We extend a heuristic method for automatic dimensionality selection, which maximizes a profile likelihood to identify "elbows" in scree plots. Our extension enables researchers to make automatic choices of multiple hyper-parameters simultaneously. To facilitate our extension to multi-dimensions, we propose a "softened" profile likelihood. We present two distinct parameterizations of our solution and demonstrate our approach on elastic nets, support vector machines, and neural networks. We also briefly discuss applications of our method to other data-analytic tasks than hyper-parameter selection.

翻译：本文拓展了一种用于自动维度选择的启发式方法，该方法通过最大化轮廓似然来识别碎石图中的“拐点”。我们的拓展使研究者能够同时自动选择多个超参数。为实现多维拓展，我们提出了一种“软化”轮廓似然。我们展示了两种不同的参数化解决方案，并在弹性网络、支持向量机和神经网络上验证了该方法。此外，我们简要讨论了本方法在超参数选择之外的其他数据分析任务中的应用前景。