class revrand.basis_functions.SigmoidalBasis(centres, lenscale=Parameter(value=1.0, bounds=Positive(upper=None), shape=()), regularizer=None)

Sigmoidal Basis.

\[\phi(\mathbf{X}) = \sigma \left( \frac{\|\mathbf{X} - \mathbf{C}\|}{l} \right)\]

where \(\mathbf{C}\) are sigmoidal basis centres, \(l\) is a length scale and \(\sigma\) is the logistic sigmoid function defined by

\[\sigma(a) = \frac{1}{1+e^{-a}}.\]
  • centres (ndarray) – array of shape (Dxd) where D is the number of centres for the bases, and d is the dimensionality of X.
  • lenscale (Parameter, optional) – A scalar parameter to bound and initialise the length scales for optimization.
  • regularizer (None, Parameter, optional) – The (initial) value of the regularizer/prior variance to apply to the regression weights of this basis function. The Parameter object must have a scalar value. If it is not set, it will take on a default value of Parameter(gamma(1.), Positive()).
__init__(centres, lenscale=Parameter(value=1.0, bounds=Positive(upper=None), shape=()), regularizer=None)

See this class’s docstring.


__init__(centres[, lenscale, bounds, shape, ...]) See this class’s docstring.
get_dim(X) Get the output dimensionality of this basis.
grad(X[, lenscale]) Get the gradients of this basis w.r.t. the length scale.
params_values() Get a list of the Parameter values if they have a value.
regularizer_diagonal(X[, regularizer]) Get the diagonal of the prior variance on the weights (regularizer).
transform(X[, lenscale]) Apply the sigmoid basis function to X.


params Get this basis’ Parameter types.
regularizer Get the Parameter value of this basis’ regularizer.