论文标题
使用虚拟卷积的功能输出回归：探索Huber和$ε$不敏感的损失
Functional Output Regression with Infimal Convolution: Exploring the Huber and $ε$-insensitive Losses
论文作者
论文摘要
本文的重点是功能输出回归（用于复杂损失）。尽管大多数现有的工作都考虑了正方形损失设置，但我们利用了Huber的扩展和$ε$不敏感的损失（由虚拟卷积引起），并提出了一个灵活的框架，能够处理家庭中各种形式的异常值和稀疏性。我们得出了依靠二元性来解决矢量值重现内核希尔伯特空间的二元任务的计算算法。该方法的效率与合成和现实基准的经典平方损耗设置相反。
The focus of the paper is functional output regression (FOR) with convoluted losses. While most existing work consider the square loss setting, we leverage extensions of the Huber and the $ε$-insensitive loss (induced by infimal convolution) and propose a flexible framework capable of handling various forms of outliers and sparsity in the FOR family. We derive computationally tractable algorithms relying on duality to tackle the resulting tasks in the context of vector-valued reproducing kernel Hilbert spaces. The efficiency of the approach is demonstrated and contrasted with the classical squared loss setting on both synthetic and real-world benchmarks.
