gluonts.mx.kernels package

class gluonts.mx.kernels.Kernel

Bases: object

kernel_matrix(x1: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], x2: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])

class gluonts.mx.kernels.KernelOutput

Bases: object

Class to connect a network to a kernel.

static compute_std(F, data: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], axis: int) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]

This function computes the standard deviation of the data along a given axis.

Parameters

• F (ModuleType) – A module that can either refer to the Symbol API or the NDArray API in MXNet.

• data (Tensor) – Data to be used to compute the standard deviation.

• axis (int) – Axis along which to compute the standard deviation.

Returns

The standard deviation of the given data.

Return type

Tensor

get_args_proj(float_type: Type) → mxnet.gluon.block.HybridBlock

kernel(args) → gluonts.mx.kernels._kernel.Kernel

class gluonts.mx.kernels.KernelOutputDict

Bases: gluonts.mx.kernels._kernel_output.KernelOutput

args_dim: Dict[str, int]

domain_map(F, *args: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])

get_args_proj(float_type: typing.Type = <class 'numpy.float32'>) → gluonts.mx.distribution.distribution_output.ArgProj

This method calls the ArgProj block in distribution_output to project from a dense layer to kernel arguments.

Parameters

float_type (Type) – Determines whether to use single or double precision.

Return type

ArgProj

get_num_args() → int

gp_params_scaling(F, past_target: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], past_time_feat: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → tuple

kernel(kernel_args) → gluonts.mx.kernels._kernel.Kernel

Parameters

kernel_args – Variable length argument list.

Returns

Instantiated specified Kernel subclass object.

Return type

gluonts.mx.kernels.Kernel

kernel_cls: type

class gluonts.mx.kernels.PeriodicKernel(amplitude: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], length_scale: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], frequency: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], F=None)

Bases: gluonts.mx.kernels._kernel.Kernel

Computes a covariance matrix based on the Periodic kernel between inputs \(\mathbf{x_1}\) and \(\mathbf{x_2}\): \(k_{\text{Per}}(\mathbf{x_1}, \mathbf{x_2}) = \theta_0 \exp \left (\frac{-2\sin^2(\theta_2 \pi \|\mathbf{x_1} - \mathbf{x_2}\|)} {\theta_1^2} \right)\), where \(\theta_0\) is the amplitude parameter, \(\theta_1\) is the length scale parameter and \(\theta_2\) is the frequency parameter.

kernel_matrix(x1: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], x2: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]

Parameters

• x1 (Tensor) – Feature data of shape (batch_size, history_length, num_features).

• x2 (Tensor) – Feature data of shape (batch_size, history_length, num_features).

Returns

Periodic kernel matrix of shape (batch_size, history_length, history_length).

Return type

Tensor

class gluonts.mx.kernels.PeriodicKernelOutput

Bases: gluonts.mx.kernels._kernel_output.KernelOutputDict

args_dim: Dict[str, int] = {'amplitude': 1, 'frequency': 1, 'length_scale': 1}

classmethod domain_map(F, amplitude, length_scale, frequency)

This function applies the softmax to the Periodic Kernel hyper- parameters.

Parameters

• F – A module that can either refer to the Symbol API or the NDArray API in MXNet.

• amplitude – Periodic kernel amplitude hyper-parameter of shape (batch_size, 1, 1).

• length_scale – Periodic kernel length scale hyper-parameter of of shape (batch_size, 1, 1).

• frequency – Periodic kernel hyper-parameter of shape (batch_size, 1, 1).

Returns

Three GP Periodic kernel hyper-parameters. Each is a Tensor of shape: (batch_size, 1, 1).

Return type

Tuple[Tensor, Tensor, Tensor]

gp_params_scaling(F, past_target: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], past_time_feat: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Tuple[Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]]

This function returns the scales for the GP Periodic Kernel hyper- parameters by using the standard deviations of the past_target and past_time_features.

Parameters

• F (ModuleType) – A module that can either refer to the Symbol API or the NDArray API in MXNet.

• past_target (Tensor) – Training time series values of shape (batch_size, context_length).

• past_time_feat (Tensor) – Training features of shape (batch_size, context_length, num_features).

Returns

Three scaled GP hyper-parameters for the Periodic Kernel and scaled model noise hyper-parameter. Each is a Tensor of shape (batch_size, 1, 1).

Return type

Tuple

kernel_cls

alias of gluonts.mx.kernels._periodic_kernel.PeriodicKernel

class gluonts.mx.kernels.RBFKernel(amplitude: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], length_scale: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], F=None)

Bases: gluonts.mx.kernels._kernel.Kernel

Computes a covariance matrix based on the RBF (squared exponential) kernel between inputs \(\mathbf{x_1}\) and \(\mathbf{x_2}\): \(k_{\text{RBF}}(\mathbf{x_1}, \mathbf{x_2}) = \theta_0 \exp \left ( -\frac{\|\mathbf{x_1} - \mathbf{x_2}\|^2} {2\theta_1^2} \right)\), where \(\theta_0\) is the amplitude parameter and \(\theta_1\) is the length scale parameter.

kernel_matrix(x1: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], x2: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]

Parameters

• x1 (Tensor) – Feature data of shape (batch_size, history_length, num_features).

• x2 (Tensor) – Feature data of shape (batch_size, history_length, num_features).

Returns

RBF kernel matrix of shape (batch_size, history_length, history_length).

Return type

Tensor

class gluonts.mx.kernels.RBFKernelOutput

Bases: gluonts.mx.kernels._kernel_output.KernelOutputDict

args_dim: Dict[str, int] = {'amplitude': 1, 'length_scale': 1}

domain_map(F, amplitude, length_scale)

This function applies the softmax to the RBF Kernel hyper-parameters.

Parameters

• F – A module that can either refer to the Symbol API or the NDArray API in MXNet.

• amplitude – RBF kernel amplitude hyper-parameter of shape (batch_size, 1, 1).

• length_scale – RBF kernel length scale hyper-parameter of of shape (batch_size, 1, 1).

Returns

Two GP RBF kernel hyper-parameters. Each is a Tensor of shape: (batch_size, 1, 1).

Return type

Tuple[Tensor, Tenspr]

gp_params_scaling(F, past_target: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], past_time_feat: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Tuple[Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]]

This function returns the scales for the GP RBF Kernel hyper- parameters by using the standard deviations of the past_target and past_time_features.

Parameters

• F – A module that can either refer to the Symbol API or the NDArray API in MXNet.

• past_target – Training time series values of shape (batch_size, context_length).

• past_time_feat – Training features of shape (batch_size, context_length, num_features).

Returns

Two scaled GP hyper-parameters for the RBF Kernel and scaled model noise hyper-parameter. Each is a Tensor of shape (batch_size, 1, 1).

Return type

Tuple

kernel_cls

alias of gluonts.mx.kernels._rbf_kernel.RBFKernel