Data is being generated at a tremendous rate in modern applications as diverse as internet applications, genomics, health care, energy management and social network analysis. There is a great need for developing scalable methods for analyzing these data sets. In this talk, I will present some new Divide-and-Conquer algorithms for various challenging problems in large-scale data analysis. Divide-and-Conquer has been a common paradigm that has been widely used in computer science and scientific computing, for example, in sorting, scalable computation of n-body interactions via the fast multipole method and eigenvalue computations of symmetric matrices. However, this paradigm has not been widely employed in problems that arise in machine learning. I will introduce some recent divide-and-conquer methods that we have developed for three representative problems: (i) classification using kernel support vector machines, (ii) dimensionality reduction for large-scale social network analysis, and (iii) structure learning of graphical models. For each of these problems, we develop specialized algorithms, in particular, tailored ways of “dividing” the problem into subproblems, solving the subproblems, and finally “conquering” them. It should be noted that the subproblem solutions yield localized models for analyzing the data; an intriguing question is whether the hierarchy of localized models can be combined to yield models that are not only easier to compute, but are also statistically more robust.
This is joint work with Cho-Jui Hsieh, Pradeep Ravikumar, Donghyuk Shin and Si Si.