This paper addresses a new active learning strategy for regression problems.
The presented Wasserstein active regression model is based on the principles of
distribution-matching to measure the representativeness of the labeled dataset.
The Wasserstein distance is computed using GroupSort Neural Networks. The use
of such networks provides theoretical foundations giving a way to quantify
errors with explicit bounds for their size and depth. This solution is combined
with another uncertainty-based approach that is more outlier-tolerant to
complete the query strategy. Finally, this method is compared with other
classical and recent solutions. The study empirically shows the pertinence of
such a representativity-uncertainty approach, which provides good estimation
all along the query procedure. Moreover, the Wasserstein active regression
often achieves more precise estimations and tends to improve accuracy faster
than other models.

本文提出了一种用于回归问题的新型主动学习策略，所提出的 Wasserstein 主动回归模型基于分布匹配原理来衡量标记数据集的代表性，使用 GroupSort 神经网络计算 Wasserstein 距离，该网络提供了理论基础，能够以明确的边界量化错误的大小和深度。该解决方案与另一种基于不确定性的方法相结合，该方法对异常值更具容忍性，以完成查询策略。最后，将该方法与其他经典和最近的解决方案进行对比。实证研究表明，这种代表性 - 不确定性方法具有一致的良好估计，并且 Wasserstein 主动回归模型通常能够更精确地估计并且倾向于更快地提高准确性。

基于 Wasserstein 距离和 GroupSort 神经网络的回归主动学习

Active Learning for Regression based on Wasserstein distance and  GroupSort Neural Networks

Recent advances in adversarial attacks and Wasserstein GANs have advocated
for use of neural networks with restricted Lipschitz constants. Motivated by
these observations, we study the recently introduced GroupSort neural networks,
with constraints on the weights, and make a theoretical step towards a better
understanding of their expressive power. We show in particular how these
networks can represent any Lipschitz continuous piecewise linear functions. We
also prove that they are well-suited for approximating Lipschitz continuous
functions and exhibit upper bounds on both the depth and size. To conclude, the
efficiency of GroupSort networks compared with more standard ReLU networks is
illustrated in a set of synthetic experiments.

本研究介绍了 GroupSort 神经网络，探讨了它对利普希茨连续分段线性函数的表示能力，证明了它们适合近似利普希茨连续函数，并展示了其在合成实验中相对于标准的 ReLU 网络的高效性。