一种探讨核的非线性的经验方法
An Empirical Approach For Probing the Definiteness of Kernels
摘要：
像支持向量机或高斯过程回归这样的模型通常需要半正定核。这些核可以基于距离函数。虽然对于常见的距离和内核证明了确定性，但是对于仅仅着眼于实际使用的用户来说，新内核的证明可能需要太多的时间和精力。此外，设计确定的距离或核可能同样复杂。最后，可以使模型能够使用不确定的内核。这可能会降低模型的准确性或计算成本。因此，需要一种有效的方法来确定确定性。我们提出了一个经验的方法。我们表明，采样以及优化与进化算法可以用来确定确定。我们提供了一个概念验证与16个不同的距离措施的排列。我们的方法允许反证确定性，如果一个相应的反例被发现。它也可以提供一个估计，它是如何可能获得不确定的核矩阵。这提供了一个简单、有效的工具来决定是否应该在设计/选择更合适的内核或算法上花费额外的努力。
英文摘要：
Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof-of-concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counter-example is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm.
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