#!/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.
r"""
Posterior module to be used with GPyTorch models.
"""
from __future__ import annotations
from contextlib import ExitStack
from typing import Optional, Tuple, TYPE_CHECKING, Union
import torch
from botorch.exceptions.errors import BotorchTensorDimensionError
from botorch.posteriors.base_samples import _reshape_base_samples_non_interleaved
from botorch.posteriors.torch import TorchPosterior
from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
from linear_operator import settings as linop_settings
from linear_operator.operators import (
BlockDiagLinearOperator,
DenseLinearOperator,
LinearOperator,
SumLinearOperator,
)
from torch import Tensor
from torch.distributions import Normal
if TYPE_CHECKING:
from botorch.posteriors.posterior_list import PosteriorList # pragma: no cover
[docs]
class GPyTorchPosterior(TorchPosterior):
r"""A posterior based on GPyTorch's multi-variate Normal distributions."""
distribution: MultivariateNormal
def __init__(self, distribution: MultivariateNormal) -> None:
r"""A posterior based on GPyTorch's multi-variate Normal distributions.
Args:
distribution: A GPyTorch MultivariateNormal (single-output case) or
MultitaskMultivariateNormal (multi-output case).
"""
super().__init__(distribution=distribution)
self._is_mt = isinstance(distribution, MultitaskMultivariateNormal)
@property
def mvn(self) -> MultivariateNormal:
r"""Expose the distribution as a backwards-compatible attribute."""
return self.distribution
@property
def base_sample_shape(self) -> torch.Size:
r"""The shape of a base sample used for constructing posterior samples."""
return self.distribution.batch_shape + self.distribution.base_sample_shape
@property
def batch_range(self) -> Tuple[int, int]:
r"""The t-batch range.
This is used in samplers to identify the t-batch component of the
`base_sample_shape`. The base samples are expanded over the t-batches to
provide consistency in the acquisition values, i.e., to ensure that a
candidate produces same value regardless of its position on the t-batch.
"""
if self._is_mt:
return (0, -2)
else:
return (0, -1)
def _extended_shape(
self, sample_shape: torch.Size = torch.Size() # noqa: B008
) -> torch.Size:
r"""Returns the shape of the samples produced by the posterior with
the given `sample_shape`.
"""
base_shape = self.distribution.batch_shape + self.distribution.event_shape
if not self._is_mt:
base_shape += torch.Size([1])
return sample_shape + base_shape
[docs]
def rsample_from_base_samples(
self,
sample_shape: torch.Size,
base_samples: Tensor,
) -> Tensor:
r"""Sample from the posterior (with gradients) using base samples.
This is intended to be used with a sampler that produces the corresponding base
samples, and enables acquisition optimization via Sample Average Approximation.
Args:
sample_shape: A `torch.Size` object specifying the sample shape. To
draw `n` samples, set to `torch.Size([n])`. To draw `b` batches
of `n` samples each, set to `torch.Size([b, n])`.
base_samples: A Tensor of `N(0, I)` base samples of shape
`sample_shape x base_sample_shape`, typically obtained from
a `Sampler`. This is used for deterministic optimization.
Returns:
Samples from the posterior, a tensor of shape
`self._extended_shape(sample_shape=sample_shape)`.
"""
if base_samples.shape[: len(sample_shape)] != sample_shape:
raise RuntimeError(
"`sample_shape` disagrees with shape of `base_samples`. "
f"Got {sample_shape=} and {base_samples.shape=}."
)
if self._is_mt:
base_samples = _reshape_base_samples_non_interleaved(
mvn=self.distribution,
base_samples=base_samples,
sample_shape=sample_shape,
)
with ExitStack() as es:
if linop_settings._fast_covar_root_decomposition.is_default():
es.enter_context(linop_settings._fast_covar_root_decomposition(False))
samples = self.distribution.rsample(
sample_shape=sample_shape, base_samples=base_samples
)
if not self._is_mt:
samples = samples.unsqueeze(-1)
return samples
[docs]
def rsample(self, sample_shape: Optional[torch.Size] = None) -> Tensor:
r"""Sample from the posterior (with gradients).
Args:
sample_shape: A `torch.Size` object specifying the sample shape. To
draw `n` samples, set to `torch.Size([n])`. To draw `b` batches
of `n` samples each, set to `torch.Size([b, n])`.
Returns:
Samples from the posterior, a tensor of shape
`self._extended_shape(sample_shape=sample_shape)`.
"""
if sample_shape is None:
sample_shape = torch.Size([1])
with ExitStack() as es:
if linop_settings._fast_covar_root_decomposition.is_default():
es.enter_context(linop_settings._fast_covar_root_decomposition(False))
samples = self.distribution.rsample(sample_shape=sample_shape)
# make sure there always is an output dimension
if not self._is_mt:
samples = samples.unsqueeze(-1)
return samples
@property
def mean(self) -> Tensor:
r"""The posterior mean."""
mean = self.distribution.mean
if not self._is_mt:
mean = mean.unsqueeze(-1)
return mean
@property
def variance(self) -> Tensor:
r"""The posterior variance."""
variance = self.distribution.variance
if not self._is_mt:
variance = variance.unsqueeze(-1)
return variance
[docs]
def quantile(self, value: Tensor) -> Tensor:
r"""Compute the quantiles of the marginal distributions."""
if value.numel() > 1:
return torch.stack([self.quantile(v) for v in value], dim=0)
marginal = Normal(loc=self.mean, scale=self.variance.sqrt())
return marginal.icdf(value)
[docs]
def density(self, value: Tensor) -> Tensor:
r"""The probability density of the marginal distributions."""
if value.numel() > 1:
return torch.stack([self.density(v) for v in value], dim=0)
marginal = Normal(loc=self.mean, scale=self.variance.sqrt())
return marginal.log_prob(value).exp()
def _validate_scalarize_inputs(weights: Tensor, m: int) -> None:
if weights.ndim > 1:
raise BotorchTensorDimensionError("`weights` must be one-dimensional")
if m != weights.size(0):
raise RuntimeError(
f"Output shape not equal to that of weights. Output shape is {m} and "
f"weights are {weights.shape}"
)
[docs]
def scalarize_posterior_gpytorch(
posterior: GPyTorchPosterior,
weights: Tensor,
offset: float = 0.0,
) -> Tuple[Tensor, Union[Tensor, LinearOperator]]:
r"""Helper function for `scalarize_posterior`, producing a mean and
variance.
This mean and variance are consumed by `scalarize_posterior` to produce
a `GPyTorchPosterior`.
Args:
posterior: The posterior over `m` outcomes to be scalarized.
Supports `t`-batching.
weights: A tensor of weights of size `m`.
offset: The offset of the affine transformation.
Returns:
The transformed (single-output) posterior. If the input posterior has
mean `mu` and covariance matrix `Sigma`, this posterior has mean
`weights^T * mu` and variance `weights^T Sigma w`.
Example:
Example for a model with two outcomes:
>>> X = torch.rand(1, 2)
>>> posterior = model.posterior(X)
>>> weights = torch.tensor([0.5, 0.25])
>>> mean, cov = scalarize_posterior_gpytorch(posterior, weights=weights)
>>> mvn = MultivariateNormal(mean, cov)
>>> new_posterior = GPyTorchPosterior
"""
mean = posterior.mean
q, m = mean.shape[-2:]
_validate_scalarize_inputs(weights, m)
batch_shape = mean.shape[:-2]
mvn = posterior.distribution
cov = mvn.lazy_covariance_matrix if mvn.islazy else mvn.covariance_matrix
if m == 1: # just scaling, no scalarization necessary
new_mean = offset + (weights[0] * mean).view(*batch_shape, q)
new_cov = weights[0] ** 2 * cov
return new_mean, new_cov
new_mean = offset + (mean @ weights).view(*batch_shape, q)
if q == 1:
new_cov = weights.unsqueeze(-2) @ (cov @ weights.unsqueeze(-1))
else:
# we need to handle potentially different representations of the multi-task mvn
if mvn._interleaved:
w_cov = weights.repeat(q).unsqueeze(0)
sum_shape = batch_shape + torch.Size([q, m, q, m])
sum_dims = (-1, -2)
else:
# special-case the independent setting
if isinstance(cov, BlockDiagLinearOperator):
new_cov = SumLinearOperator(
*[
cov.base_linear_op[..., i, :, :] * weights[i].pow(2)
for i in range(cov.base_linear_op.size(-3))
]
)
return new_mean, new_cov
w_cov = torch.repeat_interleave(weights, q).unsqueeze(0)
sum_shape = batch_shape + torch.Size([m, q, m, q])
sum_dims = (-2, -3)
cov_scaled = w_cov * cov * w_cov.transpose(-1, -2)
# TODO: Do not instantiate full covariance for LinearOperators
# (ideally we simplify this in GPyTorch:
# https://github.com/cornellius-gp/gpytorch/issues/1055)
if isinstance(cov_scaled, LinearOperator):
cov_scaled = cov_scaled.to_dense()
new_cov = cov_scaled.view(sum_shape).sum(dim=sum_dims[0]).sum(dim=sum_dims[1])
new_cov = DenseLinearOperator(new_cov)
return new_mean, new_cov
[docs]
def scalarize_posterior(
posterior: Union[GPyTorchPosterior, PosteriorList],
weights: Tensor,
offset: float = 0.0,
) -> GPyTorchPosterior:
r"""Affine transformation of a multi-output posterior.
Args:
posterior: The posterior over `m` outcomes to be scalarized.
Supports `t`-batching. Can be either a `GPyTorchPosterior`,
or a `PosteriorList` that contains GPyTorchPosteriors all with q=1.
weights: A tensor of weights of size `m`.
offset: The offset of the affine transformation.
Returns:
The transformed (single-output) posterior. If the input posterior has
mean `mu` and covariance matrix `Sigma`, this posterior has mean
`weights^T * mu` and variance `weights^T Sigma w`.
Example:
Example for a model with two outcomes:
>>> X = torch.rand(1, 2)
>>> posterior = model.posterior(X)
>>> weights = torch.tensor([0.5, 0.25])
>>> new_posterior = scalarize_posterior(posterior, weights=weights)
"""
# GPyTorchPosterior case
if hasattr(posterior, "distribution"):
mean, cov = scalarize_posterior_gpytorch(posterior, weights, offset)
mvn = MultivariateNormal(mean, cov)
return GPyTorchPosterior(mvn)
# PosteriorList case
if not hasattr(posterior, "posteriors"):
raise NotImplementedError(
"scalarize_posterior only works with a posterior that has an attribute "
"`distribution`, such as a GPyTorchPosterior, or a posterior that contains "
"sub-posteriors in an attribute `posteriors`, as in a PosteriorList."
)
mean = posterior.mean
q, m = mean.shape[-2:]
_validate_scalarize_inputs(weights, m)
batch_shape = mean.shape[:-2]
if q != 1:
raise NotImplementedError(
"scalarize_posterior only works with a PosteriorList if each sub-posterior "
"has q=1."
)
means = [post.mean for post in posterior.posteriors]
if {mean.shape[-1] for mean in means} != {1}:
raise NotImplementedError(
"scalarize_posterior only works with a PosteriorList if each sub-posterior "
"has one outcome."
)
new_mean = offset + (mean @ weights).view(*batch_shape, q)
new_cov = (posterior.variance @ (weights**2))[:, None]
mvn = MultivariateNormal(new_mean, new_cov)
return GPyTorchPosterior(mvn)
