Tuesday, October 27, 2009
101 Stanley Thomas Hall
Tulane University (Uptown)
Performance of Event Prediction Models Can be Improved by Considering More Than One Type of Variation Along Principal Components
Predicting the response of a system to future inputs based on observations of past inputs and outputs is a common problem across a range of science and engineering fields. In complex systems, there is often a huge set of possible inputs driving the system, and the first step in predicting a particular type of response is to find a smaller subset of the input space that retains as much as possible of the information that drives the response of interest. Many powerful approaches to this problem are based on the low-order statistics of the response-conditioned input ensemble. The mean of the conditional ensemble may be sufficient for predicting the response of a mostly-linear system, but additional dimensions are often needed, and these are often derived from the covariance. Principal component analysis (PCA) is one of the best known techniques for extracting dimensions of interest from a covariance structure. PCA calculates eigenvectors of the covariance matrix, and is usually used to isolate a few vectors corresponding to the largest eigenvalues, which can be interpreted as the dimensions where values are often far from the mean. Typically, these are considered to the most interesting dimensions, following the mean. This is not always the case, however. It is easy to show that in some systems principal components associated to large eigenvalues are the least informative dimensions to use in a predictive model. In other types of systems, however, these dimensions may be the most informative. I present a technique for classifying dimensions extracted from the conditional covariance, allowing the informative ones to be used in an appropriate way, while the uninformative ones are discarded. I show that this technique improves performance of response prediction in several complex systems relative to several existing prediction techniques.
Center for Computational Science, Stanley Thomas Hall 402, New Orleans, LA 70118 email@example.com