gluonts.mx.distribution.lowrank_multivariate_gaussian module#
- class gluonts.mx.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: Optional[Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]] = None)[source]#
Bases:
gluonts.mx.distribution.distribution.Distribution
Multivariate Gaussian distribution, with covariance matrix parametrized as the sum of a diagonal matrix and a low-rank matrix.
\[\Sigma = D + W W^T\]When W = None the covariance matrix is just diagonal.
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) Optional; if not provided, the covariance matrix is just diagonal.
- property F#
- arg_names: Tuple#
- property batch_shape: Tuple#
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: int#
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: Tuple#
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.
- classmethod fit(F, samples: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], rank: int = 0) gluonts.mx.distribution.distribution.Distribution [source]#
Returns an instance of LowrankMultivariateGaussian after fitting parameters to the given data. Only the special case of rank = 0 is supported at the moment.
- Parameters
F –
samples – Tensor of shape (num_samples, batch_size, seq_len, target_dim)
rank – Rank of W
- Return type
Distribution instance of type LowrankMultivariateGaussian.
- 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: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]#
Tensor containing the mean of the distribution.
- sample_rep(num_samples: typing.Optional[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.
- Return type
tensor with shape (num_samples, …, dim)
- property variance: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]#
Tensor containing the variance of the distribution.
- class gluonts.mx.distribution.lowrank_multivariate_gaussian.LowrankMultivariateGaussianOutput(dim: int, rank: int, sigma_init: float = 1.0, sigma_minimum: float = 0.001)[source]#
Bases:
gluonts.mx.distribution.distribution_output.DistributionOutput
- args_dim: Dict[str, int]#
- distr_cls: type#
- distribution(distr_args, loc=None, scale=None, **kwargs) 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, mu_vector, D_vector, W_vector=None)[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
- property event_shape: Tuple#
Shape of each individual event contemplated by the distributions that this object constructs.
- get_args_proj(prefix: Optional[str] = None) gluonts.mx.distribution.distribution_output.ArgProj [source]#
- gluonts.mx.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)) –
- Return type
the capacitance matrix \(I + W^T D^{-1} W\)
- gluonts.mx.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.mx.distribution.lowrank_multivariate_gaussian.lowrank_log_likelihood(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.mx.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)