Adaptive streaming discriminant analysis regularization, error rate estimation, and semi-supervised learning

Abstract

Streaming data will become one of the main areas of theoretical and practical interest in the coming years for the statistician. Business applications abound due to the competitive advantages that come from quickly extractinginsights from data. In order to face streaming data head on, new statistical methods will need to be created, while existing ones and their corresponding implementations will need to be revised and made more adaptive to current trends, both new and revised methods also need to be computationally lean enough to rapidly process large amounts of high velocity data. Discriminant analysis is the standard algorithm for classification of random data. Several streaming versions of discriminant analysis exist, however, Anagnostopoulos et.al (2012) provide a variation that has its foundations in the adaptive filtering (Haykin (1996)) and weighted likelihood Hu and Zidek (2002) approaches. Their algorithm focuses on providing adaptive estimates of the parameters (mean, covariance matrix, along with prior probabilities for each group), which then provide adaptive classification boundaries flexibly modeling the data over time. This research seeks to expand on this algorithm by pursuing alternative estimation strategies as well as investigating ancillary items that are often overlooked when developing new methods such as error rate estimation and handling of missing data.