# revrand.basis_functions.SigmoidalBasis¶

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

$\sigma(a) = \frac{1}{1+e^{-a}}.$
Parameters: 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.

Methods

 __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.

Attributes

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