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：对于存在缺失值的不规则采样多元时间序列进行概率预测，是医疗健康、天文学和气候学等众多领域的重要问题。现有最先进方法仅能估计单通道单时间点观测值的边缘分布，且假设其服从固定形状的参数分布。本文提出一种新型模型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。该模型基于过去观测值及查询通道与时间点，学习时间序列未来值的联合分布，无需对基础分布形状作任何假设。作为模型组件，我们创新性地提出了全实数域上的可逆三角注意力层与可逆非线性激活函数。在四个数据集上的大量实验表明，所提模型的似然函数值较先前最优模型提升4倍。