Outstanding achievements of graph neural networks for spatiotemporal time
series analysis show that relational constraints introduce an effective
inductive bias into neural forecasting architectures. Often, however, the
relational information characterizing the underlying data-generating process is
unavailable and the practitioner is left with the problem of inferring from
data which relational graph to use in the subsequent processing stages. We
propose novel, principled - yet practical - probabilistic score-based methods
that learn the relational dependencies as distributions over graphs while
maximizing end-to-end the performance at task. The proposed graph learning
framework is based on consolidated variance reduction techniques for Monte
Carlo score-based gradient estimation, is theoretically grounded, and, as we
show, effective in practice. In this paper, we focus on the time series
forecasting problem and show that, by tailoring the gradient estimators to the
graph learning problem, we are able to achieve state-of-the-art performance
while controlling the sparsity of the learned graph and the computational
scalability. We empirically assess the effectiveness of the proposed method on
synthetic and real-world benchmarks, showing that the proposed solution can be
used as a stand-alone graph identification procedure as well as a graph
learning component of an end-to-end forecasting architecture.

本文提出了一种基于分数的概率方法，学习图的关系依赖性。该方法可用于时间序列预测，可在最大化任务性能的同时控制图的稀疏性和计算可扩展性，同时提高了准确性。

时空序列中的稀疏图学习

Sparse Graph Learning from Spatiotemporal Time Series

We consider stochastic optimization problems where data is drawn from a
Markov chain. Existing methods for this setting crucially rely on knowing the
mixing time of the chain, which in real-world applications is usually unknown.
We propose the first optimization method that does not require the knowledge of
the mixing time, yet obtains the optimal asymptotic convergence rate when
applied to convex problems. We further show that our approach can be extended
to: (i) finding stationary points in non-convex optimization with Markovian
data, and (ii) obtaining better dependence on the mixing time in temporal
difference (TD) learning; in both cases, our method is completely oblivious to
the mixing time. Our method relies on a novel combination of multi-level Monte
Carlo (MLMC) gradient estimation together with an adaptive learning method.

本研究提出了一种新颖的多层蒙特卡罗渐进优化方法，针对含有 Markov 链随机数据的优化问题，能够在不知道 Markov 链混合时间的情况下获得最佳渐进收敛速率，并适用于非凸优化求解及在时间差分 (TD) 学习中获取更好的混合时间依赖性。