Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The stable spline kernel and the diagonal correlated kernel are two kernels that have been tested extensively in kernel-based regularization methods for LTI system identification. As shown in our recent works, although these two kernels are introduced in different ways, they share some common features, e.g., they all belong to the class of exponentially convex locally stationary kernels, and state-space model induced kernels. In this work,  further show that similar to the derivation of the stable spline kernel, the continuous-time diagonal correlated kernel can be derived by applying the same “stable” coordinate change to a “generalized” first order spline kernel, and thus can be interpreted as a stable generalized first order spline kernel. This interpretation provides new facets to understand the properties of the diagonal correlated kernel. Due to this interpretation, new eigendecompositions, explicit expression of the norm, and new maximum entropy interpretation of the diagonal correlated kernel are derived accordingly.
['Tianshi Chen', 'Gianluigi Pillonetto', 'Alessandro Chiuso', 'Lennart Ljung']
I am writing a research paper on a idea Continuous-time DC kernel — A stable generalized first order spline kernel
[{"from": "human", "value": "I am writing a research paper on a idea Continuous-time DC kernel \u2014 A stable generalized first order spline kernel"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The stable spline kernel and the diagonal correlated kernel are two kernels that have been tested extensively in kernel-based regularization methods for LTI system identification. As shown in our recent works, although these two kernels are introduced in different ways, they share some common features, e.g., they all belong to the class of exponentially convex locally stationary kernels, and state-space model induced kernels. In this work,  further show that similar to the derivation of the stable spline kernel, the continuous-time diagonal correlated kernel can be derived by applying the same \u201cstable\u201d coordinate change to a \u201cgeneralized\u201d first order spline kernel, and thus can be interpreted as a stable generalized first order spline kernel. This interpretation provides new facets to understand the properties of the diagonal correlated kernel. Due to this interpretation, new eigendecompositions, explicit expression of the norm, and new maximum entropy interpretation of the diagonal correlated kernel are derived accordingly."}]