Source code for gpflow.models.svgp

# Copyright 2016-2020 The GPflow Contributors. All Rights Reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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from typing import Optional

import numpy as np
import tensorflow as tf

from .. import kullback_leiblers, posteriors
from ..base import AnyNDArray, InputData, MeanAndVariance, Parameter, RegressionData
from ..conditionals import conditional
from ..config import default_float
from ..experimental.check_shapes import check_shapes, inherit_check_shapes
from ..inducing_variables import InducingVariables
from ..kernels import Kernel
from ..likelihoods import Likelihood
from ..mean_functions import MeanFunction
from ..utilities import positive, triangular
from .model import GPModel
from .training_mixins import ExternalDataTrainingLossMixin
from .util import InducingVariablesLike, inducingpoint_wrapper


[docs]class SVGP_deprecated(GPModel, ExternalDataTrainingLossMixin): """ This is the Sparse Variational GP (SVGP). The key reference is :cite:t:`hensman2014scalable`. """ @check_shapes( "q_mu: [M, P]", "q_sqrt: [M, P] if q_diag", "q_sqrt: [P, M, M] if (not q_diag)", ) def __init__( self, kernel: Kernel, likelihood: Likelihood, inducing_variable: InducingVariablesLike, *, mean_function: Optional[MeanFunction] = None, num_latent_gps: int = 1, q_diag: bool = False, q_mu: Optional[tf.Tensor] = None, q_sqrt: Optional[tf.Tensor] = None, whiten: bool = True, num_data: Optional[tf.Tensor] = 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.whiten = whiten self.inducing_variable: InducingVariables = 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) @check_shapes( "q_mu: [M, P]", "q_sqrt: [M, P] if q_diag", "q_sqrt: [P, M, M] if (not q_diag)", ) def _init_variational_parameters( self, num_inducing: int, q_mu: Optional[AnyNDArray], q_sqrt: Optional[AnyNDArray], q_diag: bool, ) -> None: """ 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: Number of inducing variables, typically refered to as M. :param q_mu: 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: 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: 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 q_diag: ones: AnyNDArray = np.ones( (num_inducing, self.num_latent_gps), dtype=default_float() ) self.q_sqrt = Parameter(ones, transform=positive()) # [M, P] else: np_q_sqrt: AnyNDArray = np.array( [ np.eye(num_inducing, dtype=default_float()) for _ in range(self.num_latent_gps) ] ) self.q_sqrt = Parameter(np_q_sqrt, transform=triangular()) # [P, M, M] else: if q_diag: self.num_latent_gps = q_sqrt.shape[1] self.q_sqrt = Parameter(q_sqrt, transform=positive()) # [M, L|P] else: 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] @check_shapes( "return: []", ) 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 ) # type-ignore is because of changed method signature:
[docs] @inherit_check_shapes def maximum_log_likelihood_objective(self, data: RegressionData) -> tf.Tensor: # type: ignore[override] return self.elbo(data)
[docs] @check_shapes( "return: []", ) 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(X, 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
@inherit_check_shapes def predict_f( self, Xnew: InputData, full_cov: bool = False, full_output_cov: bool = 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 :cite:t:`hensman2014scalable`. This class provides a posterior() method that enables caching for faster subsequent predictions. """
[docs] def posterior( self, precompute_cache: posteriors.PrecomputeCacheType = posteriors.PrecomputeCacheType.TENSOR, ) -> posteriors.BasePosterior: """ 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] @inherit_check_shapes def predict_f( self, Xnew: InputData, full_cov: bool = False, full_output_cov: bool = 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