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Found 5 papers, 1 papers with code
Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimension
Kernel methods such as kernel ridge regression and Gaussian process regressions with Matern type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials informatics.
Orders-of-coupling representation with a single neural network with optimal neuron activation functions and without nonlinear parameter optimization
Here, we show that neural network models of orders-of-coupling representations can be easily built by using a recently proposed neural network with optimal neuron activation functions computed with a first-order additive Gaussian process regression [arXiv:2301. 05567] and avoiding non-linear parameter optimization.
Neural network with optimal neuron activation functions based on additive Gaussian process regression
While even a single-hidden layer NN is a universal approximator, its expressive power is limited by the use of simple neuron activation functions (such as sigmoid functions) that are typically the same for all neurons.
The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfaces
It is also critical to the formulation of multi-zeta type basis functions widely used in computational chemistry We show, on the example of fitting of molecular potential energy surfaces of increasing dimensionality, the practical disappearance of the property of locality of a Gaussian-like kernel in high dimensionality.
Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for representing multidimensional functions with machine-learned lower-dimensional terms allowing insight with a general method
We present a Python implementation for RS-HDMR-GPR (Random Sampling High Dimensional Model Representation Gaussian Process Regression).
