Source code for botorch.posteriors.multitask

# Copyright (c) Facebook, Inc. and its affiliates.
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.

from typing import Optional, Union, Tuple

import torch
from botorch.posteriors.gpytorch import GPyTorchPosterior
from gpytorch.distributions import MultivariateNormal
from gpytorch.lazy import LazyTensor, lazify
from torch import Tensor

[docs]class MultitaskGPPosterior(GPyTorchPosterior): def __init__( self, mvn: MultivariateNormal, joint_covariance_matrix: LazyTensor, test_train_covar: LazyTensor, train_diff: Tensor, test_mean: Tensor, train_train_covar: LazyTensor, train_noise: Union[LazyTensor, Tensor], test_noise: Optional[Union[LazyTensor, Tensor]] = None, ): r""" Posterior class for a Kronecker Multi-task GP model using with ICM kernel. Extends the standard GPyTorch posterior class by overwriting the rsample method. In general, this posterior should ONLY be used for MTGP models that have structured covariances. It should also only be used internally when called from the KroneckerMultiTaskGP.posterior(...) method. Args: mvn: Posterior multivariate normal distribution joint_covariance_matrix: Joint test train covariance matrix over the entire tensor train_train_covar: covariance matrix of train points in the data space test_obs_covar: covariance matrix of test x train points in the data space train_diff: difference between train mean and train responses train_noise: training noise covariance test_noise: Only used if posterior should contain observation noise. testing noise covariance """ super().__init__(mvn=mvn) self._is_mt = True self.joint_covariance_matrix = joint_covariance_matrix self.test_train_covar = test_train_covar self.train_diff = train_diff self.test_mean = test_mean self.train_train_covar = train_train_covar self.train_noise = train_noise self.test_noise = test_noise self.observation_noise = self.test_noise is not None self.num_train = self.train_diff.shape[-2] self.num_tasks = self.test_train_covar.lazy_tensors[-1].shape[-1] @property def base_sample_shape(self) -> torch.Size: # overwrites the standard base sample shape call to inform samplers that # n + 2 n_train samples need to be drawn rather than n samples batch_shape = self.joint_covariance_matrix.shape[:-2] sampling_shape = ( self.joint_covariance_matrix.shape[-2] + self.train_noise.shape[-2] ) if self.observation_noise: sampling_shape = sampling_shape + self.test_noise.shape[-2] return batch_shape + torch.Size((sampling_shape,)) @property def device(self) -> torch.device: r"""The torch device of the posterior.""" return self.test_mean.device @property def dtype(self) -> torch.dtype: r"""The torch dtype of the posterior.""" return self.test_mean.dtype def _prepare_base_samples( self, sample_shape: torch.Size, base_samples: Tensor = None ) -> Tuple[Tensor, Tensor]: covariance_matrix = self.joint_covariance_matrix joint_size = covariance_matrix.shape[-1] batch_shape = covariance_matrix.batch_shape # pre-allocated this as None test_noise_base_samples = None 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." f"provided base sample shape is {base_samples.shape} while" f"the expected shape is {sample_shape}." ) if base_samples.shape[-1] != 1: base_samples = base_samples.unsqueeze(-1) unsqueezed_dim = -2 appended_shape = joint_size + self.train_train_covar.shape[-1] if self.observation_noise: appended_shape = appended_shape + self.test_noise.shape[-1] if appended_shape != base_samples.shape[unsqueezed_dim]: # get base_samples to the correct shape by expanding as sample shape, # batch shape, then rest of dimensions. We have to add first the sample # shape, then the batch shape of the model, and then finally the shape # of the test data points squeezed into a single dimension, accessed # from the test_train_covar. base_sample_shapes = ( sample_shape + batch_shape + self.test_train_covar.shape[-2:-1] ) if base_samples.nelement() == base_sample_shapes.numel(): base_samples = base_samples.reshape(base_sample_shapes) new_base_samples = torch.randn( *sample_shape, *batch_shape, appended_shape - base_samples.shape[-1], ) base_samples =, new_base_samples), dim=-1) base_samples = base_samples.unsqueeze(-1) else: # nuke the base samples if we cannot use them. base_samples = None if base_samples is None: # TODO: Allow qMC sampling base_samples = torch.randn( *sample_shape, *batch_shape, joint_size, 1, device=covariance_matrix.device, dtype=covariance_matrix.dtype, ) noise_base_samples = torch.randn( *sample_shape, *batch_shape, self.train_train_covar.shape[-1], 1, device=covariance_matrix.device, dtype=covariance_matrix.dtype, ) if self.observation_noise: test_noise_base_samples = torch.randn( *sample_shape, *self.test_noise.shape[:-1], 1, device=covariance_matrix.device, dtype=covariance_matrix.dtype, ) else: # finally split up the base samples noise_base_samples = base_samples[..., joint_size:, :] base_samples = base_samples[..., :joint_size, :] if self.observation_noise: test_noise_base_samples = noise_base_samples[ ..., -self.test_noise.shape[-1] :, : ] noise_base_samples = noise_base_samples[ ..., : -self.test_noise.shape[-1], : ] return base_samples, noise_base_samples, test_noise_base_samples
[docs] def rsample( self, sample_shape: Optional[torch.Size] = None, base_samples: Optional[Tensor] = None, train_diff: Optional[Tensor] = None, ) -> Tensor: if sample_shape is None: sample_shape = torch.Size([1]) if train_diff is None: train_diff = self.train_diff ( base_samples, noise_base_samples, test_noise_base_samples, ) = self._prepare_base_samples( sample_shape=sample_shape, base_samples=base_samples ) joint_samples = self._draw_from_base_covar( self.joint_covariance_matrix, base_samples ) noise_samples = self._draw_from_base_covar(self.train_noise, noise_base_samples) # pluck out the train + test samples and add the likelihood's noise to the # train side. This should be fine for higher rank likelihoods. n_obs = self.num_tasks * self.num_train n_test = joint_samples.shape[-1] - n_obs obs_samples, test_samples = torch.split(joint_samples, [n_obs, n_test], dim=-1) updated_obs_samples = obs_samples + noise_samples obs_minus_samples = ( train_diff.reshape(*train_diff.shape[:-2], -1) - updated_obs_samples ) train_covar_plus_noise = self.train_train_covar + self.train_noise obs_solve = train_covar_plus_noise.inv_matmul(obs_minus_samples.unsqueeze(-1)) # and multiply the test-observed matrix against the result of the solve updated_samples = self.test_train_covar.matmul(obs_solve).squeeze(-1) # finally, we add the conditioned samples to the prior samples final_samples = test_samples + updated_samples # add in likelihood noise if necessary if self.observation_noise: test_noise_samples = self._draw_from_base_covar( self.test_noise, test_noise_base_samples ) final_samples = final_samples + test_noise_samples # and reshape final_samples = final_samples.reshape( *final_samples.shape[:-1], self.test_mean.shape[-2], self.num_tasks ) final_samples = final_samples + self.test_mean return final_samples
def _draw_from_base_covar( self, covar: Union[Tensor, LazyTensor], base_samples: Tensor ) -> Tensor: # Now reparameterize those base samples if not isinstance(covar, LazyTensor): covar = lazify(covar) covar_root = covar.root_decomposition().root # If necessary, adjust base_samples for rank of root decomposition if covar_root.shape[-1] < base_samples.shape[-2]: base_samples = base_samples[..., : covar_root.shape[-1], :] elif covar_root.shape[-1] > base_samples.shape[-2]: raise RuntimeError("Incompatible dimension of `base_samples`") # the mean is included in the posterior forwards so is not included here res = covar_root.matmul(base_samples) return res.squeeze(-1)