We introduce a new model for multivariate probabilistic time series
prediction, designed to flexibly address a range of tasks including
forecasting, interpolation, and their combinations. Building on copula theory,
we propose a simplified objective for the recently-introduced transformer-based
attentional copulas (TACTiS), wherein the number of distributional parameters
now scales linearly with the number of variables instead of factorially. The
new objective requires the introduction of a training curriculum, which goes
hand-in-hand with necessary changes to the original architecture. We show that
the resulting model has significantly better training dynamics and achieves
state-of-the-art performance across diverse real-world forecasting tasks, while
maintaining the flexibility of prior work, such as seamless handling of
unaligned and unevenly-sampled time series.

多元概率时间序列预测的新模型引入了 copula 理论，提出了基于 transformer 的简化目标函数 TACTiS，其分布参数数量与变量数量成线性关系。新目标函数引入了训练计划，并对原始架构进行必要的改变。结果表明，该模型在各种真实世界预测任务中具有显著改进的训练动力学，并实现了最先进的性能，同时保持了如处理不对齐和采样不均匀的时间序列等先前工作的灵活性。

TACTiS-2: 用于多元时间序列的更好、更快、更简单的注意力联合分布

TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate  Time Series

Detection of effects of the parameters of the synthetic process on the
microstructure of materials is an important, yet elusive goal of materials
science. We develop a method for detecting effects based on copula theory, high
dimensional distribution distances, and permutational statistics to analyze a
designed experiment synthesizing plutonium oxide from Pu(III) Oxalate. We
detect effects of strike order and oxalic acid feed on the microstructure of
the resulting plutonium oxide, which match the literature well. We also detect
excess bivariate effects between the pairs of acid concentration, strike order
and precipitation temperature.

应用联合分布理论、高维分布统计和置换统计方法，探测化学合成过程参数对材料微结构的影响。以铀盐为原材料，检测醛酸盐及攻击顺序等因素对二氧化钚晶体结构的影响及二度影响