# 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"""Multi-task Gaussian Process Regression models with fully Bayesian inference.
"""
from typing import Any, Dict, List, Mapping, NoReturn, Optional, Tuple
import pyro
import torch
from botorch.acquisition.objective import PosteriorTransform
from botorch.models.fully_bayesian import (
matern52_kernel,
MIN_INFERRED_NOISE_LEVEL,
PyroModel,
reshape_and_detach,
SaasPyroModel,
)
from botorch.models.multitask import MultiTaskGP
from botorch.models.transforms.input import InputTransform
from botorch.models.transforms.outcome import OutcomeTransform
from botorch.posteriors.fully_bayesian import FullyBayesianPosterior, MCMC_DIM
from botorch.utils.datasets import SupervisedDataset
from gpytorch.distributions.multivariate_normal import MultivariateNormal
from gpytorch.kernels import MaternKernel
from gpytorch.kernels.kernel import Kernel
from gpytorch.likelihoods.likelihood import Likelihood
from gpytorch.means.mean import Mean
from torch import Tensor
from torch.nn.parameter import Parameter
[docs]class MultitaskSaasPyroModel(SaasPyroModel):
r"""
Implementation of the multi-task sparse axis-aligned subspace priors (SAAS) model.
The multi-task model uses an ICM kernel. The data kernel is same as the single task
SAAS model in order to handle high-dimensional parameter spaces. The task kernel
is a Matern-5/2 kernel using learned task embeddings as the input.
"""
[docs] def sample(self) -> None:
r"""Sample from the SAAS model.
This samples the mean, noise variance, outputscale, and lengthscales according
to the SAAS prior.
"""
tkwargs = {"dtype": self.train_X.dtype, "device": self.train_X.device}
base_idxr = torch.arange(self.ard_num_dims, **{"device": tkwargs["device"]})
base_idxr[self.task_feature :] += 1 # exclude task feature
task_indices = self.train_X[..., self.task_feature].to(
device=tkwargs["device"], dtype=torch.long
)
outputscale = self.sample_outputscale(concentration=2.0, rate=0.15, **tkwargs)
mean = self.sample_mean(**tkwargs)
noise = self.sample_noise(**tkwargs)
lengthscale = self.sample_lengthscale(dim=self.ard_num_dims, **tkwargs)
K = matern52_kernel(X=self.train_X[..., base_idxr], lengthscale=lengthscale)
# compute task covar matrix
task_latent_features = self.sample_latent_features(**tkwargs)[task_indices]
task_lengthscale = self.sample_task_lengthscale(**tkwargs)
task_covar = matern52_kernel(
X=task_latent_features, lengthscale=task_lengthscale
)
K = K.mul(task_covar)
K = outputscale * K + noise * torch.eye(self.train_X.shape[0], **tkwargs)
pyro.sample(
"Y",
pyro.distributions.MultivariateNormal(
loc=mean.view(-1).expand(self.train_X.shape[0]),
covariance_matrix=K,
),
obs=self.train_Y.squeeze(-1),
)
[docs] def sample_latent_features(self, **tkwargs: Any):
return pyro.sample(
"latent_features",
pyro.distributions.Normal(
torch.tensor(0.0, **tkwargs),
torch.tensor(1.0, **tkwargs),
).expand(torch.Size([self.num_tasks, self.task_rank])),
)
[docs] def sample_task_lengthscale(
self, concentration: float = 6.0, rate: float = 3.0, **tkwargs: Any
):
return pyro.sample(
"task_lengthscale",
pyro.distributions.Gamma(
torch.tensor(concentration, **tkwargs),
torch.tensor(rate, **tkwargs),
).expand(torch.Size([self.task_rank])),
)
[docs] def load_mcmc_samples(
self, mcmc_samples: Dict[str, Tensor]
) -> Tuple[Mean, Kernel, Likelihood, Kernel, Parameter]:
r"""Load the MCMC samples into the mean_module, covar_module, and likelihood."""
tkwargs = {"device": self.train_X.device, "dtype": self.train_X.dtype}
num_mcmc_samples = len(mcmc_samples["mean"])
batch_shape = torch.Size([num_mcmc_samples])
mean_module, covar_module, likelihood = super().load_mcmc_samples(
mcmc_samples=mcmc_samples
)
task_covar_module = MaternKernel(
nu=2.5,
ard_num_dims=self.task_rank,
batch_shape=batch_shape,
).to(**tkwargs)
task_covar_module.lengthscale = reshape_and_detach(
target=task_covar_module.lengthscale,
new_value=mcmc_samples["task_lengthscale"],
)
latent_features = Parameter(
torch.rand(
batch_shape + torch.Size([self.num_tasks, self.task_rank]),
requires_grad=True,
**tkwargs,
)
)
latent_features = reshape_and_detach(
target=latent_features,
new_value=mcmc_samples["latent_features"],
)
return mean_module, covar_module, likelihood, task_covar_module, latent_features
[docs]class SaasFullyBayesianMultiTaskGP(MultiTaskGP):
r"""A fully Bayesian multi-task GP model with the SAAS prior.
This model assumes that the inputs have been normalized to [0, 1]^d and that the
output has been stratified standardized to have zero mean and unit variance for
each task.The SAAS model [Eriksson2021saasbo]_ with a Matern-5/2 is used as data
kernel by default.
You are expected to use `fit_fully_bayesian_model_nuts` to fit this model as it
isn't compatible with `fit_gpytorch_model`.
Example:
>>> X1, X2 = torch.rand(10, 2), torch.rand(20, 2)
>>> i1, i2 = torch.zeros(10, 1), torch.ones(20, 1)
>>> train_X = torch.cat([
>>> torch.cat([X1, i1], -1), torch.cat([X2, i2], -1),
>>> ])
>>> train_Y = torch.cat(f1(X1), f2(X2)).unsqueeze(-1)
>>> train_Yvar = 0.01 * torch.ones_like(train_Y)
>>> mtsaas_gp = SaasFullyBayesianFixedNoiseMultiTaskGP(
>>> train_X, train_Y, train_Yvar, task_feature=-1,
>>> )
>>> fit_fully_bayesian_model_nuts(mtsaas_gp)
>>> posterior = mtsaas_gp.posterior(test_X)
"""
def __init__(
self,
train_X: Tensor,
train_Y: Tensor,
train_Yvar: Optional[Tensor],
task_feature: int,
output_tasks: Optional[List[int]] = None,
rank: Optional[int] = None,
outcome_transform: Optional[OutcomeTransform] = None,
input_transform: Optional[InputTransform] = None,
pyro_model: Optional[PyroModel] = None,
) -> None:
r"""Initialize the fully Bayesian multi-task GP model.
Args:
train_X: Training inputs (n x (d + 1))
train_Y: Training targets (n x 1)
train_Yvar: Observed noise variance (n x 1). If None, we infer the noise.
Note that the inferred noise is common across all tasks.
task_feature: The index of the task feature (`-d <= task_feature <= d`).
output_tasks: A list of task indices for which to compute model
outputs for. If omitted, return outputs for all task indices.
rank: The num of learned task embeddings to be used in the task kernel.
If omitted, set it to be 1.
outcome_transform: An outcome transform that is applied to the
training data during instantiation and to the posterior during
inference (that is, the `Posterior` obtained by calling
`.posterior` on the model will be on the original scale).
input_transform: An input transform that is applied to the inputs `X`
in the model's forward pass.
pyro_model: Optional `PyroModel`, defaults to `MultitaskSaasPyroModel`.
"""
if not (
train_X.ndim == train_Y.ndim == 2
and len(train_X) == len(train_Y)
and train_Y.shape[-1] == 1
):
raise ValueError(
"Expected train_X to have shape n x d and train_Y to have shape n x 1"
)
if train_Yvar is not None and train_Y.shape != train_Yvar.shape:
raise ValueError(
"Expected train_Yvar to be None or have the same shape as train_Y"
)
with torch.no_grad():
transformed_X = self.transform_inputs(
X=train_X, input_transform=input_transform
)
if outcome_transform is not None:
train_Y, train_Yvar = outcome_transform(train_Y, train_Yvar)
if train_Yvar is not None: # Clamp after transforming
train_Yvar = train_Yvar.clamp(MIN_INFERRED_NOISE_LEVEL)
super().__init__(
train_X=train_X,
train_Y=train_Y,
train_Yvar=train_Yvar,
task_feature=task_feature,
output_tasks=output_tasks,
)
self.to(train_X)
self.mean_module = None
self.covar_module = None
self.likelihood = None
self.task_covar_module = None
self.register_buffer("latent_features", None)
if pyro_model is None:
pyro_model = MultitaskSaasPyroModel()
pyro_model.set_inputs(
train_X=transformed_X,
train_Y=train_Y,
train_Yvar=train_Yvar,
task_feature=task_feature,
task_rank=rank,
)
self.pyro_model = pyro_model
if outcome_transform is not None:
self.outcome_transform = outcome_transform
if input_transform is not None:
self.input_transform = input_transform
[docs] def train(self, mode: bool = True) -> None:
r"""Puts the model in `train` mode."""
super().train(mode=mode)
if mode:
self.mean_module = None
self.covar_module = None
self.likelihood = None
self.task_covar_module = None
@property
def median_lengthscale(self) -> Tensor:
r"""Median lengthscales across the MCMC samples."""
self._check_if_fitted()
lengthscale = self.covar_module.base_kernel.lengthscale.clone()
return lengthscale.median(0).values.squeeze(0)
@property
def num_mcmc_samples(self) -> int:
r"""Number of MCMC samples in the model."""
self._check_if_fitted()
return len(self.covar_module.outputscale)
@property
def batch_shape(self) -> torch.Size:
r"""Batch shape of the model, equal to the number of MCMC samples.
Note that `SaasFullyBayesianMultiTaskGP` does not support batching
over input data at this point.
"""
self._check_if_fitted()
return torch.Size([self.num_mcmc_samples])
[docs] def fantasize(self, *args, **kwargs) -> NoReturn:
raise NotImplementedError("Fantasize is not implemented!")
def _check_if_fitted(self):
r"""Raise an exception if the model hasn't been fitted."""
if self.covar_module is None:
raise RuntimeError(
"Model has not been fitted. You need to call "
"`fit_fully_bayesian_model_nuts` to fit the model."
)
[docs] def load_mcmc_samples(self, mcmc_samples: Dict[str, Tensor]) -> None:
r"""Load the MCMC hyperparameter samples into the model.
This method will be called by `fit_fully_bayesian_model_nuts` when the model
has been fitted in order to create a batched MultiTaskGP model.
"""
(
self.mean_module,
self.covar_module,
self.likelihood,
self.task_covar_module,
self.latent_features,
) = self.pyro_model.load_mcmc_samples(mcmc_samples=mcmc_samples)
[docs] def posterior(
self,
X: Tensor,
output_indices: Optional[List[int]] = None,
observation_noise: bool = False,
posterior_transform: Optional[PosteriorTransform] = None,
**kwargs: Any,
) -> FullyBayesianPosterior:
r"""Computes the posterior over model outputs at the provided points.
Returns:
A `FullyBayesianPosterior` object. Includes observation noise if specified.
"""
self._check_if_fitted()
posterior = super().posterior(
X=X,
output_indices=output_indices,
observation_noise=observation_noise,
posterior_transform=posterior_transform,
**kwargs,
)
posterior = FullyBayesianPosterior(distribution=posterior.distribution)
return posterior
[docs] def forward(self, X: Tensor) -> MultivariateNormal:
self._check_if_fitted()
X = X.unsqueeze(MCMC_DIM)
x_basic, task_idcs = self._split_inputs(X)
mean_x = self.mean_module(x_basic)
covar_x = self.covar_module(x_basic)
tsub_idcs = task_idcs.squeeze(-3).squeeze(-1)
latent_features = self.latent_features[:, tsub_idcs, :]
if X.ndim > 3:
# batch eval mode
# for X (batch_shape x num_samples x q x d), task_idcs[:,i,:,] are the same
# reshape X to (batch_shape x num_samples x q x d)
latent_features = latent_features.permute(
[-i for i in range(X.ndim - 1, 2, -1)]
+ [0]
+ [-i for i in range(2, 0, -1)]
)
# Combine the two in an ICM fashion
covar_i = self.task_covar_module(latent_features)
covar = covar_x.mul(covar_i)
return MultivariateNormal(mean_x, covar)
[docs] def load_state_dict(self, state_dict: Mapping[str, Any], strict: bool = True):
r"""Custom logic for loading the state dict.
The standard approach of calling `load_state_dict` currently doesn't play well
with the `SaasFullyBayesianMultiTaskGP` since the `mean_module`, `covar_module`
and `likelihood` aren't initialized until the model has been fitted. The reason
for this is that we don't know the number of MCMC samples until NUTS is called.
Given the state dict, we can initialize a new model with some dummy samples and
then load the state dict into this model. This currently only works for a
`MultitaskSaasPyroModel` and supporting more Pyro models likely requires moving
the model construction logic into the Pyro model itself.
TODO: If this were to inherif from `SaasFullyBayesianSingleTaskGP`, we could
simplify this method and eliminate some others.
"""
if not isinstance(self.pyro_model, MultitaskSaasPyroModel):
raise NotImplementedError( # pragma: no cover
"load_state_dict only works for MultitaskSaasPyroModel"
)
raw_mean = state_dict["mean_module.raw_constant"]
num_mcmc_samples = len(raw_mean)
dim = self.pyro_model.train_X.shape[-1] - 1 # Removing 1 for the task feature.
task_rank = self.pyro_model.task_rank
tkwargs = {"device": raw_mean.device, "dtype": raw_mean.dtype}
# Load some dummy samples
mcmc_samples = {
"mean": torch.ones(num_mcmc_samples, **tkwargs),
"lengthscale": torch.ones(num_mcmc_samples, dim, **tkwargs),
"outputscale": torch.ones(num_mcmc_samples, **tkwargs),
"task_lengthscale": torch.ones(num_mcmc_samples, task_rank, **tkwargs),
"latent_features": torch.ones(
num_mcmc_samples, self._rank, task_rank, **tkwargs
),
}
if self.pyro_model.train_Yvar is None:
mcmc_samples["noise"] = torch.ones(num_mcmc_samples, **tkwargs)
(
self.mean_module,
self.covar_module,
self.likelihood,
self.task_covar_module,
self.latent_features,
) = self.pyro_model.load_mcmc_samples(mcmc_samples=mcmc_samples)
# Load the actual samples from the state dict
super().load_state_dict(state_dict=state_dict, strict=strict)
