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 typing import Tuple

import torch
from gpytorch.utils.broadcasting import _mul_broadcast_shape
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.log(1 + 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
[docs]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.exp(Cov) - 1) * torch.exp(b.unsqueeze(-1) + b.unsqueeze(-2)) return mu_ln, Cov_ln
[docs]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)
[docs]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.exp(var) - 1) * torch.exp(2 * b)
[docs]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 `input_batch_shape x batch_shape x n x d`-dim tensor of inputs """ err_msg = ( f"Provided batch shape ({batch_shape}) and input batch shape " f"({X.shape[:-2]}) are not broadcastable." ) batch_shape = _mul_broadcast_shape(X.shape[:-2], batch_shape, error_msg=err_msg) expand_shape = batch_shape + X.shape[-2:] return X.expand(expand_shape).clone()