gpflux.architectures.constant_input_dim_deep_gp

This module provides build_constant_input_dim_deep_gp() to build a Deep GP of arbitrary depth where each hidden layer has the same input dimensionality as the data.

Module Contents

class Config

The configuration used by build_constant_input_dim_deep_gp().

num_inducing: int

The number of inducing variables, M. The Deep GP uses the same number of inducing variables in each layer.

inner_layer_qsqrt_factor: float

A multiplicative factor used to rescale the hidden layers’ q_sqrt. Typically this value is chosen to be small (e.g., 1e-5) to reduce noise at the start of training.

likelihood_noise_variance: float

The variance of the Gaussian likelihood that is used by the Deep GP.

whiten: bool = True

Determines the parameterisation of the inducing variables. If True, :math:p(u) = N(0, I), otherwise :math:p(u) = N(0, K_{uu}). .. seealso:: gpflux.layers.GPLayer.whiten

_construct_kernel(input_dim: int, is_last_layer: bool) → gpflow.kernels.SquaredExponential

Return a gpflow.kernels.SquaredExponential kernel with ARD lengthscales set to 2 and a small kernel variance of 1e-6 if the kernel is part of a hidden layer; otherwise, the kernel variance is set to 1.0.

Parameters:

• input_dim – The input dimensionality of the layer.

• is_last_layer – Whether the kernel is part of the last layer in the Deep GP.

build_constant_input_dim_deep_gp(X: numpy.ndarray, num_layers: int, config: Config) → gpflux.models.DeepGP

Build a Deep GP consisting of num_layers GPLayers. All the hidden layers have the same input dimension as the data, that is, X.shape[1].

The architecture is largely based on Salimbeni and Deisenroth [SD17], with the most notable difference being that we keep the hidden dimension equal to the input dimensionality of the data.

Note

This architecture might be slow for high-dimensional data.

Note

This architecture assumes a Gaussian likelihood for regression tasks. Specify a different likelihood for performing other tasks such as classification.

Parameters:

• X – The training input data, used to retrieve the number of datapoints and the input dimension and to initialise the inducing point locations using k-means. A tensor of rank two with the dimensions [num_data, input_dim].

• num_layers – The number of layers in the Deep GP.

• config – The configuration for (hyper)parameters. See Config for details.