Kernels and ensembles for horizontal and vertical information selection

以支持向量机和AdaBoost算法为例，核方法和集成方法构成了过去十年统计机器学习中的许多新研究。我提议的研究将集中于这两类方法的发展，以解决两个非常普遍的数据分析问题，我称之为水平和垂直信息选择。 假设我们得到一个数据矩阵，其中行是观测值，列是变量。所谓“垂直”选择，是指选择重要的行。在应用程序中，这些行可以是“坏人”(例如，欺诈性金融交易)或“好人”(例如，可能抑制某种病毒的化学分子)。所谓“横向”选择，就是选择重要栏目。在应用中，这些柱是影响感兴趣结果的最重要因素(例如，用于检测特定疾病的生物标记物，或与特定癌症相关的基因)。由于这些选择问题的性质非常普遍，我提出的研究预计将具有广泛的实践意义。例如，构建用于垂直选择的非常高效的核机器的通用范例可以使从欺诈检测到药物发现的广泛的应用研究受益。 我将学习我所提出的新想法，例如“深度核机器”和“变量选择集合”，以及建立一个分析和信息学实验室(AI实验室；http://www.math.uwaterloo.ca/~ailab).对DKMS和VSE的深入理解将进一步推动统计机器学习领域的发展。AI实验室将通过在互联网上创建数据驱动的应用程序，如推荐系统，为学生提供一个在机器学习和数据挖掘方面接受培训和进行研究的平台。这些系统与我提案的主题密切相关。它们分析列是项，行是用户的数据矩阵，目标是向每个用户推荐几个项，或者共同解决每个固定垂直维度的水平选择问题。

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.