that affect the outcome of interest (e.g., biomarkers for detecting a certain disease, or genes associated with a certain cancer). Due to the very general nature of these selection problems, my proposed research is expected to have broad practical implications. For example, a general paradigm for constructing very efficient kernel machines for vertical selection can benefit a wide spectrum of applied research, ranging from fraud detection to drug discovery. I will be studying new ideas that I have proposed, such as "deep kernel machines" (DKMs) and "variable-selection ensembles" (VSEs), as well as establishing an Analytics and Informatics Laboratory (AI Lab; http://www.math.uwaterloo.ca/~ailab). Deeper understandings of DKMs and VSEs will further advance the field of statistical machine learning. The AI Lab will provide a platform for students to receive training and conduct research in machine learning and data mining by creating data-driven applications on the internet, such as recommendation systems. These systems are closely related to the theme of my proposal. They analyze data matrices whose columns are items and whose rows are users, and the objective is to recommend a few items to each user, or to collectively solve a horizontal selection problem for each fixed vertical dimension.