论文标题
比例不变的过程回归：朝向贝叶斯ML的假设最小
Scale invariant process regression: Towards Bayesian ML with minimal assumptions
论文作者
论文摘要
当前的机器学习中正规化方法需要相当特定的模型假设（例如，内核形状），这些假设不是从有关应用程序的先验知识中得出的，而只能仅施加才能使该方法起作用。我们在本文中表明，实际上可以通过假设不变性原则（W.R.T.缩放，翻译和输入和输出空间的旋转）以及真实函数的不同程度来实现正则化。 具体而言，我们从上述最小的假设中得出了一种新颖的（非高斯）随机过程，并提出了一种相应的贝叶斯推断方法进行回归方法。平均后部事实证明是多谐波样条，后验过程是T过程的混合物。 与高斯过程回归相比，提出的方法显示出同样的性能，并且具有（i）任意较少（无选择的内核）（ii）的优点可能更快（无核参数优化），并且（iii）具有更好的外推行为。 我们认为，所提出的理论对于正则化和机器学习的概念基础具有至关重要的重要性，并且在超出回归的ML领域具有巨大的潜力。
Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We show in this paper that regularization can indeed be achieved by assuming nothing but invariance principles (w.r.t. scaling, translation, and rotation of input and output space) and the degree of differentiability of the true function. Concretely, we derive a novel (non-Gaussian) stochastic process from the above minimal assumptions, and we present a corresponding Bayesian inference method for regression. The mean posterior turns out to be a polyharmonic spline, and the posterior process is a mixture of t-processes. Compared with Gaussian process regression, the proposed method shows equal performance and has the advantages of being (i) less arbitrary (no choice of kernel) (ii) potentially faster (no kernel parameter optimization), and (iii) having better extrapolation behavior. We believe that the proposed theory has central importance for the conceptual foundations of regularization and machine learning and also has great potential to enable practical advances in ML areas beyond regression.
