Development of an accurate, flexible, and numerically efficient uncertainty quantification (UQ) method is one of fundamental challenges in machine learning. Previously, a UQ method called DISCO Nets has been proposed (Bouchacourt et al., 2016), which trains a neural network by minimizing the energy score. In this method, a random noise vector in $\mathbb{R}^{10\text{--}100}$ is concatenated with the original input vector in order to produce a diverse ensemble forecast despite using a single neural network. While this method has shown promising performance on a hand pose estimation task in computer vision, it remained unexplored whether this method works as nicely for regression on tabular data, and how it competes with more recent advanced UQ methods such as NGBoost. In this paper, we propose an improved neural architecture of DISCO Nets that admits faster and more stable training while only using a compact noise vector of dimension $\sim \mathcal{O}(1)$. We benchmark this approach on miscellaneous real-world tabular datasets and confirm that it is competitive with or even superior to standard UQ baselines. Moreover we observe that it exhibits better point forecast performance than a neural network of the same size trained with the conventional mean squared error. As another advantage of the proposed method, we show that local feature importance computation methods such as SHAP can be easily applied to any subregion of the predictive distribution. A new elementary proof for the validity of using the energy score to learn predictive distributions is also provided.
翻译:开发准确、灵活和数字高效的不确定性量化方法(UQ)是机器学习的根本挑战之一。 之前, 已经提出了名为 DISCO Nets 的 UQ 方法( Bouchacourt et al., 2016 ), 该方法通过最大限度地减少能源分数来培训神经网络。 在这个方法中, 一个随机噪音矢量以$mathbb{R ⁇ 10\ text{-}100}] 与原始输入矢量相融合, 尽管使用单一神经网络, 却可以产生一个多样的混合组合值预测。 虽然这种方法显示手头上的表现很有希望在计算机视野中做出估计任务, 但仍无法探讨这种方法是否适合表格数据回归, 以及如何通过NGBoost等最新先进的 UQ 方法对神经网络进行竞争。 在本文中, 我们将这一方法作为基础的精确度的精确度作为基准, 并且用一个经过培训的SEVA 的网络优势来证明, 与另一个常规的SEV 模型相比, 更能显示我们所观测到的RA 。