Probabilistic forecasting of irregularly sampled multivariate time series with missing values is an important problem in many fields, including health care, astronomy, and climate. State-of-the-art methods for the task estimate only marginal distributions of observations in single channels and at single timepoints, assuming a fixed-shape parametric distribution. In this work, we propose a novel model, ProFITi, for probabilistic forecasting of irregularly sampled time series with missing values using conditional normalizing flows. The model learns joint distributions over the future values of the time series conditioned on past observations and queried channels and times, without assuming any fixed shape of the underlying distribution. As model components, we introduce a novel invertible triangular attention layer and an invertible non-linear activation function on and onto the whole real line. We conduct extensive experiments on four datasets and demonstrate that the proposed model provides $4$ times higher likelihood over the previously best model.

翻译：不规则采样且存在缺失值的多元时间序列的概率预测是医疗、天文和气候等多个领域的重要问题。现有最先进方法仅能估计单通道单时间点观测的边缘分布，且假设分布具有固定参数形式。本文提出创新模型ProFITi，通过条件归一化流实现对含缺失值不规则采样时间序列的概率预测。该模型在无需预设分布形态的前提下，学习以历史观测值、查询通道及时间点为条件的未来时间序列值联合分布。模型组件包括：新型可逆三角注意力层，以及定义在全实数域上的可逆非线性激活函数。我们在四个数据集上开展广泛实验，结果表明所提模型的似然值较此前最优模型提升4倍。