Research Statement

My research is on theoretical foundations of machine learning. During graduate school, I primarily analyzed standard algorithms under practical assumptions, particularly in areas not covered by existing theory. While this was satisfying and the understanding it granted will color all my future work, during my postdoctoral studies I have been more interested in design of new algorithms. In this research statement I will exemplify these two phases with the following two groups of works. Theoretical analyses under practical assumptions. Consider clustering, the task of partitioning data into k groups according to some notion of similarity. Clustering is one of the oldest statistical tech-niques, and continues to be a tool of choice in modern data analysis. Consequently, it is applied to data of arbitrary shapes and sizes; by contrast, the theory often dictates specific algorithms, specific properties of the data, and even a specific model generating the data. To address this, I investigated standard clustering methods under only the assumption of bounded moments, and showed the proce-dures are still statistically well-behaved, meaning good performance on a data sample will translate to future data points. This result will be discussed in Section 1, along with some of my work on standard linear prediction algorithms. Representation learning. Consider boosting, an algorithm which takes a collection of elementary classi