GQFormer: A Multi-Quantile Generative Transformer for Time Series Forecasting

We propose GQFormer, a probabilistic time series forecasting method that models the quantile function of the forecast distribution. Our methodology is rooted in the Implicit Quantile modeling approach, where samples from the Uniform distribution $\mathcal{U}\left( {0,1} \right)$ are reparameterized to quantile values of the target distribution. This allows implicit generative quantile modeling without any prior assumptions on the data distribution like Gaussianity, common in prior works. Our work is distinguished from prior quantile forecasting methods by novel methodological advances that relate to directly modeling the correlations among multiple quantile estimations at each forecasting horizon. To this end, we firstly develop a parameters haring architecture that implicitly models multiple quantile estimations efficiently and secondly regularize these through a novel multi-task loss function formulation that optimizes for quantile estimations to be sharper estimations individually and on the whole be spread maximally apart to capture the various modes of the underlying distribution. We experimentally validate the superiority of the method to state-of-the-art probabilistic forecasting baselines and ablations to the loss formulation.