# gluonts.mx.distribution.dirichlet module¶

class gluonts.mx.distribution.dirichlet.Dirichlet(alpha: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], float_type: gluonts.core.component.DType = <class 'numpy.float32'>)[source]

Dirichlet distribution, specified by the concentration vector alpha of length d. https://en.wikipedia.org/wiki/Dirichlet_distribution

The Dirichlet distribution is defined on the open (d-1)-simplex, which means that a sample (or observation) x = (x_0,…, x_{d-1}) must satisfy:

sum_k x_k = 1 and for all k, x_k > 0.

Parameters
• alpha – concentration vector, of shape (…, d)

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

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.

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 = False
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.

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

property variance

Tensor containing the variance of the distribution.

class gluonts.mx.distribution.dirichlet.DirichletOutput(dim: int)[source]
distr_cls = None
distribution(distr_args, loc=None, scale=None) → gluonts.mx.distribution.distribution.Distribution[source]

Construct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.

Parameters
• distr_args – Constructor arguments for the underlying Distribution type.

• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.

• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.

domain_map(F, alpha_vector)[source]

Converts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.

property event_shape

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