#!/usr/bin/env python3
from typing import Optional
import torch
from linear_operator.operators import LinearOperator
from torch import Tensor
from ..distributions import MultivariateNormal
from ..utils.memoize import add_to_cache, cached
from ._variational_distribution import _VariationalDistribution
from ._variational_strategy import _VariationalStrategy
from .delta_variational_distribution import DeltaVariationalDistribution
[docs]class OrthogonallyDecoupledVariationalStrategy(_VariationalStrategy):
r"""
Implements orthogonally decoupled VGPs as defined in `Salimbeni et al. (2018)`_.
This variational strategy uses a different set of inducing points for the mean and covariance functions.
The idea is to use more inducing points for the (computationally efficient) mean and fewer inducing points for the
(computationally expensive) covaraince.
This variational strategy defines the inducing points/:obj:`~gpytorch.variational._VariationalDistribution`
for the mean function.
It then wraps a different :obj:`~gpytorch.variational._VariationalStrategy` which
defines the covariance inducing points.
:param covar_variational_strategy:
The variational strategy for the covariance term.
:param inducing_points: Tensor containing a set of inducing
points to use for variational inference.
:param variational_distribution: A
VariationalDistribution object that represents the form of the variational distribution :math:`q(\mathbf u)`
:param jitter_val: Amount of diagonal jitter to add for Cholesky factorization numerical stability
Example:
>>> mean_inducing_points = torch.randn(1000, train_x.size(-1), dtype=train_x.dtype, device=train_x.device)
>>> covar_inducing_points = torch.randn(100, train_x.size(-1), dtype=train_x.dtype, device=train_x.device)
>>>
>>> covar_variational_strategy = gpytorch.variational.VariationalStrategy(
>>> model, covar_inducing_points,
>>> gpytorch.variational.CholeskyVariationalDistribution(covar_inducing_points.size(-2)),
>>> learn_inducing_locations=True
>>> )
>>>
>>> variational_strategy = gpytorch.variational.OrthogonallyDecoupledVariationalStrategy(
>>> covar_variational_strategy, mean_inducing_points,
>>> gpytorch.variational.DeltaVariationalDistribution(mean_inducing_points.size(-2)),
>>> )
.. _Salimbeni et al. (2018):
https://arxiv.org/abs/1809.08820
"""
def __init__(
self,
covar_variational_strategy: _VariationalStrategy,
inducing_points: Tensor,
variational_distribution: _VariationalDistribution,
jitter_val: Optional[float] = None,
):
if not isinstance(variational_distribution, DeltaVariationalDistribution):
raise NotImplementedError(
"OrthogonallyDecoupledVariationalStrategy currently works with DeltaVariationalDistribution"
)
super().__init__(
covar_variational_strategy,
inducing_points,
variational_distribution,
learn_inducing_locations=True,
jitter_val=jitter_val,
)
self.base_variational_strategy = covar_variational_strategy
@property
@cached(name="prior_distribution_memo")
def prior_distribution(self) -> MultivariateNormal:
out = self.model(self.inducing_points)
res = MultivariateNormal(out.mean, out.lazy_covariance_matrix.add_jitter(self.jitter_val))
return res
def forward(
self,
x: Tensor,
inducing_points: Tensor,
inducing_values: Tensor,
variational_inducing_covar: Optional[LinearOperator] = None,
**kwargs,
) -> MultivariateNormal:
if variational_inducing_covar is not None:
raise NotImplementedError(
"OrthogonallyDecoupledVariationalStrategy currently works with DeltaVariationalDistribution"
)
num_data = x.size(-2)
full_output = self.model(torch.cat([x, inducing_points], dim=-2), **kwargs)
full_mean = full_output.mean
full_covar = full_output.lazy_covariance_matrix
if self.training:
induc_mean = full_mean[..., num_data:]
induc_induc_covar = full_covar[..., num_data:, num_data:]
prior_dist = MultivariateNormal(induc_mean, induc_induc_covar)
add_to_cache(self, "prior_distribution_memo", prior_dist)
test_mean = full_mean[..., :num_data]
data_induc_covar = full_covar[..., :num_data, num_data:]
predictive_mean = (data_induc_covar @ inducing_values.unsqueeze(-1)).squeeze(-1).add(test_mean)
predictive_covar = full_covar[..., :num_data, :num_data]
# Return the distribution
return MultivariateNormal(predictive_mean, predictive_covar)
def kl_divergence(self) -> Tensor:
mean = self.variational_distribution.mean
induc_induc_covar = self.prior_distribution.lazy_covariance_matrix
kl = self.model.kl_divergence() + ((induc_induc_covar @ mean.unsqueeze(-1)).squeeze(-1) * mean).sum(-1).mul(0.5)
return kl