# gluonts.mx.distribution.gaussian module¶

class gluonts.mx.distribution.gaussian.Gaussian(mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], sigma: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]

Gaussian distribution.

Parameters
• mu – Tensor containing the means, of shape (*batch_shape, *event_shape).

• std – Tensor containing the standard deviations, of shape (*batch_shape, *event_shape).

• F

property F
arg_names = None
property args
property batch_shape

Layout of the set of events contemplated by the distribution.

Invoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.

This property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.

cdf(x)[source]

Returns the value of the cumulative distribution function evaluated at x

property event_dim

Number of event dimensions, i.e., length of the event_shape tuple.

This is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.

property event_shape

Shape of each individual event contemplated by the distribution.

For example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.

Invoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.

This property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.

is_reparameterizable = True
log_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]

Compute the log-density of the distribution at x.

Parameters

x – Tensor of shape (*batch_shape, *event_shape).

Returns

Tensor of shape batch_shape containing the log-density of the distribution for each event in x.

Return type

Tensor

property mean

Tensor containing the mean of the distribution.

quantile(level: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]

Calculates quantiles for the given levels.

Parameters

level – Level values to use for computing the quantiles. level should be a 1d tensor of level values between 0 and 1.

Returns

Quantile values corresponding to the levels passed. The return shape is

(num_levels, …DISTRIBUTION_SHAPE…),

where DISTRIBUTION_SHAPE is the shape of the underlying distribution.

Return type

quantiles

sample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]

Draw samples from the distribution.

If num_samples is given the first dimension of the output will be num_samples.

Parameters
• num_samples – Number of samples to to be drawn.

• dtype – Data-type of the samples.

Returns

A tensor containing samples. This has shape (*batch_shape, *eval_shape) if num_samples = None and (num_samples, *batch_shape, *eval_shape) otherwise.

Return type

Tensor

sample_rep(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]
property stddev

Tensor containing the standard deviation of the distribution.

class gluonts.mx.distribution.gaussian.GaussianOutput[source]
args_dim: Dict[str, int] = {'mu': 1, 'sigma': 1}
distr_cls

alias of Gaussian

classmethod domain_map(F, mu, sigma)[source]

Maps raw tensors to valid arguments for constructing a Gaussian distribution.

Parameters
• F

• mu – Tensor of shape (*batch_shape, 1)

• sigma – Tensor of shape (*batch_shape, 1)

Returns

Two squeezed tensors, of shape (*batch_shape): the first has the same entries as mu and the second has entries mapped to the positive orthant.

Return type

Tuple[Tensor, Tensor]

property event_shape

Shape of each individual event contemplated by the distributions that this object constructs.