# Questions tagged [rbf-kernel]

The RBF kernel, i.e., radial-basis-function kernel, occurs in the context of kernel methods in machine learning.

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### Why do my GaussianProcessRegressor prediction results converge to 0?

I am using sklearn GaussianProcessRegressor to predict a time series. The kernel I use is this: ...
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### Explanation of the multiplier of gaussian process kernels in sklearn document

I have read the basic materials about gaussian process regression and understand its ideas. https://scikit-learn.org/stable/modules/gaussian_process.html However, when I look into the sklearn page, I ...
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### Gaussian Process Covariance Guaranteed to be PSD?

I have a question regarding a proof to show that the covariance matrix of a Gaussian process is Positive SemiDefinite (PSD). Given the equation, $cov(\bar{f}) = K_{**} - K_{*f}K_{ff}^{-1}K_{f*}$ how ...
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### Does a gaussian kernel suffer from the curse of dimensionality?

Some embedding methods map a data vector in original space to a new space with significantly high dimension and then calculate dot product between these mapped high dimensional vectors. Don't they ...
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### Can different kernels be used when performing Gaussian Process Regression?

Given the equations for exact Gaussian process regression: \begin{equation} \bar{\boldsymbol{f}_*} = \boldsymbol{m}(X_*) + K_{*f}(K_{ff} + \sigma^2I_N)^{-1}K_{f*}(\boldsymbol{y} - \boldsymbol{m}(X)), \...
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### Kernel trick in feature space

I am working on KPCA based fault detection. I have question concerning the kernel trick in the feature space. We all know that the dot product in the feature space is computed using kernel function. I ...
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### Featue map for RBF kenel when dimension is more than 1

i saw the post that write the feature map for RBF kernel but that was when dimension was 1 can anybody help me writing feature map for higher dimensions?
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### How do I interpolate a field that is divergence-free and curl-free at the same time?

A magnetic field is divergence free. At the points where there is no current, and no changing electric field, it is also curl free. There exist divergence-free and curl-free RBF kernels, and I could ...
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### What is the difference between a covariance matrix created by an RBF kernel and a covariance matrix created by

I can't explain something simple to myself and it is probably a matter of vocabulary, I am not sure... If I create and random normal $Z \in \mathbb{R}^{3\times5}$, each row and column has a mean of 0. ...
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### In the broadest sense, what is a "kernel"?

In MCMC sampling methods, a transition kernel, as found in Metropolis(/Hastings) algorithm, is the comparison of the likelihood of the current position and the likelihood of the proposed position. ...