Bayesian Detection of Infrequent Differences in Sets of Time Series with Shared Structure
Abstract
We present a hierarchical Bayesian model for sets of related, but different, classes of time series data. Our model performs alignment simultaneously across all classes, while detecting and characterizing class-specific differences. During inference the model produces, for each class, a distribution over a canonical representation of the class. These class-specific canonical representations are automatically aligned to one another -- preserving common sub-structures, and highlighting differences. We apply our model to compare and contrast solenoid valve current data, and also, liquid-chromatography-ultraviolet-diode array data from a study of the plant Arabidopsis thaliana. 1 Aligning Time Series From Different Classes Many practical problems over a wide range of domains require synthesizing information from several noisy examples of one or more categories in order to build a model which captures common structure and also learns the patterns of variability between categories. In time series analysis, these modeling goals manifest themselves in the tasks of alignment and difference detection. These tasks have diverse applicability, spanning speech & music processing, equipment & industrial plant diagnosis/monitoring, and analysis of biological time series such as microarray & liquid/gas chromatography-based laboratory data (including mass spectrometry and ultraviolet diode arrays). Although alignment and difference detection have been extensively studied as separate problems in the signal processing and statistical pattern recognition communities, to our knowledge, no existing model performs both tasks in a unified way. Single class alignment algorithms attempt to align a set of time series all together, assuming that variability across different time series is attributable purely to noise. In many real-world situations, however, we have time series from multiple classes (categories) and our prior belief is that there is both substantial shared structure between the