高斯过程的无限平移不变分组多任务学习
Infinite Shift-invariant Grouped Multi-task Learning for Gaussian Processes
摘要：
多任务学习利用数据集之间的共享信息来提高单个任务的学习性能。本文应用这个框架的数据，其中每个任务是一个相移周期性的时间序列。特别是，我们开发了一种新的贝叶斯非参数模型捕捉混合高斯过程，其中每个任务是一个特定于组的功能和组件捕捉个体的变化，除了每个任务被相移的总和。我们开发了一个有效的\textsc{em}算法来学习模型的参数。作为一种特殊情况，我们得到了移相周期时间序列的高斯混合模型和\textsc{em}算法。此外，我们通过使用Dirichlet过程先验扩展了所提出的模型，从而导致能够进行自动模型选择的无限混合模型。一个变分贝叶斯方法开发的推理在这个模型中。在回归，分类和类发现的实验表明，所提出的模型使用合成数据和真实世界的时间序列数据从天体物理的性能。当时间序列是稀疏和非同步采样时，我们的方法特别有用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
