Idris2Doc : Model.Kernel

Model.Kernel

Kernel functions, as used in Gaussian processes.

Definitions

0Kernel : (0_ : Shape) ->Type
  A `Kernel` function maps pairs of points in a feature space to the covariance between those two
points in some target space.

@features The shape of the feature domain.

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rbf : Tensor [] F64->Kernel [Sd]
  The radial basis function, or squared exponential kernel. This is a stationary kernel with form

(\mathbf x_i, \mathbf x_j) \mapsto \exp \left(- \frac{r^2}{2l^2} \right)

where `r^2 = (\mathbf x_i - \mathbf x_j)^ \intercal (\mathbf x_i - \mathbf x_j)` and the
length scale `l > 0`.

Two points that are close in feature space will be more tightly correlated than points that
are further apart. The distance over which the correlation reduces is given by the length
scale `l`. Smaller length scales result in faster-varying target values.

@lengthScale The length scale `l`.

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matern52 : Tensor [] F64->Tensor [] F64->Kernel [Sd]
  The Matern kernel for parameter 5/2. This is a stationary kernel with form

(\mathbf x_i, \mathbf x_j) \mapsto \sigma^2 \left(
1 + \frac{\sqrt{5}r}{l} + \frac{5 r^2}{3 l^2}
\right) \exp \left( -\frac{\sqrt{5}r}{l} \right)

where `r^2 = (\mathbf x_i - \mathbf x_j)^ \intercal (\mathbf x_i - \mathbf x_j)` and the
length scale `l > 0`.

@amplitude The amplitude `\sigma`.
@length_scale The length scale `l`.

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