kernels | R Documentation |

Create and combine Gaussian process kernels (covariance functions) for use in Gaussian process models.

```
bias(variance)
constant(variance)
white(variance)
iid(variance, columns = 1)
rbf(lengthscales, variance, columns = seq_along(lengthscales))
rational_quadratic(
lengthscales,
variance,
alpha,
columns = seq_along(lengthscales)
)
linear(variances, columns = seq_along(variances))
polynomial(variances, offset, degree, columns = seq_along(variances))
expo(lengthscales, variance, columns = seq_along(lengthscales))
mat12(lengthscales, variance, columns = seq_along(lengthscales))
mat32(lengthscales, variance, columns = seq_along(lengthscales))
mat52(lengthscales, variance, columns = seq_along(lengthscales))
cosine(lengthscales, variance, columns = seq_along(lengthscales))
periodic(period, lengthscale, variance)
```

`variance, variances` |
(scalar/vector) the variance of a Gaussian process
prior in all dimensions ( |

`columns` |
(scalar/vector integer, not a greta array) the columns of the data matrix on which this kernel acts. Must have the same dimensions as lengthscale parameters. |

`alpha` |
(scalar) additional parameter in rational quadratic kernel |

`offset` |
(scalar) offset in polynomial kernel |

`degree` |
(scalar) degree of polynomial kernel |

`period` |
(scalar) the period of the Gaussian process |

`lengthscale, lengthscales` |
(scalar/vector) the correlation decay
distance along all dimensions ( |

The kernel constructor functions each return a *function* (of
class `greta_kernel`

) which can be executed on greta arrays to compute
the covariance matrix between points in the space of the Gaussian process.
The `+`

and `*`

operators can be used to combine kernel functions
to create new kernel functions.

Note that `bias`

and `constant`

are identical names for the same
underlying kernel.

`iid`

is equivalent to `bias`

where all entries in `columns`

match (where the absolute euclidean distance is less than
1e-12), and `white`

where they don't; i.e. an independent Gaussian
random effect.

greta kernel with class "greta_kernel"

```
## Not run:
# create a radial basis function kernel on two dimensions
k1 <- rbf(lengthscales = c(0.1, 0.2), variance = 0.6)
# evaluate it on a greta array to get the variance-covariance matrix
x <- greta_array(rnorm(8), dim = c(4, 2))
k1(x)
# non-symmetric covariance between two sets of points
x2 <- greta_array(rnorm(10), dim = c(5, 2))
k1(x, x2)
# create a bias kernel, with the variance as a variable
k2 <- bias(variance = lognormal(0, 1))
# combine two kernels and evaluate
K <- k1 + k2
K(x, x2)
# other kernels
constant(variance = lognormal(0, 1))
white(variance = lognormal(0, 1))
iid(variance = lognormal(0,1))
rational_quadratic(lengthscales = c(0.1, 0.2), alpha = 0.5, variance = 0.6)
linear(variances = 0.1)
polynomial(variances = 0.6, offset = 0.8, degree = 2)
expo(lengthscales = 0.6 ,variance = 0.9)
mat12(lengthscales = 0.5, variance = 0.7)
mat32(lengthscales = 0.4, variance = 0.8)
mat52(lengthscales = 0.3, variance = 0.9)
cosine(lengthscales = 0.68, variance = 0.8)
periodic(period = 0.71, lengthscale = 0.59, variance = 0.2)
## End(Not run)
```

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