Class Linear

gpflow/kernels/linears.py:25–68

The linear kernel. Functions drawn from a GP with this kernel are linear, i.e. f(x) = cx. The kernel equation is k(x, y) = σ²xy where σ² is the variance parameter.

class Linear(Kernel):
    """
    The linear kernel. Functions drawn from a GP with this kernel are linear, i.e. f(x) = cx.
    The kernel equation is

        k(x, y) = σ²xy

    where σ² is the variance parameter.
    """

    @check_shapes(
        "variance: [broadcast n_active_dims]",
    )
    def __init__(
        self, variance: TensorType = 1.0, active_dims: Optional[ActiveDims] = None
    ) -> None:
        """
        :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 active_dims: a slice or list specifying which columns of X are used
        """
        super().__init__(active_dims)
        self.variance = Parameter(variance, transform=positive())
        self._validate_ard_active_dims(self.variance)

    @property
    def ard(self) -> bool:
        """
        Whether ARD behaviour is active.
        """
        ndims: int = self.variance.shape.ndims
        return ndims > 0

    @inherit_check_shapes
    def K(self, X: TensorType, X2: Optional[TensorType] = None) -> tf.Tensor:
        if X2 is None:
            return tf.matmul(X * self.variance, X, transpose_b=True)
        else:
            return tf.tensordot(X * self.variance, X2, [[-1], [-1]])

    @inherit_check_shapes
    def K_diag(self, X: TensorType) -> tf.Tensor:
        return tf.reduce_sum(tf.square(X) * self.variance, axis=-1)


class Polynomial(Linear):