mxfusion.components.distributions.gp.kernels.stationary

Members

class mxfusion.components.distributions.gp.kernels.stationary.StationaryKernel(input_dim, ARD=False, variance=1.0, lengthscale=1.0, name='stationary', active_dims=None, dtype=None, ctx=None)

Bases: mxfusion.components.distributions.gp.kernels.kernel.NativeKernel

The base class for Stationary kernels (covariance functions).

Stationary kernels (covariance functions). Stationary covariance function depend only on r^2, where r^2 is defined as .. math:

r2(x, x') = \sum_{q=1}^Q (x_q - x'_q)^2

The covariance function k(x, x’ can then be written k(r).

In this implementation, r is scaled by the lengthscales parameter(s): .. math:

r2(x, x') = \sum_{q=1}^Q \frac{(x_q - x'_q)^2}{\ell_q^2}.

By default, there’s only one lengthscale: separate lengthscales for each dimension can be enables by setting ARD=True.

Parameters:

• input_dim (int) – the number of dimensions of the kernel. (The total number of active dimensions).
• ARD – a binary switch for Automatic Relevance Determination (ARD). If true, the squared distance is divided

by a lengthscale for individual dimensions. :type ARD: boolean :param variance: the initial value for the variance parameter (scalar), which scales the whole covariance matrix. :type variance: float or MXNet NDArray :param lengthscale: the initial value for the lengthscale parameter. :type lengthscale: float or MXNet NDArray :param name: the name of the kernel. The name is used to access kernel parameters. :type name: str :param active_dims: The dimensions of the inputs that are taken for the covariance matrix computation. (default: None, taking all the dimensions). :type active_dims: [int] or None :param dtype: the data type for float point numbers. :type dtype: numpy.float32 or numpy.float64 :param ctx: the mxnet context (default: None/current context). :type ctx: None or mxnet.cpu or mxnet.gpu

replicate_self(attribute_map=None)

The copy constructor for a kernel.