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Get gradient of PredictorFunction with respect to input?

Posted 1 year ago
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For special forms of the PredictorFunction, there is an analytical formula for the gradient of the predictor wrt the input, x. For example, in a Gaussian Process, the prediction at $x$ is the posterior mean $m(x)$, and it is a linear combination of the kernel used

$$ m(x) = \sum a_{n} * k(x_n, x) $$

Hence, it is possible to obtain analytically the gradient of the mean wrt $x$ by taking a linear combination of the gradient of $k$. I was wondering, is it already implemented in the Wolfram function Predict[] or maybe PredictorFunction[] ? If not, is there an easy way to find the pieces needed? E.g. kernel parameters and kernel used, and possibly its gradient wrt $x$?

Thanks

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