Source code for botorch.posteriors.gpytorch

#!/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.

Posterior Module to be used with GPyTorch models.

from __future__ import annotations

from contextlib import ExitStack
from typing import Optional

import torch
from botorch.exceptions.errors import BotorchTensorDimensionError
from botorch.posteriors.base_samples import _reshape_base_samples_non_interleaved
from botorch.posteriors.posterior import Posterior
from gpytorch import settings as gpt_settings
from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
from gpytorch.lazy import BlockDiagLazyTensor, LazyTensor, SumLazyTensor
from torch import Tensor

[docs]class GPyTorchPosterior(Posterior): r"""A posterior based on GPyTorch's multi-variate Normal distributions.""" def __init__(self, mvn: MultivariateNormal) -> None: r"""A posterior based on GPyTorch's multi-variate Normal distributions. Args: mvn: A GPyTorch MultivariateNormal (single-output case) or MultitaskMultivariateNormal (multi-output case). """ self.mvn = mvn self._is_mt = isinstance(mvn, MultitaskMultivariateNormal) @property def base_sample_shape(self) -> torch.Size: r"""The shape of a base sample used for constructing posterior samples.""" shape = self.mvn.batch_shape + self.mvn.base_sample_shape if not self._is_mt: shape += torch.Size([1]) return shape @property def device(self) -> torch.device: r"""The torch device of the posterior.""" return self.mvn.loc.device @property def dtype(self) -> torch.dtype: r"""The torch dtype of the posterior.""" return self.mvn.loc.dtype @property def event_shape(self) -> torch.Size: r"""The event shape (i.e. the shape of a single sample) of the posterior.""" shape = self.mvn.batch_shape + self.mvn.event_shape if not self._is_mt: shape += torch.Size([1]) return shape
[docs] def rsample( self, sample_shape: Optional[torch.Size] = None, base_samples: Optional[Tensor] = 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])`. base_samples: An (optional) Tensor of `N(0, I)` base samples of appropriate dimension, typically obtained from a `Sampler`. This is used for deterministic optimization. Returns: A `sample_shape x event_shape`-dim Tensor of samples from the posterior. """ if sample_shape is None: sample_shape = torch.Size([1]) if base_samples is not None: if base_samples.shape[: len(sample_shape)] != sample_shape: raise RuntimeError("sample_shape disagrees with shape of base_samples.") # get base_samples to the correct shape base_samples = base_samples.expand(sample_shape + self.event_shape) if self._is_mt: base_samples = _reshape_base_samples_non_interleaved( mvn=self.mvn, base_samples=base_samples, sample_shape=sample_shape ) # remove output dimension in single output case else: base_samples = base_samples.squeeze(-1) with ExitStack() as es: if gpt_settings._fast_covar_root_decomposition.is_default(): es.enter_context(gpt_settings._fast_covar_root_decomposition(False)) samples = self.mvn.rsample( sample_shape=sample_shape, base_samples=base_samples ) # 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.mvn.mean if not self._is_mt: mean = mean.unsqueeze(-1) return mean @property def variance(self) -> Tensor: r"""The posterior variance.""" variance = self.mvn.variance if not self._is_mt: variance = variance.unsqueeze(-1) return variance
[docs]def scalarize_posterior( posterior: GPyTorchPosterior, 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. 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) """ if weights.ndim > 1: raise BotorchTensorDimensionError("`weights` must be one-dimensional") mean = posterior.mean q, m = mean.shape[-2:] batch_shape = mean.shape[:-2] if m != weights.size(0): raise RuntimeError("Output shape not equal to that of weights") mvn = posterior.mvn 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 new_mvn = MultivariateNormal(new_mean, new_cov) return GPyTorchPosterior(new_mvn) 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, BlockDiagLazyTensor): new_cov = SumLazyTensor( *[ cov.base_lazy_tensor[..., i, :, :] * weights[i].pow(2) for i in range(cov.base_lazy_tensor.size(-3)) ] ) new_mvn = MultivariateNormal(new_mean, new_cov) return GPyTorchPosterior(new_mvn) 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 lazy tensors (ideally we simplify # this in GPyTorch: if isinstance(cov_scaled, LazyTensor): cov_scaled = cov_scaled.evaluate() new_cov = cov_scaled.view(sum_shape).sum(dim=sum_dims[0]).sum(dim=sum_dims[1]) new_mvn = MultivariateNormal(new_mean, new_cov) return GPyTorchPosterior(new_mvn)