Multi-task learning requires accurate identification of the correlations between tasks. In real-world time-series, tasks are rarely perfectly temporally aligned; traditional multi-task models do not account for this and subsequent errors in correlation estimation will result in poor predictive performance and uncertainty quantification. We introduce a method that automatically accounts for temporal misalignment in a unified generative model that improves predictive performance. Our method uses Gaussian processes (GPs) to model the correlations both within and between the tasks. Building on the previous work by Kazlauskaiteet al. [2019], we include a separate monotonic warp of the input data to model temporal misalignment. In contrast to previous work, we formulate a lower bound that accounts for uncertainty in both the estimates of the warping process and the underlying functions. Also, our new take on a monotonic stochastic process, with efficient path-wise sampling for the warp functions, allows us to perform full Bayesian inference in the model rather than MAP estimates. Missing data experiments, on synthetic and real time-series, demonstrate the advantages of accounting for misalignments (vs standard unaligned method) as well as modelling the uncertainty in the warping process(vs baseline MAP alignment approach).
翻译:多任务学习要求准确确定任务之间的关联。在现实世界的时间序列中,任务很少完全在时间上一致;传统的多任务模型没有考虑到这一点,因此,相关估计中后来的错误将导致预测性业绩差和不确定性的量化。我们引入了一种方法,在统一基因模型中自动说明时间错配,以提高预测性能。我们的方法使用高斯进程(GPs)来模拟任务内部和任务之间的相关性。根据Kazlauskaiteet al. [2019] 的以往工作,我们包括一个单独的输入数据单词拼凑,以模拟时间错配。与以往的工作相比,我们为扭曲过程和基本功能的不确定性制定了一个较低的组合。此外,我们的新采用一个单一的随机过程,为调和功能提供有效的路径性取样,使我们能够在模型中而不是MAP估计中进行全巴耶斯式的推断。在合成和真实的时间序列中缺少数据实验,以显示对调方法的不确定性进行会计的优势,作为调和调的基线方法。