Back to Departmental Colloquium: Spring 2017
Departmental Colloquium
Date: Tuesday, Jan 17, 2017
Time: 4:00PM
Location: JWB 335
Wenjing Liao
Johns Hopkins University
Title |
Data analysis with low-dimensional structures |
Abstract |
High-dimensional data arise in many fields of contemporary science and introduce new challenges in statistical learning. We model data sets as samples from a probability measure in R^D. When D is large, the well-known curse of dimensionality implies that an enormous amount of training data are required to achieve certain accuracy in statistical learning, making many tasks unfeasible. Fortunately many data sets in applications exhibit a low-dimensional structure, for example, a low-dimensional manifold. We are interested in building efficient representations of such data for the purpose of compression and inference. In this talk, I will present a multiscale algorithm that yields a data-driven dictionary, together with a fast transform mapping data into low-dimensional coefficients, and an inverse of such a map. Our algorithm offers a tool for the dimension reduction of manifold data, and we can further use the low-dimensional coefficients for manifold inference. I will include several numerical experiments on both synthetic and real data, confirming our theoretical results on finite-sample analysis and demonstrating the effectiveness of our algorithm. |
Probability