Description Usage Arguments Details Value See Also Examples
Construct a radial basis function (A.K.A. squared-exponential) kernel.
1 |
columns |
a string vector giving the names of features on which the kernel acts. These will be used to access columns from a dataframe when the kernel is later used in a GP model. |
sigma |
a positive scalar parameter giving (the square-root of) the overall variance of the kernel |
l |
a positive scalar or vector parameter giving the characteristic lengthscale
of the kernel (how rapidly the covariance decays with difference in the
value of the covariate). Larger values of |
The rbf kernel takes the form:
k_{rbf}(\mathbf{x}, \mathbf{x}') = σ^2 exp≤ft(-\frac{\mathbf{r} ^ 2}{2}\right)
\mathbf{r} = {√{∑\limits_{d=1}^D ≤ft(\frac{(x_d - x_d')}{2l_d^2}\right) ^ 2}}
where \mathbf{x} are the covariates on which the kernel is active, l_d are the characteristic lengthscales for each covariate (column) x_d and σ^2 is the overall variance.
Larger values of l_i correspond to functions in which change less rapidly over the values of the covariates.
A kernel object for which there are a range of associated functions, see kernel
and access
for details.
Other kernel.constructors: composition
,
expo
, iid
, int
,
lin
, mat32
,
mat52
, per
, rq
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