Infinite Shift-invariant Grouped Multi-task Learning for Gaussian Processes
This work addresses multi-task learning for phase-shifted periodic time series, offering incremental improvements in handling sparse and asynchronous data in domains like astrophysics.
The paper tackled the problem of learning from multiple phase-shifted periodic time series by developing a Bayesian nonparametric model that combines group-specific and individual variations, with an efficient EM algorithm and extension to infinite mixtures using Dirichlet Process priors. Experiments on synthetic and astrophysics data showed improved performance, especially for sparsely and non-synchronously sampled time series.
Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we develop a novel Bayesian nonparametric model capturing a mixture of Gaussian processes where each task is a sum of a group-specific function and a component capturing individual variation, in addition to each task being phase shifted. We develop an efficient \textsc{em} algorithm to learn the parameters of the model. As a special case we obtain the Gaussian mixture model and \textsc{em} algorithm for phased-shifted periodic time series. Furthermore, we extend the proposed model by using a Dirichlet Process prior and thereby leading to an infinite mixture model that is capable of doing automatic model selection. A Variational Bayesian approach is developed for inference in this model. Experiments in regression, classification and class discovery demonstrate the performance of the proposed models using both synthetic data and real-world time series data from astrophysics. Our methods are particularly useful when the time series are sparsely and non-synchronously sampled.