Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   propose a novel Bayesian kernel based solution for regression in complex fields.  develop the formulation of the Gaussian process for regression (GPR) to deal with complex-valued outputs. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued one. Hover, based on the results in complex-valued linear theory,  prove that both a kernel and a pseudo-kernel are to be included in the solution. This is the starting point to develop the new formulation for the complex-valued GPR. The obtained formulation resembles the one of the widely linear minimum mean-squared (WLMMSE) approach. Just in the particular case where the outputs are proper, the pseudo-kernel cancels and the solution simplifies to a real-valued GPR structure, as the WLMMSE does into a strictly linear solution.  include some numerical experiments to show that the novel solution, denoted as widely non-linear complex GPR (WCGPR), outperforms a strictly complex GPR where a pseudo-kernel is not included.
['Rafael Boloix-Tortosa', 'Eva Arias-de-Reyna', 'F. Javier Payan-Somet', 'Juan José Murillo-Fuentes']
I am writing a research paper on a idea Complex-Valued Gaussian Processes for Regression: A Widely Non-Linear Approach
[{"from": "human", "value": "I am writing a research paper on a idea Complex-Valued Gaussian Processes for Regression: A Widely Non-Linear Approach"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   propose a novel Bayesian kernel based solution for regression in complex fields.  develop the formulation of the Gaussian process for regression (GPR) to deal with complex-valued outputs. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued one. Hover, based on the results in complex-valued linear theory,  prove that both a kernel and a pseudo-kernel are to be included in the solution. This is the starting point to develop the new formulation for the complex-valued GPR. The obtained formulation resembles the one of the widely linear minimum mean-squared (WLMMSE) approach. Just in the particular case where the outputs are proper, the pseudo-kernel cancels and the solution simplifies to a real-valued GPR structure, as the WLMMSE does into a strictly linear solution.  include some numerical experiments to show that the novel solution, denoted as widely non-linear complex GPR (WCGPR), outperforms a strictly complex GPR where a pseudo-kernel is not included."}]