Class Polynomial

gpflow/kernels/linears.py:71–112

The Polynomial kernel. Functions drawn from a GP with this kernel are polynomials of degree `d`. The kernel equation is k(x, y) = (σ²xy + γ)ᵈ where: σ² is the variance parameter, γ is the offset parameter, d is the degree parameter.

class Polynomial(Linear):
    """
    The Polynomial kernel. Functions drawn from a GP with this kernel are
    polynomials of degree `d`. The kernel equation is

        k(x, y) = (σ²xy + γ)ᵈ

    where:
    σ² is the variance parameter,
    γ is the offset parameter,
    d is the degree parameter.
    """

    @check_shapes(
        "variance: [broadcast n_active_dims]",
    )
    def __init__(
        self,
        degree: TensorType = 3.0,
        variance: TensorType = 1.0,
        offset: TensorType = 1.0,
        active_dims: Optional[ActiveDims] = None,
    ) -> None:
        """
        :param degree: the degree of the polynomial
        :param variance: the (initial) value for the variance parameter(s),
            to induce ARD behaviour this must be initialised as an array the same
            length as the the number of active dimensions e.g. [1., 1., 1.]
        :param offset: the offset of the polynomial
        :param active_dims: a slice or list specifying which columns of X are used
        """
        super().__init__(variance, active_dims)
        self.degree = degree
        self.offset = Parameter(offset, transform=positive())

    @inherit_check_shapes
    def K(self, X: TensorType, X2: Optional[TensorType] = None) -> tf.Tensor:
        return (super().K(X, X2) + self.offset) ** self.degree

    @inherit_check_shapes
    def K_diag(self, X: TensorType) -> tf.Tensor:
        return (super().K_diag(X) + self.offset) ** self.degree