Source code for botorch.models.transforms.utils
#!/usr/bin/env python3
# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
from __future__ import annotations
from functools import wraps
import torch
from torch import Tensor
[docs]
def lognorm_to_norm(mu: Tensor, Cov: Tensor) -> tuple[Tensor, Tensor]:
"""Compute mean and covariance of a MVN from those of the associated log-MVN
If `Y` is log-normal with mean mu_ln and covariance Cov_ln, then
`X ~ N(mu_n, Cov_n)` with
Cov_n_{ij} = log(1 + Cov_ln_{ij} / (mu_ln_{i} * mu_n_{j}))
mu_n_{i} = log(mu_ln_{i}) - 0.5 * log(1 + Cov_ln_{ii} / mu_ln_{i}**2)
Args:
mu: A `batch_shape x n` mean vector of the log-Normal distribution.
Cov: A `batch_shape x n x n` covariance matrix of the log-Normal
distribution.
Returns:
A two-tuple containing:
- The `batch_shape x n` mean vector of the Normal distribution
- The `batch_shape x n x n` covariance matrix of the Normal distribution
"""
Cov_n = torch.log1p(Cov / (mu.unsqueeze(-1) * mu.unsqueeze(-2)))
mu_n = torch.log(mu) - 0.5 * torch.diagonal(Cov_n, dim1=-1, dim2=-2)
return mu_n, Cov_n
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def norm_to_lognorm(mu: Tensor, Cov: Tensor) -> tuple[Tensor, Tensor]:
"""Compute mean and covariance of a log-MVN from its MVN sufficient statistics
If `X ~ N(mu, Cov)` and `Y = exp(X)`, then `Y` is log-normal with
mu_ln_{i} = exp(mu_{i} + 0.5 * Cov_{ii})
Cov_ln_{ij} = exp(mu_{i} + mu_{j} + 0.5 * (Cov_{ii} + Cov_{jj})) *
(exp(Cov_{ij}) - 1)
Args:
mu: A `batch_shape x n` mean vector of the Normal distribution.
Cov: A `batch_shape x n x n` covariance matrix of the Normal distribution.
Returns:
A two-tuple containing:
- The `batch_shape x n` mean vector of the log-Normal distribution.
- The `batch_shape x n x n` covariance matrix of the log-Normal
distribution.
"""
diag = torch.diagonal(Cov, dim1=-1, dim2=-2)
b = mu + 0.5 * diag
mu_ln = torch.exp(b)
Cov_ln = torch.special.expm1(Cov) * torch.exp(b.unsqueeze(-1) + b.unsqueeze(-2))
return mu_ln, Cov_ln
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def norm_to_lognorm_mean(mu: Tensor, var: Tensor) -> Tensor:
"""Compute mean of a log-MVN from its MVN marginals
Args:
mu: A `batch_shape x n` mean vector of the Normal distribution.
var: A `batch_shape x n` variance vectorof the Normal distribution.
Returns:
The `batch_shape x n` mean vector of the log-Normal distribution.
"""
return torch.exp(mu + 0.5 * var)
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def norm_to_lognorm_variance(mu: Tensor, var: Tensor) -> Tensor:
"""Compute variance of a log-MVN from its MVN marginals
Args:
mu: A `batch_shape x n` mean vector of the Normal distribution.
var: A `batch_shape x n` variance vectorof the Normal distribution.
Returns:
The `batch_shape x n` variance vector of the log-Normal distribution.
"""
b = mu + 0.5 * var
return torch.special.expm1(var) * torch.exp(2 * b)
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def expand_and_copy_tensor(X: Tensor, batch_shape: torch.Size) -> Tensor:
r"""Expand and copy X according to batch_shape.
Args:
X: A `input_batch_shape x n x d`-dim tensor of inputs.
batch_shape: The new batch shape.
Returns:
A `new_batch_shape x n x d`-dim tensor of inputs, where `new_batch_shape`
is `input_batch_shape` against `batch_shape`.
"""
try:
batch_shape = torch.broadcast_shapes(X.shape[:-2], batch_shape)
except RuntimeError:
raise RuntimeError(
f"Provided batch shape ({batch_shape}) and input batch shape "
f"({X.shape[:-2]}) are not broadcastable."
)
expand_shape = batch_shape + X.shape[-2:]
return X.expand(expand_shape).clone()
