基于深度格网络的非参数累积分布函数多时间跨度时间序列预测
Multi-Horizon Time Series Forecasting of non-parametric CDFs with Deep Lattice Networks
AI总结：
本文针对时间序列概率预测中点预测易漏突变、传统参数化CDF建模受限、分位数回归易出现交叉的问题，适配深度格网络结合LSTM实现非参数CDF多跨度预测，在太阳辐照度预测任务中性能优于对比方法。
摘要：
概率预测不仅能为未来预测补充更多信息，还能弥补点预测的固有缺陷：时间序列中的突变仍可被累积分布函数（CDF）捕捉，而点预测往往会完全遗漏这类突变。历史上，预测场景下的CDF建模长期局限于参数化方法，但随着近期技术进展，这一限制已被打破。本研究旨在打通概率预测与单调网络领域，提出一种可预测隐式、完整非参数CDF的方法。为此，我们对深度格网络（DLN）进行适配，使其可在时间序列预测中完成带单调约束的同步/隐式分位数回归。分位数回归通常会出现分位数交叉问题，必须避免该问题才能得到合法的CDF。我们采用长短期记忆单元（LSTM）作为嵌入层，将分位数输入传递到输出规模扩展后的DLN的所有子格中，依托DLN的单调约束能力避免分位数交叉，最终实现隐式CDF的多时间跨度预测。我们在极具实际应用价值的时间序列预测场景——提前一天的逐小时太阳辐照度观测预测中，将所提方法与相关当前最优方法进行性能对比评估。实验结果表明，适配后的DLN性能与无约束方法相当甚至更优；进一步将其与可扩展单调神经网络对比发现，我们的方法表现更好。我们希望通过本次对DLN的适配，推动更多针对单调神经网络与概率预测技术的交叉研究。
英文摘要：
Probabilistic forecasting is not only a way to add more information to a prediction of the future, but it also builds on weaknesses in point prediction. Sudden changes in a time series can still be captured by a cumulative distribution function (CDF), while a point prediction is likely to miss it entirely. The modeling of CDFs within forecasts has historically been limited to parametric approaches, but due to recent advances, this no longer has to be the case. We aim to advance the fields of probabilistic forecasting and monotonic networks by connecting them and propose an approach that permits the forecasting of implicit, complete, and nonparametric CDFs. For this purpose, we propose an adaptation to deep lattice networks (DLN) for monotonically constrained simultaneous/implicit quantile regression in time series forecasting. Quantile regression usually produces quantile crossovers, which need to be prevented to achieve a legitimate CDF. By leveraging long short term memory units (LSTM) as the embedding layer, and spreading quantile inputs to all sub-lattices of a DLN with an extended output size, we can produce a multi-horizon forecast of an implicit CDF due to the monotonic constraintability of DLNs that prevent quantile crossovers. We compare and evaluate our approach's performance to relevant state of the art within the context of a highly relevant application of time series forecasting: Day-ahead, hourly forecasts of solar irradiance observations. Our experiments show that the adaptation of a DLN performs just as well or even better than an unconstrained approach. Further comparison of the adapted DLN against a scalable monotonic neural network shows that our approach performs better. With this adaptation of DLNs, we intend to create more interest and crossover investigations in techniques of monotonic neural networks and probabilistic forecasting.
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