Traditional regression and prediction tasks often only provide deterministic point estimates. To estimate the uncertainty or distribution information of the response variable, methods such as Bayesian inference, model ensembling, or MC Dropout are typically used. These methods either assume that the posterior distribution of samples follows a Gaussian process or require thousands of forward passes for sample generation. We propose a novel approach called DistPred for regression and forecasting tasks, which overcomes the limitations of existing methods while remaining simple and powerful. Specifically, we transform proper scoring rules that measure the discrepancy between the predicted distribution and the target distribution into a differentiable discrete form and use it as a loss function to train the model end-to-end. This allows the model to sample numerous samples in a single forward pass to estimate the potential distribution of the response variable. We have compared our method with several existing approaches on multiple datasets and achieved state-of-the-art performance. Additionally, our method significantly improves computational efficiency. For example, compared to state-of-the-art models, DistPred has a 90x faster inference speed. Experimental results can be reproduced through https://github.com/Anoise/DistPred.

翻译：传统的回归与预测任务通常仅提供确定性的点估计。为估计响应变量的不确定性或分布信息，通常采用贝叶斯推断、模型集成或MC Dropout等方法。这些方法要么假设样本的后验分布服从高斯过程，要么需要数千次前向传播以生成样本。我们提出了一种称为DistPred的新方法用于回归与预测任务，该方法克服了现有方法的局限性，同时保持简洁与高效。具体而言，我们将衡量预测分布与目标分布之间差异的适当评分规则转化为可微分的离散形式，并将其作为损失函数对模型进行端到端训练。这使得模型能够通过单次前向传播采样大量样本，从而估计响应变量的潜在分布。我们在多个数据集上将本方法与若干现有方法进行了比较，并取得了最先进的性能。此外，本方法显著提升了计算效率。例如，与当前最优模型相比，DistPred的推理速度提升了90倍。实验结果可通过https://github.com/Anoise/DistPred复现。