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import numpy as np
import tensorflow as tf
from .. import kullback_leiblers, posteriors
from ..base import InputData, MeanAndVariance, Parameter, RegressionData
from ..conditionals import conditional
from ..config import default_float
from ..utilities import positive, triangular
from .model import GPModel
from .training_mixins import ExternalDataTrainingLossMixin
from .util import inducingpoint_wrapper
[docs]class SVGP_deprecated(GPModel, ExternalDataTrainingLossMixin):
"""
This is the Sparse Variational GP (SVGP). The key reference is
::
@inproceedings{hensman2014scalable,
title={Scalable Variational Gaussian Process Classification},
author={Hensman, James and Matthews, Alexander G. de G. and Ghahramani, Zoubin},
booktitle={Proceedings of AISTATS},
year={2015}
}
"""
def __init__(
self,
kernel,
likelihood,
inducing_variable,
*,
mean_function=None,
num_latent_gps: int = 1,
q_diag: bool = False,
q_mu=None,
q_sqrt=None,
whiten: bool = True,
num_data=None,
):
"""
- kernel, likelihood, inducing_variables, mean_function are appropriate
GPflow objects
- num_latent_gps is the number of latent processes to use, defaults to 1
- q_diag is a boolean. If True, the covariance is approximated by a
diagonal matrix.
- whiten is a boolean. If True, we use the whitened representation of
the inducing points.
- num_data is the total number of observations, defaults to X.shape[0]
(relevant when feeding in external minibatches)
"""
# init the super class, accept args
super().__init__(kernel, likelihood, mean_function, num_latent_gps)
self.num_data = num_data
self.q_diag = q_diag
self.whiten = whiten
self.inducing_variable = inducingpoint_wrapper(inducing_variable)
# init variational parameters
num_inducing = self.inducing_variable.num_inducing
self._init_variational_parameters(num_inducing, q_mu, q_sqrt, q_diag)
def _init_variational_parameters(self, num_inducing, q_mu, q_sqrt, q_diag):
"""
Constructs the mean and cholesky of the covariance of the variational Gaussian posterior.
If a user passes values for `q_mu` and `q_sqrt` the routine checks if they have consistent
and correct shapes. If a user does not specify any values for `q_mu` and `q_sqrt`, the routine
initializes them, their shape depends on `num_inducing` and `q_diag`.
Note: most often the comments refer to the number of observations (=output dimensions) with P,
number of latent GPs with L, and number of inducing points M. Typically P equals L,
but when certain multioutput kernels are used, this can change.
Parameters
----------
:param num_inducing: int
Number of inducing variables, typically refered to as M.
:param q_mu: np.array or None
Mean of the variational Gaussian posterior. If None the function will initialise
the mean with zeros. If not None, the shape of `q_mu` is checked.
:param q_sqrt: np.array or None
Cholesky of the covariance of the variational Gaussian posterior.
If None the function will initialise `q_sqrt` with identity matrix.
If not None, the shape of `q_sqrt` is checked, depending on `q_diag`.
:param q_diag: bool
Used to check if `q_mu` and `q_sqrt` have the correct shape or to
construct them with the correct shape. If `q_diag` is true,
`q_sqrt` is two dimensional and only holds the square root of the
covariance diagonal elements. If False, `q_sqrt` is three dimensional.
"""
q_mu = np.zeros((num_inducing, self.num_latent_gps)) if q_mu is None else q_mu
self.q_mu = Parameter(q_mu, dtype=default_float()) # [M, P]
if q_sqrt is None:
if self.q_diag:
ones = np.ones((num_inducing, self.num_latent_gps), dtype=default_float())
self.q_sqrt = Parameter(ones, transform=positive()) # [M, P]
else:
q_sqrt = [
np.eye(num_inducing, dtype=default_float()) for _ in range(self.num_latent_gps)
]
q_sqrt = np.array(q_sqrt)
self.q_sqrt = Parameter(q_sqrt, transform=triangular()) # [P, M, M]
else:
if q_diag:
assert q_sqrt.ndim == 2
self.num_latent_gps = q_sqrt.shape[1]
self.q_sqrt = Parameter(q_sqrt, transform=positive()) # [M, L|P]
else:
assert q_sqrt.ndim == 3
self.num_latent_gps = q_sqrt.shape[0]
num_inducing = q_sqrt.shape[1]
self.q_sqrt = Parameter(q_sqrt, transform=triangular()) # [L|P, M, M]
def prior_kl(self) -> tf.Tensor:
return kullback_leiblers.prior_kl(
self.inducing_variable, self.kernel, self.q_mu, self.q_sqrt, whiten=self.whiten
)
[docs] def maximum_log_likelihood_objective(self, data: RegressionData) -> tf.Tensor:
return self.elbo(data)
[docs] def elbo(self, data: RegressionData) -> tf.Tensor:
"""
This gives a variational bound (the evidence lower bound or ELBO) on
the log marginal likelihood of the model.
"""
X, Y = data
kl = self.prior_kl()
f_mean, f_var = self.predict_f(X, full_cov=False, full_output_cov=False)
var_exp = self.likelihood.variational_expectations(f_mean, f_var, Y)
if self.num_data is not None:
num_data = tf.cast(self.num_data, kl.dtype)
minibatch_size = tf.cast(tf.shape(X)[0], kl.dtype)
scale = num_data / minibatch_size
else:
scale = tf.cast(1.0, kl.dtype)
return tf.reduce_sum(var_exp) * scale - kl
def predict_f(self, Xnew: InputData, full_cov=False, full_output_cov=False) -> MeanAndVariance:
mu, var = conditional(
Xnew,
self.inducing_variable,
self.kernel,
self.q_mu,
q_sqrt=self.q_sqrt,
full_cov=full_cov,
white=self.whiten,
full_output_cov=full_output_cov,
)
# tf.debugging.assert_positive(var) # We really should make the tests pass with this here
return mu + self.mean_function(Xnew), var
[docs]class SVGP_with_posterior(SVGP_deprecated):
"""
This is the Sparse Variational GP (SVGP). The key reference is
::
@inproceedings{hensman2014scalable,
title={Scalable Variational Gaussian Process Classification},
author={Hensman, James and Matthews, Alexander G. de G. and Ghahramani, Zoubin},
booktitle={Proceedings of AISTATS},
year={2015}
}
This class provides a posterior() method that enables caching for faster subsequent predictions.
"""
[docs] def posterior(self, precompute_cache=posteriors.PrecomputeCacheType.TENSOR):
"""
Create the Posterior object which contains precomputed matrices for
faster prediction.
precompute_cache has three settings:
- `PrecomputeCacheType.TENSOR` (or `"tensor"`): Precomputes the cached
quantities and stores them as tensors (which allows differentiating
through the prediction). This is the default.
- `PrecomputeCacheType.VARIABLE` (or `"variable"`): Precomputes the cached
quantities and stores them as variables, which allows for updating
their values without changing the compute graph (relevant for AOT
compilation).
- `PrecomputeCacheType.NOCACHE` (or `"nocache"` or `None`): Avoids
immediate cache computation. This is useful for avoiding extraneous
computations when you only want to call the posterior's
`fused_predict_f` method.
"""
return posteriors.create_posterior(
self.kernel,
self.inducing_variable,
self.q_mu,
self.q_sqrt,
whiten=self.whiten,
mean_function=self.mean_function,
precompute_cache=precompute_cache,
)
[docs] def predict_f(self, Xnew: InputData, full_cov=False, full_output_cov=False) -> MeanAndVariance:
"""
For backwards compatibility, SVGP's predict_f uses the fused (no-cache)
computation, which is more efficient during training.
For faster (cached) prediction, predict directly from the posterior object, i.e.,:
model.posterior().predict_f(Xnew, ...)
"""
return self.posterior(posteriors.PrecomputeCacheType.NOCACHE).fused_predict_f(
Xnew, full_cov=full_cov, full_output_cov=full_output_cov
)
[docs]class SVGP(SVGP_with_posterior):
# subclassed to ensure __class__ == "SVGP"
pass