#!/usr/bin/env python3
import warnings
from typing import Any
import torch
from torch import Tensor
from ..constraints import GreaterThan
from ..distributions import base_distributions
from ..functions import add_diag
from ..lazy import (
BlockDiagLazyTensor,
DiagLazyTensor,
KroneckerProductLazyTensor,
MatmulLazyTensor,
RootLazyTensor,
lazify,
)
from ..likelihoods import Likelihood, _GaussianLikelihoodBase
from ..utils.warnings import OldVersionWarning
from .noise_models import MultitaskHomoskedasticNoise
class _MultitaskGaussianLikelihoodBase(_GaussianLikelihoodBase):
"""Base class for multi-task Gaussian Likelihoods, supporting general heteroskedastic noise models. """
def __init__(self, num_tasks, noise_covar, rank=0, task_correlation_prior=None, batch_shape=torch.Size()):
"""
Args:
num_tasks (int):
Number of tasks.
noise_covar (:obj:`gpytorch.module.Module`):
A model for the noise covariance. This can be a simple homoskedastic noise model, or a GP
that is to be fitted on the observed measurement errors.
rank (int):
The rank of the task noise covariance matrix to fit. If `rank` is set to 0, then a diagonal covariance
matrix is fit.
task_correlation_prior (:obj:`gpytorch.priors.Prior`):
Prior to use over the task noise correlation matrix. Only used when `rank` > 0.
batch_shape (torch.Size):
Number of batches.
"""
super().__init__(noise_covar=noise_covar)
if rank != 0:
if rank > num_tasks:
raise ValueError(f"Cannot have rank ({rank}) greater than num_tasks ({num_tasks})")
tidcs = torch.tril_indices(num_tasks, rank, dtype=torch.long)
self.tidcs = tidcs[:, 1:] # (1, 1) must be 1.0, no need to parameterize this
task_noise_corr = torch.randn(*batch_shape, self.tidcs.size(-1))
self.register_parameter("task_noise_corr", torch.nn.Parameter(task_noise_corr))
if task_correlation_prior is not None:
self.register_prior(
"MultitaskErrorCorrelationPrior", task_correlation_prior, lambda: self._eval_corr_matrix
)
elif task_correlation_prior is not None:
raise ValueError("Can only specify task_correlation_prior if rank>0")
self.num_tasks = num_tasks
self.rank = rank
# Handle deprecation of parameterization - TODO: Remove in future release
self._register_load_state_dict_pre_hook(deprecate_task_noise_corr)
def _eval_corr_matrix(self):
tnc = self.task_noise_corr
fac_diag = torch.ones(*tnc.shape[:-1], self.num_tasks, device=tnc.device, dtype=tnc.dtype)
Cfac = torch.diag_embed(fac_diag)
Cfac[..., self.tidcs[0], self.tidcs[1]] = self.task_noise_corr
# squared rows must sum to one for this to be a correlation matrix
C = Cfac / Cfac.pow(2).sum(dim=-1, keepdim=True).sqrt()
return C @ C.transpose(-1, -2)
def _shaped_noise_covar(self, base_shape, *params):
if len(base_shape) >= 2:
*batch_shape, n, _ = base_shape
else:
*batch_shape, n = base_shape
# compute the noise covariance
if len(params) > 0:
shape = None
else:
shape = base_shape if len(base_shape) == 1 else base_shape[:-1]
noise_covar = self.noise_covar(*params, shape=shape)
if self.rank > 0:
# if rank > 0, compute the task correlation matrix
# TODO: This is inefficient, change repeat so it can repeat LazyTensors w/ multiple batch dimensions
task_corr = self._eval_corr_matrix()
exp_shape = torch.Size([*batch_shape, n]) + task_corr.shape[-2:]
task_corr_exp = lazify(task_corr.unsqueeze(-3).expand(exp_shape))
noise_sem = noise_covar.sqrt()
task_covar_blocks = MatmulLazyTensor(MatmulLazyTensor(noise_sem, task_corr_exp), noise_sem)
else:
# otherwise tasks are uncorrelated
task_covar_blocks = noise_covar
if len(batch_shape) == 1:
# TODO: Properly support general batch shapes in BlockDiagLazyTensor (no shape arithmetic)
tcb_eval = task_covar_blocks.evaluate()
task_covar = BlockDiagLazyTensor(lazify(tcb_eval), block_dim=-3)
else:
task_covar = BlockDiagLazyTensor(task_covar_blocks)
return task_covar
def forward(self, function_samples: Tensor, *params: Any, **kwargs: Any) -> base_distributions.Normal:
noise = self._shaped_noise_covar(function_samples.shape, *params, **kwargs).diag()
noise = noise.view(*noise.shape[:-1], *function_samples.shape[-2:])
return base_distributions.Independent(base_distributions.Normal(function_samples, noise.sqrt()), 1)
class MultitaskGaussianLikelihood(_MultitaskGaussianLikelihoodBase):
"""
A convenient extension of the :class:`gpytorch.likelihoods.GaussianLikelihood` to the multitask setting that allows
for a full cross-task covariance structure for the noise. The fitted covariance matrix has rank `rank`.
If a strictly diagonal task noise covariance matrix is desired, then rank=0 should be set. (This option still
allows for a different `log_noise` parameter for each task.). This likelihood assumes homoskedastic noise.
Like the Gaussian likelihood, this object can be used with exact inference.
"""
def __init__(
self,
num_tasks,
rank=0,
task_correlation_prior=None,
batch_shape=torch.Size(),
noise_prior=None,
noise_constraint=None,
):
"""
Args:
num_tasks (int): Number of tasks.
rank (int): The rank of the task noise covariance matrix to fit. If `rank` is set to 0,
then a diagonal covariance matrix is fit.
task_correlation_prior (:obj:`gpytorch.priors.Prior`): Prior to use over the task noise correlaton matrix.
Only used when `rank` > 0.
"""
if noise_constraint is None:
noise_constraint = GreaterThan(1e-4)
noise_covar = MultitaskHomoskedasticNoise(
num_tasks=num_tasks, noise_prior=noise_prior, noise_constraint=noise_constraint, batch_shape=batch_shape
)
super().__init__(
num_tasks=num_tasks,
noise_covar=noise_covar,
rank=rank,
task_correlation_prior=task_correlation_prior,
batch_shape=batch_shape,
)
self.register_parameter(name="raw_noise", parameter=torch.nn.Parameter(torch.zeros(*batch_shape, 1)))
self.register_constraint("raw_noise", noise_constraint)
@property
def noise(self):
return self.raw_noise_constraint.transform(self.raw_noise)
@noise.setter
def noise(self, value):
self._set_noise(value)
def _set_noise(self, value):
if not torch.is_tensor(value):
value = torch.as_tensor(value).to(self.raw_noise)
self.initialize(raw_noise=self.raw_noise_constraint.inverse_transform(value))
def _shaped_noise_covar(self, base_shape, *params):
noise_covar = super()._shaped_noise_covar(base_shape, *params)
noise = self.noise
return noise_covar.add_diag(noise)
class MultitaskGaussianLikelihoodKronecker(_MultitaskGaussianLikelihoodBase):
"""
A convenient extension of the :class:`gpytorch.likelihoods.GaussianLikelihood` to the multitask setting that allows
for a full cross-task covariance structure for the noise. The fitted covariance matrix has rank `rank`.
If a strictly diagonal task noise covariance matrix is desired, then rank=0 should be set. (This option still
allows for a different `noise` parameter for each task.)
Like the Gaussian likelihood, this object can be used with exact inference.
Note: This Likelihood is scheduled to be deprecated and replaced by an improved version of
`MultitaskGaussianLikelihood`. Use this only for compatibility with batched Multitask models.
"""
def __init__(
self, num_tasks, rank=0, task_prior=None, batch_shape=torch.Size(), noise_prior=None, noise_constraint=None
):
"""
Args:
num_tasks (int): Number of tasks.
rank (int): The rank of the task noise covariance matrix to fit. If `rank` is set to 0,
then a diagonal covariance matrix is fit.
task_prior (:obj:`gpytorch.priors.Prior`): Prior to use over the task noise covariance matrix if
`rank` > 0, or a prior over the log of just the diagonal elements, if `rank` == 0.
"""
super(Likelihood, self).__init__()
if noise_constraint is None:
noise_constraint = GreaterThan(1e-4)
self.register_parameter(name="raw_noise", parameter=torch.nn.Parameter(torch.zeros(*batch_shape, 1)))
if rank == 0:
self.register_parameter(
name="raw_task_noises", parameter=torch.nn.Parameter(torch.zeros(*batch_shape, num_tasks))
)
if task_prior is not None:
raise RuntimeError("Cannot set a `task_prior` if rank=0")
else:
self.register_parameter(
name="task_noise_covar_factor", parameter=torch.nn.Parameter(torch.randn(*batch_shape, num_tasks, rank))
)
if task_prior is not None:
self.register_prior("MultitaskErrorCovariancePrior", task_prior, self._eval_covar_matrix)
self.num_tasks = num_tasks
self.rank = rank
self.register_constraint("raw_noise", noise_constraint)
@property
def noise(self):
return self.raw_noise_constraint.transform(self.raw_noise)
@noise.setter
def noise(self, value):
self._set_noise(value)
def _set_noise(self, value):
self.initialize(raw_noise=self.raw_noise_constraint.inverse_transform(value))
def _eval_covar_matrix(self):
covar_factor = self.task_noise_covar_factor
noise = self.noise
D = noise * torch.eye(self.num_tasks, dtype=noise.dtype, device=noise.device)
return covar_factor.matmul(covar_factor.transpose(-1, -2)) + D
def marginal(self, function_dist, *params, **kwargs):
r"""
Adds the task noises to the diagonal of the covariance matrix of the supplied
:obj:`gpytorch.distributions.MultivariateNormal` or :obj:`gpytorch.distributions.MultitaskMultivariateNormal`,
in case of `rank` == 0. Otherwise, adds a rank `rank` covariance matrix to it.
To accomplish this, we form a new :obj:`gpytorch.lazy.KroneckerProductLazyTensor` between :math:`I_{n}`,
an identity matrix with size equal to the data and a (not necessarily diagonal) matrix containing the task
noises :math:`D_{t}`.
We also incorporate a shared `noise` parameter from the base
:class:`gpytorch.likelihoods.GaussianLikelihood` that we extend.
The final covariance matrix after this method is then :math:`K + D_{t} \otimes I_{n} + \sigma^{2}I_{nt}`.
Args:
function_dist (:obj:`gpytorch.distributions.MultitaskMultivariateNormal`): Random variable whose covariance
matrix is a :obj:`gpytorch.lazy.LazyTensor` we intend to augment.
Returns:
:obj:`gpytorch.distributions.MultitaskMultivariateNormal`: A new random variable whose covariance
matrix is a :obj:`gpytorch.lazy.LazyTensor` with :math:`D_{t} \otimes I_{n}` and :math:`\sigma^{2}I_{nt}`
added.
"""
mean, covar = function_dist.mean, function_dist.lazy_covariance_matrix
if self.rank == 0:
task_noises = self.raw_noise_constraint.transform(self.raw_task_noises)
task_var_lt = DiagLazyTensor(task_noises)
dtype, device = task_noises.dtype, task_noises.device
else:
task_noise_covar_factor = self.task_noise_covar_factor
task_var_lt = RootLazyTensor(task_noise_covar_factor)
dtype, device = task_noise_covar_factor.dtype, task_noise_covar_factor.device
eye_lt = DiagLazyTensor(
torch.ones(*covar.batch_shape, covar.size(-1) // self.num_tasks, dtype=dtype, device=device)
)
task_var_lt = task_var_lt.expand(*covar.batch_shape, *task_var_lt.matrix_shape)
covar_kron_lt = KroneckerProductLazyTensor(eye_lt, task_var_lt)
covar = covar + covar_kron_lt
noise = self.noise
covar = add_diag(covar, noise)
return function_dist.__class__(mean, covar)
def deprecate_task_noise_corr(state_dict, prefix, local_metadata, strict, missing_keys, unexpected_keys, error_msgs):
if prefix + "task_noise_corr_factor" in state_dict:
# Remove after 1.0
warnings.warn(
"Loading a deprecated parameterization of _MultitaskGaussianLikelihoodBase. Consider re-saving your model.",
OldVersionWarning,
)
# construct the task correlation matrix from the factors using the old parameterization
corr_factor = state_dict.pop(prefix + "task_noise_corr_factor").squeeze(0)
corr_diag = state_dict.pop(prefix + "task_noise_corr_diag").squeeze(0)
num_tasks, rank = corr_factor.shape[-2:]
M = corr_factor.matmul(corr_factor.transpose(-1, -2))
idx = torch.arange(M.shape[-1], dtype=torch.long, device=M.device)
M[..., idx, idx] += corr_diag
sem_inv = 1 / torch.diagonal(M, dim1=-2, dim2=-1).sqrt().unsqueeze(-1)
C = M * sem_inv.matmul(sem_inv.transpose(-1, -2))
# perform a Cholesky decomposition and extract the required entries
L = torch.cholesky(C)
tidcs = torch.tril_indices(num_tasks, rank)[:, 1:]
task_noise_corr = L[..., tidcs[0], tidcs[1]]
state_dict[prefix + "task_noise_corr"] = task_noise_corr
