Source code for gpytorch.variational.variational_strategy

#!/usr/bin/env python3

import warnings

import torch

from .. import settings
from ..distributions import MultivariateNormal
from ..lazy import DiagLazyTensor, MatmulLazyTensor, RootLazyTensor, SumLazyTensor, TriangularLazyTensor, delazify
from ..settings import trace_mode
from ..utils.cholesky import psd_safe_cholesky
from ..utils.memoize import cached, clear_cache_hook, pop_from_cache
from ..utils.warnings import OldVersionWarning
from ._variational_strategy import _VariationalStrategy


def _ensure_updated_strategy_flag_set(
    state_dict, prefix, local_metadata, strict, missing_keys, unexpected_keys, error_msgs
):
    device = state_dict[list(state_dict.keys())[0]].device
    if prefix + "updated_strategy" not in state_dict:
        state_dict[prefix + "updated_strategy"] = torch.tensor(False, device=device)
        warnings.warn(
            "You have loaded a variational GP model (using `VariationalStrategy`) from a previous version of "
            "GPyTorch. We have updated the parameters of your model to work with the new version of "
            "`VariationalStrategy` that uses whitened parameters.\nYour model will work as expected, but we "
            "recommend that you re-save your model.",
            OldVersionWarning,
        )


[docs]class VariationalStrategy(_VariationalStrategy): r""" The standard variational strategy, as defined by `Hensman et al. (2015)`_. This strategy takes a set of :math:`m \ll n` inducing points :math:`\mathbf Z` and applies an approximate distribution :math:`q( \mathbf u)` over their function values. (Here, we use the common notation :math:`\mathbf u = f(\mathbf Z)`. The approximate function distribution for any abitrary input :math:`\mathbf X` is given by: .. math:: q( f(\mathbf X) ) = \int p( f(\mathbf X) \mid \mathbf u) q(\mathbf u) \: d\mathbf u This variational strategy uses "whitening" to accelerate the optimization of the variational parameters. See `Matthews (2017)`_ for more info. :param ~gpytorch.models.ApproximateGP model: Model this strategy is applied to. Typically passed in when the VariationalStrategy is created in the __init__ method of the user defined model. :param torch.Tensor inducing_points: Tensor containing a set of inducing points to use for variational inference. :param ~gpytorch.variational.VariationalDistribution variational_distribution: A VariationalDistribution object that represents the form of the variational distribution :math:`q(\mathbf u)` :param learn_inducing_locations: (Default True): Whether or not the inducing point locations :math:`\mathbf Z` should be learned (i.e. are they parameters of the model). :type learn_inducing_locations: `bool`, optional .. _Hensman et al. (2015): http://proceedings.mlr.press/v38/hensman15.pdf .. _Matthews (2017): https://www.repository.cam.ac.uk/handle/1810/278022 """ def __init__(self, model, inducing_points, variational_distribution, learn_inducing_locations=True): super().__init__(model, inducing_points, variational_distribution, learn_inducing_locations) self.register_buffer("updated_strategy", torch.tensor(True)) self._register_load_state_dict_pre_hook(_ensure_updated_strategy_flag_set) @cached(name="cholesky_factor", ignore_args=True) def _cholesky_factor(self, induc_induc_covar): L = psd_safe_cholesky(delazify(induc_induc_covar).double(), jitter=settings.cholesky_jitter.value()) return TriangularLazyTensor(L) @property @cached(name="prior_distribution_memo") def prior_distribution(self): zeros = torch.zeros_like(self.variational_distribution.mean) ones = torch.ones_like(zeros) res = MultivariateNormal(zeros, DiagLazyTensor(ones)) return res def forward(self, x, inducing_points, inducing_values, variational_inducing_covar=None): # Compute full prior distribution full_inputs = torch.cat([inducing_points, x], dim=-2) full_output = self.model.forward(full_inputs) full_covar = full_output.lazy_covariance_matrix # Covariance terms num_induc = inducing_points.size(-2) test_mean = full_output.mean[..., num_induc:] induc_induc_covar = full_covar[..., :num_induc, :num_induc].add_jitter() induc_data_covar = full_covar[..., :num_induc, num_induc:].evaluate() data_data_covar = full_covar[..., num_induc:, num_induc:] # Compute interpolation terms # K_ZZ^{-1/2} K_ZX # K_ZZ^{-1/2} \mu_Z L = self._cholesky_factor(induc_induc_covar) if L.shape != induc_induc_covar.shape: # Aggressive caching can cause nasty shape incompatibilies when evaluating with different batch shapes # TODO: Use a hook fo this pop_from_cache(self, "cholesky_factor") L = self._cholesky_factor(induc_induc_covar) interp_term = L.inv_matmul(induc_data_covar.double()).to(full_inputs.dtype) # Compute the mean of q(f) # k_XZ K_ZZ^{-1/2} (m - K_ZZ^{-1/2} \mu_Z) + \mu_X predictive_mean = ( torch.matmul( interp_term.transpose(-1, -2), (inducing_values - self.prior_distribution.mean).unsqueeze(-1) ).squeeze(-1) + test_mean ) # Compute the covariance of q(f) # K_XX + k_XZ K_ZZ^{-1/2} (S - I) K_ZZ^{-1/2} k_ZX middle_term = self.prior_distribution.lazy_covariance_matrix.mul(-1) if variational_inducing_covar is not None: middle_term = SumLazyTensor(variational_inducing_covar, middle_term) if trace_mode.on(): predictive_covar = ( data_data_covar.add_jitter(1e-4).evaluate() + interp_term.transpose(-1, -2) @ middle_term.evaluate() @ interp_term ) else: predictive_covar = SumLazyTensor( data_data_covar.add_jitter(1e-4), MatmulLazyTensor(interp_term.transpose(-1, -2), middle_term @ interp_term), ) # Return the distribution return MultivariateNormal(predictive_mean, predictive_covar) def __call__(self, x, prior=False): if not self.updated_strategy.item() and not prior: with torch.no_grad(): # Get unwhitened p(u) prior_function_dist = self(self.inducing_points, prior=True) prior_mean = prior_function_dist.loc L = self._cholesky_factor(prior_function_dist.lazy_covariance_matrix.add_jitter()) # Temporarily turn off noise that's added to the mean orig_mean_init_std = self._variational_distribution.mean_init_std self._variational_distribution.mean_init_std = 0.0 # Change the variational parameters to be whitened variational_dist = self.variational_distribution mean_diff = (variational_dist.loc - prior_mean).unsqueeze(-1).double() whitened_mean = L.inv_matmul(mean_diff).squeeze(-1).to(variational_dist.loc.dtype) covar_root = variational_dist.lazy_covariance_matrix.root_decomposition().root.evaluate().double() whitened_covar = RootLazyTensor(L.inv_matmul(covar_root).to(variational_dist.loc.dtype)) whitened_variational_distribution = variational_dist.__class__(whitened_mean, whitened_covar) self._variational_distribution.initialize_variational_distribution(whitened_variational_distribution) # Reset the random noise parameter of the model self._variational_distribution.mean_init_std = orig_mean_init_std # Reset the cache clear_cache_hook(self) # Mark that we have updated the variational strategy self.updated_strategy.fill_(True) return super().__call__(x, prior=prior)