# Kernel warping

A nonlinear way of transforming stationary kernels into non-stationary ones by transforming their inputs .

This is of interest in the context of composing kernels to have known desirable properties by known transforms, and also learning (somwhat) arbitrary transforms to attain stationarity.

## Stationary reducible kernels

The main idea is to find a new feature space where stationarity or local stationarity can be achieved.

summarises:

We say that a nonstationary kernel $$K(\mathbf{x}, \mathbf{z})$$ is stationary reducible if there exist a bijective deformation $$\Phi$$ such that: $K(\mathbf{x}, \mathbf{z})=K_{S}^{*}(\mathbf{\Phi}(\mathbf{x})-\mathbf{\Phi}(\mathbf{z}))$ where $$K_{S}^{*}$$ is a stationary kernel.

## References

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