Table Of Contents
Table Of Contents

gluonts.distribution.lowrank_multivariate_gaussian module

class gluonts.distribution.lowrank_multivariate_gaussian.LowrankMultivariateGaussian(dim: int, rank: int, mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], D: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], W: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]

Bases: gluonts.distribution.distribution.Distribution

Multivariate Gaussian distribution, with covariance matrix parametrized as the sum of a diagonal matrix and a low-rank matrix

\[\Sigma = D + W W^T\]

The implementation is strongly inspired from Pytorch: https://github.com/pytorch/pytorch/blob/master/torch/distributions/lowrank_multivariate_normal.py.

Complexity to compute log_prob is \(O(dim * rank + rank^3)\) per element.

Parameters:
  • dim – Dimension of the distribution’s support
  • rank – Rank of W
  • mu – Mean tensor, of shape (…, dim)
  • D – Diagonal term in the covariance matrix, of shape (…, dim)
  • W – Low-rank factor in the covariance matrix, of shape (…, dim, rank)
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.

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.

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
mean

Tensor containing the mean of the distribution.

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

Draw samples from the multivariate Gaussian distribution:

\[s = \mu + D u + W v,\]

where \(u\) and \(v\) are standard normal samples.

Parameters:
  • num_samples – number of samples to be drawn.
  • dtype – Data-type of the samples.
Returns:

Return type:

tensor with shape (num_samples, .., dim)

variance

Tensor containing the variance of the distribution.

class gluonts.distribution.lowrank_multivariate_gaussian.LowrankMultivariateGaussianOutput(dim: int, rank: int)[source]

Bases: gluonts.distribution.distribution_output.DistributionOutput

distribution(distr_args, scale=None, **kwargs) → gluonts.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.
  • scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.
domain_map(F, mu_vector, D_vector, W_vector)[source]
Parameters:
  • F
  • mu_vector – Tensor of shape (…, dim)
  • D_vector – Tensor of shape (…, dim)
  • W_vector – Tensor of shape (…, dim * rank )
Returns:

A tuple containing tensors mu, D, and W, with shapes (…, dim), (…, dim), and (…, dim, rank), respectively.

Return type:

Tuple

event_shape

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

get_args_proj(prefix: Optional[str] = None) → gluonts.distribution.distribution_output.ArgProj[source]
gluonts.distribution.lowrank_multivariate_gaussian.capacitance_tril(F, rank: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], W: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], D: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]
Parameters:
  • F
  • rank
  • W ((.., dim, rank)) –
  • D ((.., dim)) –
Returns:

Return type:

the capacitance matrix \(I + W^T D^{-1} W\)

gluonts.distribution.lowrank_multivariate_gaussian.log_det(F, batch_D: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], batch_capacitance_tril: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]

Uses the matrix determinant lemma.

\[\log|D + W W^T| = \log|C| + \log|D|,\]

where \(C\) is the capacitance matrix \(I + W^T D^{-1} W\), to compute the log determinant.

Parameters:
  • F
  • batch_D
  • batch_capacitance_tril
gluonts.distribution.lowrank_multivariate_gaussian.lowrank_log_likelihood(F, dim: int, rank: int, mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], D: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], W: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]
gluonts.distribution.lowrank_multivariate_gaussian.mahalanobis_distance(F, W: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], D: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], capacitance_tril: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]

Uses the Woodbury matrix identity

\[(W W^T + D)^{-1} = D^{-1} - D^{-1} W C^{-1} W^T D^{-1},\]

where \(C\) is the capacitance matrix \(I + W^T D^{-1} W\), to compute the squared Mahalanobis distance \(x^T (W W^T + D)^{-1} x\).

Parameters:
  • F
  • W – (…, dim, rank)
  • D – (…, dim)
  • capacitance_tril – (…, rank, rank)
  • x – (…, dim)