The estimation of time-varying quantities is a fundamental component of
decision making in fields such as healthcare and finance. However, the
practical utility of such estimates is limited by how accurately they quantify
predictive uncertainty. In this work, we address the problem of estimating the
joint predictive distribution of high-dimensional multivariate time series. We
propose a versatile method, based on the transformer architecture, that
estimates joint distributions using an attention-based decoder that provably
learns to mimic the properties of non-parametric copulas. The resulting model
has several desirable properties: it can scale to hundreds of time series,
supports both forecasting and interpolation, can handle unaligned and
non-uniformly sampled data, and can seamlessly adapt to missing data during
training. We demonstrate these properties empirically and show that our model
produces state-of-the-art predictions on multiple real-world datasets.

本文提出一种基于 Transformer 的方法来估计高维多变量时间序列的联合预测分布，该方法基于注意力机制的解码器能可靠地模拟非参数 Copulas 的特性，使得模型具有多种有用的属性，其中包括可以缩放到数百个时间序列，支持预测和插值，可以处理非对齐和不均匀采样的数据，并可以在训练期间无缝地适应缺失数据，最终的实证结果表明我们的模型在多个真实数据集上都可以产生有竞争力的预测效果。