In Gaussian process (GP) regression, predictive mean is
$$ K(X^*,X)[K(X,X)+\sigma^2I]^{-1} \textbf{y}$$
Is there a method to ensure that the predictive mean is convex with respect to the test input $X^*$?
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$\begingroup$ if you plot the predictive mean of a GP, you will see that it is insanely nonconvex. There's been some work on trying to make GPs convex by imposing constraints on the second derivative (and there's even a CV question abt this stats.stackexchange.com/questions/296051/…), but it's quite unwieldy stuff at present (second deriv constraints tout court are hard, and here we have infinitely many of (inequality) them...). Perhaps consider a quadratic response surface instead? $\endgroup$– John MaddenCommented Jul 9 at 16:59
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