Forecasting high-dimensional time series plays a crucial role in many
applications such as demand forecasting and financial predictions. Modern
datasets can have millions of correlated time-series that evolve together, i.e
they are extremely high dimensional (one dimension for each individual
time-series). There is a need for exploiting global patterns and coupling them
with local calibration for better prediction. However, most recent deep
learning approaches in the literature are one-dimensional, i.e, even though
they are trained on the whole dataset, during prediction, the future forecast
for a single dimension mainly depends on past values from the same dimension.
In this paper, we seek to correct this deficiency and propose DeepGLO, a deep
forecasting model which thinks globally and acts locally. In particular,
DeepGLO is a hybrid model that combines a global matrix factorization model
regularized by a temporal convolution network, along with another temporal
network that can capture local properties of each time-series and associated
covariates. Our model can be trained effectively on high-dimensional but
diverse time series, where different time series can have vastly different
scales, without a priori normalization or rescaling. Empirical results
demonstrate that DeepGLO can outperform state-of-the-art approaches; for
example, we see more than 25% improvement in WAPE over other methods on a
public dataset that contains more than 100K-dimensional time series.

本文提出了一种能够全局认知并在本地进行校准的深度预测模型 DeepGlo, 它是一个混合模型，将全局矩阵因式分解模型与另一个能够捕捉每个时间序列及相关协变量的局部属性的时间网络相结合，证明了 DeepGlo 对于高维时间序列的预测要比其他方法更加准确。

全球思考，本地行动：高维时间序列预测的深度神经网络方法

Think Globally, Act Locally: A Deep Neural Network Approach to  High-Dimensional Time Series Forecasting

High-dimensional time series are common in many domains. Since human
cognition is not optimized to work well in high-dimensional spaces, these areas
could benefit from interpretable low-dimensional representations. However, most
representation learning algorithms for time series data are difficult to
interpret. This is due to non-intuitive mappings from data features to salient
properties of the representation and non-smoothness over time. To address this
problem, we propose a new representation learning framework building on ideas
from interpretable discrete dimensionality reduction and deep generative
modeling. This framework allows us to learn discrete representations of time
series, which give rise to smooth and interpretable embeddings with superior
clustering performance. We introduce a new way to overcome the
non-differentiability in discrete representation learning and present a
gradient-based version of the traditional self-organizing map algorithm that is
more performant than the original. Furthermore, to allow for a probabilistic
interpretation of our method, we integrate a Markov model in the representation
space. This model uncovers the temporal transition structure, improves
clustering performance even further and provides additional explanatory
insights as well as a natural representation of uncertainty. We evaluate our
model in terms of clustering performance and interpretability on static
(Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST
images, a chaotic Lorenz attractor system with two macro states, as well as on
a challenging real world medical time series application on the eICU data set.
Our learned representations compare favorably with competitor methods and
facilitate downstream tasks on the real world data.

提出了一种针对高维时间序列数据的离散表征学习框架，通过整合可解释性离散降维和深度生成建模方法，得到在可解释性和聚类性能方面优异的平滑嵌入表征，基于自组织映射算法和马尔科夫模型实现了离散表征的概率化解释和进一步优化，实验结果显示其表现比竞争方法更好。