Timeline for Why Gaussian Process Regression (GPR) is non-parametric?
Current License: CC BY-SA 4.0
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| Nov 15 at 6:17 | comment | added | CfourPiO | Calling a method "non-parametric" simply because it lacks explicit parameters is misleading. Each realization still has an associated probability, guided by a kernel function. Poorly estimated kernel parameters can lead to aliasing and frequency broadening. As data points or sample rates increase, the variance and bias in kernel parameter estimation decrease, showing that the process remains fundamentally parametric. | |
| Nov 15 at 6:10 | comment | added | CfourPiO | Thank you for the answer. I have seen this explanation everywhere. Coming from a background where I deal with random processes (although I am not an expert at all), this explanation does not fit well. Why is it that if an estimation technique produces infinite realizations (infinite functions), it is considered non-parametric and why the hyper-parameters are only tuning parameters? For a random process with a continuous expected frequency response, the kernel decides the evolution. One can draw many realisatizations, but the underlying rule is defined by the kernel whose parameters are fixed. | |
| Nov 14 at 23:06 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Nov 14 at 22:48 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Nov 14 at 12:26 | comment | added | usεr11852 | +1. In a way, I consider GPs as semi-parametric. The choice of kernel has a massive influence as well as the hyperparameters associated with it (e.g. the length scale of a Gaussian RBF kernel). | |
| Nov 14 at 11:53 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Nov 14 at 11:40 | history | answered | Glen_b | CC BY-SA 4.0 |