SEMINAR ABSTRACT
Nonparametric Learning in High Dimensions
Han Liu, Department of
Machine Learning, Carnegie Mellon University
Despite the high dimensionality and complexity of many modern
datasets, some problems have hidden structure that makes efficient statistical
inference feasible. Examples of these hidden structures include: additivity,
sparsity, low-dimensional manifold structure, smoothness, copula structure, and
conditional independence relations.
In this talk, I will describe efficient nonparametric learning algorithms that
exploit such hidden structures to overcome the curse of dimensionality. These
algorithms have strong theoretical guarantees and provide practical methods for
many fundamentally important learning problems, ranging from unsupervised
exploratory data analysis to supervised predictive modeling.
I will use two examples of high dimensional graph estimation and multi-task
regression to illustrate the principles of developing high dimensional
nonparametric methods. The theoretical results are presented in terms of risk
consistency, estimation consistency, and model selection consistency. The
practical performance of the algorithms is illustrated on genomics and cognitive
neuroscience examples and compared to state-of-the-art parametric competitors.
This work is joint with John Lafferty and Larry Wasserman.