标题： 随机投影的加性高斯过程用于回归 显示英文标题

标题： Randomly Projected Additive Gaussian Processes for Regression

摘要： 高斯过程（GPs）提供了灵活的函数分布，其归纳偏置由核函数控制。然而，在许多应用中，即使对于适度的输入维度，高斯过程也可能遇到困难。学习一个低维投影可以帮助缓解维度灾难的问题，但会引入许多可训练的超参数，这在小数据集情况下尤其繁琐。我们使用高斯过程回归中的核函数加和，其中每个核函数对其输入的不同随机投影进行操作。令人惊讶的是，我们发现随着随机投影数量的增加，这种方法的预测性能快速收敛到在原始全维度输入上操作的核函数的性能，即使我们将输入投影到单个维度，这种现象在多种数据集上仍然成立。因此，许多问题可以显著地被简化为一维输入空间，而无需学习变换。我们证明了这种收敛性及其速率，并进一步提出了一种确定性的方法，其收敛速度比纯随机投影更快。此外，我们展示了与原始输入空间中的核函数相比，我们的方法对于高维输入可以实现更快的推理和改进的预测准确性。 显示英文摘要

摘要： Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low dimensional projection can help alleviate this curse of dimensionality, but introduces many trainable hyperparameters, which can be cumbersome, especially in the small data regime. We use additive sums of kernels for GP regression, where each kernel operates on a different random projection of its inputs. Surprisingly, we find that as the number of random projections increases, the predictive performance of this approach quickly converges to the performance of a kernel operating on the original full dimensional inputs, over a wide range of data sets, even if we are projecting into a single dimension. As a consequence, many problems can remarkably be reduced to one dimensional input spaces, without learning a transformation. We prove this convergence and its rate, and additionally propose a deterministic approach that converges more quickly than purely random projections. Moreover, we demonstrate our approach can achieve faster inference and improved predictive accuracy for high-dimensional inputs compared to kernels in the original input space.