def fit(cls, F, samples: Tensor, rank: int = 0) -> Distribution:
"""
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
Returns
-------
Distribution instance of type `LowrankMultivariateGaussian`.
"""
# TODO: Implement it for the general case: `rank` > 0
assert rank == 0, "Fit is not only implemented for the case rank = 0!"
# Compute mean and variances
mu = samples.mean(axis=0)
var = F.square(samples - samples.mean(axis=0)).mean(axis=0)
return cls(dim=samples.shape[-1], rank=rank, mu=mu, D=var)
def weighted_average(
F, x: Tensor, weights: Optional[Tensor] = None, axis: Optional[int] = None
) -> Tensor:
"""
Computes the weighted average of a given tensor across a given axis, masking values associated with weight zero,
meaning instead of `nan * 0 = nan` you will get `0 * 0 = 0`.
Parameters
----------
F
The function space to use.
x
Input tensor, of which the average must be computed.
weights
Weights tensor, of the same shape as `x`.
axis
The axis along which to average `x`
Returns
-------
Tensor:
The tensor with values averaged along the specified `axis`.
"""
if weights is not None:
weighted_tensor = F.where(
condition=weights, x=x * weights, y=F.zeros_like(x)
)
sum_weights = F.maximum(1.0, weights.sum(axis=axis))
return weighted_tensor.sum(axis=axis) / sum_weights
else:
return x.mean(axis=axis)
def weighted_average(
F,
x: Tensor,
weights: Optional[Tensor] = None,
axis: Optional[int] = None,
include_zeros_in_denominator=False,
) -> Tensor:
"""
Computes the weighted average of a given tensor across a given axis,
masking values associated with weight zero,
meaning instead of `nan * 0 = nan` you will get `0 * 0 = 0`.
Parameters
----------
F
The function space to use.
x
Input tensor, of which the average must be computed.
weights
Weights tensor, of the same shape as `x`.
axis
The axis along which to average `x`
include_zeros_in_denominator
Include zeros in the denominator. Can be useful for sparse time series
because the loss can be dominated by few observed examples.
Returns
-------
Tensor:
The tensor with values averaged along the specified `axis`.
"""
if weights is not None:
weighted_tensor = F.where(
condition=weights, x=x * weights, y=F.zeros_like(x)
)
if include_zeros_in_denominator:
sum_weights = F.maximum(1.0, F.ones_like(weights).sum(axis=axis))
else:
sum_weights = F.maximum(1.0, weights.sum(axis=axis))
return weighted_tensor.sum(axis=axis) / sum_weights
else:
return x.mean(axis=axis)
