论文标题
参数模态回归的隐式函数学习方法
An implicit function learning approach for parametric modal regression
论文作者
论文摘要
对于多值函数 - 例如，当给定输入的目标上的条件分布是多模式的---标准回归方法并非总是值得的，因为它们提供了条件均值。模态回归算法通过找到条件模式来解决此问题。但是，大多数是非参数方法，因此很难扩展。此外，参数近似值（如神经网络）有助于学习输入和目标之间的复杂关系。在这项工作中，我们提出了一种参数模态回归算法。我们使用隐式函数定理来开发一个目标，以学习输入和目标的联合函数。我们从经验上证明了几个综合问题，我们的方法（i）可以学习多价值功能并产生条件模式，（ii）尺度良好到高维输入，并且（iii）甚至可以对某些单模式问题更有效，尤其是对于高频功能。我们证明我们的方法在现实世界的模态回归问题和两个常规回归数据集中具有竞争力。
For multi-valued functions---such as when the conditional distribution on targets given the inputs is multi-modal---standard regression approaches are not always desirable because they provide the conditional mean. Modal regression algorithms address this issue by instead finding the conditional mode(s). Most, however, are nonparametric approaches and so can be difficult to scale. Further, parametric approximators, like neural networks, facilitate learning complex relationships between inputs and targets. In this work, we propose a parametric modal regression algorithm. We use the implicit function theorem to develop an objective, for learning a joint function over inputs and targets. We empirically demonstrate on several synthetic problems that our method (i) can learn multi-valued functions and produce the conditional modes, (ii) scales well to high-dimensional inputs, and (iii) can even be more effective for certain uni-modal problems, particularly for high-frequency functions. We demonstrate that our method is competitive in a real-world modal regression problem and two regular regression datasets.
