gluonts.mx.block.quantile_output module#

class gluonts.mx.block.quantile_output.IncrementalDenseLayerProjection(num_outputs: int, **kwargs)[source]#

Bases: mxnet.gluon.block.HybridBlock

A dense layer that outputs non-decreasing values.

Parameters

num_outputs – number of outputs of the layer.

hybrid_forward(F, x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]#

Overrides to construct symbolic graph for this Block.

Parameters

  • x (Symbol or NDArray) – The first input tensor.

  • *args (list of Symbol or list of NDArray) – Additional input tensors.

class gluonts.mx.block.quantile_output.IncrementalQuantileOutput(quantiles: List[float], quantile_weights: Optional[List[float]] = None)[source]#

Bases: gluonts.mx.block.quantile_output.QuantileOutput

Output layer using a quantile loss and projection layer to connect the quantile output to the network.

Differently from QuantileOutput, this class enforces the correct order relation between quantiles: this is done by parametrizing the increments between quantiles instead of the quantiles directly.

Parameters

  • quantiles – list of quantiles to compute loss over.

  • quantile_weights – weights of the quantiles.

get_loss() → mxnet.gluon.block.HybridBlock[source]#
Returns

constructs quantile loss object.

Return type

nn.HybridBlock

get_quantile_proj(**kwargs) → mxnet.gluon.block.HybridBlock[source]#
Returns

constructs projection parameter object.

Return type

nn.HybridBlock

class gluonts.mx.block.quantile_output.QuantileLoss(quantiles: List[float], quantile_weights: Optional[List[float]] = None, weight: Optional[float] = None, batch_axis: int = 0, **kwargs)[source]#

Bases: mxnet.gluon.loss.Loss

static compute_quantile_loss(F, y_true: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], y_pred_p: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], p: float) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]#

Compute the quantile loss of the given quantile.

Parameters

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

  • y_true – ground truth values to compute the loss against.

  • y_pred_p – predicted target quantile, same shape as y_true.

  • p – quantile error to compute the loss.

Returns

quantile loss, shape: (N1 x N2 x … x Nk x 1)

Return type

Tensor

hybrid_forward(F, y_true: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], y_pred: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], sample_weight=None)[source]#

Compute the weighted sum of quantile losses.

Parameters

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

  • y_true – ground truth values, shape (N1 x N2 x … x Nk)

  • y_pred – predicted target, shape (N1 x N2 x … x Nk x num_quantiles)

  • sample_weight – sample weights

Returns

weighted sum of the quantile losses, shape N1 x N1 x … Nk

Return type

Tensor

class gluonts.mx.block.quantile_output.QuantileOutput(quantiles: List[float], quantile_weights: Optional[List[float]] = None)[source]#

Bases: object

Output layer using a quantile loss and projection layer to connect the quantile output to the network.

Parameters

  • quantiles – list of quantiles to compute loss over.

  • quantile_weights – weights of the quantiles.

get_loss() → mxnet.gluon.block.HybridBlock[source]#
Returns

constructs quantile loss object.

Return type

nn.HybridBlock

get_quantile_proj(**kwargs) → mxnet.gluon.block.HybridBlock[source]#
property quantiles: List[float]#
gluonts.mx.block.quantile_output.crps_weights_pwl(quantile_levels: List[float]) → List[float][source]#

Compute the quantile loss weights making mean quantile loss equal to CRPS under linear interpolation assumption.

Quantile levels are assumed to be sorted in increasing order.

Under the assumption of linear interpolation

\[CRPS = sum_{i=0}^{n-1} 0.5 * (q_{i+1}-q_{i}) * (z_{i+1}+z_{i})\]

where \(z_i\) is the i-th quantile prediction \(q_i\). The inner terms cancel due to the telescoping sum property and we obtain

\[CRPS = sum_{i=1}^n w_i z_i\]

with the weights \(w_i = (q_{i+1}-q_{i-1})/2\) for \(i = 1, ..., n-1\), \(w_0 = (q_1-q_0)/2\) and \(w_n = (w_n - w_{n-1})/2\).

gluonts.mx.block.quantile_output.uniform_weights(objects: list) → List[float][source]#

Return uniform weights for a list of objects.

>>> uniform_weights(["a", "b", "c", "d"])
[0.25, 0.25, 0.25, 0.25]
Parameters

objects – Objects that need to be weighted.

Returns

List of weights.

Return type

List[float]