Optimization of hyperparameters of Gaussian process regression (GPR) determines success or failure of the application of the method. Such optimization is difficult with sparse data, in particular in high-dimensional spaces where the data sparsity issue cannot be resolved by adding more data. We show that parameter optimization is facilitated by rectangularization of the defining equation of GPR. On the example of a 15-dimensional molecular potential energy surface we demonstrate that this approach allows effective hyperparameter tuning even with very sparse data.
翻译:Gaussian 进程回归(GPR) 的超参数优化决定了该方法应用的成败。 这种优化在数据稀少的情况下很难实现,特别是在数据宽度问题无法通过增加更多数据来解决的高维空间。我们表明,参数优化是通过GPR定义方程的重新三角化而促进的。 关于15维分子潜在能源表面的例子,我们证明,即使数据非常稀少,这种方法也允许有效的超参数调整。