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Table 1 Kernel functions, k(x1,x2)

From: A method for efficient Bayesian optimization of self-assembly systems from scattering data

1. Matern 3/2 (ARD): \(\sigma ^{2}(1+\sqrt {3}\sqrt {r}) * exp[-\sqrt {3}\sqrt {r}]\)
2. Matern 5/2 (ARD): \(\sigma ^{2}(1+\sqrt {5}\sqrt {r}+(5r)/3) * exp[-\sqrt {5}\sqrt {r}]\)
3. Rational Quadratic (ARD): σ2(1+r/(2α)α
4. Rational Quadratic (ISO): σ2(1+s/(2α)α
5. Gabor (ARD): \(h(x_{1} \!\,-\, x_{2}); h(t) \,=\, exp[\,-\,\sum \!((t.^{2})./(diag(P.^{2})]*cos[\!2\pi \!\sum \!(t./p)]\)
6. Neural Network: \(\sigma ^{2} \arcsin {\left [x_{1}^{T}P x_{2} / \sqrt {\left (1 + x_{1}^{T}P x_{2}\right)*\left (1 + x_{1}^{T}P x_{2} \right) }\right ]} \)
7. Square Exponential (ARD): σ2exp[−r/2]
r=(x1x2)TP−1(x1x2);s=(x1x2)T(I)−1(x1x2)
P is the diagonal matrix of ARD lengthscale hyperparameters.
is a scalar lengthscale hyperparameter; I is the unit matrix.
α is a shape hyperparameter for the rational quadratic kernel.
p is a vector of period hyperparameters.