优化冗余坐标后，混合模型用更少参数达到更高精度且不易过拟合。
Gaussian Process Regression -- Neural Network Hybrid with Optimized Redundant Coordinates
- 用蒙特卡洛算法优化冗余坐标，提升模型表达能力
- 测试误差更低，所需神经元数量减少一半以上
- 适合需要高精度又怕过拟合的材料模拟场景
近期提出的高斯过程回归-神经网络混合方法（GPRNN）基于规则构建的冗余坐标上的加性核高斯过程回归，结合了神经网络的表达力与线性回归对过拟合的鲁棒性，尤其在神经元数量超过最优值时仍能保持稳定。本文提出opt-GPRNN，通过蒙特卡洛算法优化冗余坐标，发现结合坐标优化后，GPRNN在更少项数/神经元条件下达到最低测试误差，并在神经元数量增加时依然避免过拟合。该方法表达力接近多层神经网络，可在某些应用中替代深度神经网络。同时，优化后的冗余坐标实现降维可能。实例展示了其在原子间势能学习和材料信息学中的应用。
原文摘要 · Abstract (English)
Recently, a Gaussian Process Regression - neural network (GPRNN) hybrid machine learning method was proposed, which is based on additive-kernel GPR in redundant coordinates constructed by rules [J. Phys. Chem. A 127 (2023) 7823]. The method combined the expressive power of an NN with the robustness of linear regression, in particular, with respect to overfitting when the number of neurons is increased beyond optimal. We introduce opt-GPRNN, in which the redundant coordinates of GPRNN are optimized with a Monte Carlo algorithm and show that when combined with optimization of redundant coordinates, GPRNN attains the lowest test set error with much fewer terms / neurons and retains the advantage of avoiding overfitting when the number of neurons is increased beyond optimal value. The method, opt-GPRNN possesses an expressive power closer to that of a multilayer NN and could obviate the need for deep NNs in some applications. With optimized redundant coordinates, a dimensionality reduction regime is also possible. Examples of application to machine learning an interatomic potential and materials informatics are given.
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