Manifold Learning for High-Dimensional Data

• Activity Number: 195
• Type: Roundtables
• Date/Time: Monday, August 1, 2011 : 12:30 PM to 1:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): David Dunson*+
• Companies: Duke University
• Keywords: Bayesian ; Machine learning ; Dimensionality reduction ; Nonparametric ; Data fusion ; Functional Data Analysis

Abstract

There is increasing interesting in developing methods for compression, analysis and interpretation of massive dimensional data including not just vectors of continuous variables in a Euclidean space (e.g., gene expression) but also discrete data (e.g., gene sequences) and more complex objects such as functions, images, documents and movies. In addition, one often desires a joint representation and analysis of high-dimensional data of varying modalities. For example, for a patient in the emergency department, one may have data from diagnostic tests consisting of images and curves, while also having text from physician notes and categorical and continuous predictors, with the goal being to diagnose the condition and recommend an optimal treatment based on this disparate combination of data. To address such problems, methods of dimensionality reduction and joint modeling are needed. One direction to take is to suppose that the massive-dimensional observed data are concentrated near a (much) lower dimensional manifold. By "learning" this manifold, one can potentially enable compression of the data leading to dramatic storage, processing and analysis speed-ups. In this round-table