We propose a novel multi-task method for quantile forecasting with shared Linear layers. Our method is based on the Implicit quantile learning approach, where samples from the Uniform distribution $\mathcal{U}(0, 1)$ are reparameterized to quantile values of the target distribution. We combine the implicit quantile and input time series representations to directly forecast multiple quantile estimations for multiple horizons jointly. Prior works have adopted a Linear layer for the direct estimation of all forecasting horizons in a multi-task learning setup. We show that following similar intuition from multi-task learning to exploit correlations among forecast horizons, we can model multiple quantile estimates as auxiliary tasks for each of the forecast horizon to improve forecast accuracy across the quantile estimates compared to modeling only a single quantile estimate. We show learning auxiliary quantile tasks leads to state-of-the-art performance on deterministic forecasting benchmarks concerning the main-task of forecasting the 50$^{th}$ percentile estimate.

翻译：我们为共享线性层的定量预测提出了一个新的多任务方法。 我们的方法基于隐性量化学习方法, 统一分布 $\ mathcal{U} (0, 1美元) 的样本被重新量化成目标分布的四分位值。 我们将隐含的量化和输入时间序列表达方式结合起来, 直接预测多个地平线的多个量化估计值。 先前的工程在多任务学习设置中采用了直线层, 直接估算所有预测地平线。 我们显示, 在从多任务学习到利用预测地平线之间的相关性的直觉相似之后, 我们可以将多个量化估计值作为每个预测地平线的辅助任务, 以便提高每个预测地平线估计值的预测准确性, 而不是仅仅模拟单一的量化估计值。 我们显示, 在预测50 美元 百分率估计值的主值时, 学习辅助量化任务可以导致确定性预报基准的状态。