用高斯过程和蒂威分布建模间歇性时间序列，提升预测精度。
Forecasting intermittent time series with Gaussian Processes and Tweedie likelihood
- 引入高斯过程与蒂威分布结合，建模间歇性计数数据的不确定性。
- 在数千个数据集上测试，蒂威模型对高分位数估计最优。
- 适合需要精确概率预测的工业场景，如库存管理、故障预测。
我们采用高斯过程（GPs）作为潜在函数，对间歇性时间序列进行概率预测。模型在贝叶斯框架下训练，考虑潜在函数的不确定性。将潜在GP变量与两种预测分布结合：负二项分布（NegBinGP）和蒂威分布（TweedieGP）。尽管负二项分布已用于此类预测，但这是首次将完全参数化的蒂威密度应用于间歇性时间序列。我们准确评估了具有零点质量与重尾特性的蒂威分布，避免了现有模型的简化假设。在数千个间歇性计数时间序列上测试模型，结果表明我们的方法在概率预测上始终优于对比模型。特别是，TweedieGP在最高分位数估计上表现最佳，说明其灵活性超过NegBinGP。
原文摘要 · Abstract (English)
We adopt Gaussian Processes (GPs) as latent functions for probabilistic forecasting of intermittent time series. The model is trained in a Bayesian framework that accounts for the uncertainty about the latent function. We couple the latent GP variable with two types of forecast distributions: the negative binomial (NegBinGP) and the Tweedie distribution (TweedieGP). While the negative binomial has already been used in forecasting intermittent time series, this is the first time in which a fully parameterized Tweedie density is used for intermittent time series. We properly evaluate the Tweedie density, which has both a point mass at zero and heavy tails, avoiding simplifying assumptions made in existing models. We test our models on thousands of intermittent count time series. Results show that our models provide consistently better probabilistic forecasts than the competitors. In particular, TweedieGP obtains the best estimates of the highest quantiles, thus showing that it is more flexible than NegBinGP.
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