Source code for gpflow.conditionals.conditionals

# Copyright 2017-2020 The GPflow Contributors. All Rights Reserved.
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# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
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from typing import Optional

import tensorflow as tf
from check_shapes import check_shapes

from ..base import MeanAndVariance
from ..inducing_variables import InducingVariables
from ..kernels import Kernel
from ..posteriors import BasePosterior, VGPPosterior, get_posterior_class
from .dispatch import conditional


[docs]@conditional._gpflow_internal_register(object, InducingVariables, Kernel, object) @check_shapes( "Xnew: [batch..., N, D]", "inducing_variable: [M, D, broadcast R]", "f: [M, R]", "q_sqrt: [M_R_or_R_M_M...]", "return[0]: [batch..., N, R]", "return[1]: [batch..., N, R] if (not full_cov) and (not full_output_cov)", "return[1]: [batch..., R, N, N] if full_cov and (not full_output_cov)", "return[1]: [batch..., N, R, R] if (not full_cov) and full_output_cov", "return[1]: [batch..., N, R, N, R] if full_cov and full_output_cov", ) def _sparse_conditional( Xnew: tf.Tensor, inducing_variable: InducingVariables, kernel: Kernel, f: tf.Tensor, *, full_cov: bool = False, full_output_cov: bool = False, q_sqrt: Optional[tf.Tensor] = None, white: bool = False, ) -> MeanAndVariance: """ Single-output GP conditional. The covariance matrices used to calculate the conditional have the following shape: - Kuu: [M, M] - Kuf: [M, N] - Kff: [N, N] Further reference: - See `gpflow.conditionals._dense_conditional` (below) for a detailed explanation of conditional in the single-output case. - See the multiouput notebook for more information about the multiouput framework. :param Xnew: data matrix :param f: data matrix :param full_cov: return the covariance between the datapoints :param full_output_cov: return the covariance between the outputs. NOTE: as we are using a single-output kernel with repetitions these covariances will be zero. :param q_sqrt: matrix of standard-deviations or Cholesky matrices, size [M, R] or [R, M, M]. :param white: boolean of whether to use the whitened representation :return: mean and variance """ posterior_class = get_posterior_class(kernel, inducing_variable) posterior: BasePosterior = posterior_class( kernel, inducing_variable, f, q_sqrt, whiten=white, mean_function=None, precompute_cache=None, ) return posterior.fused_predict_f(Xnew, full_cov=full_cov, full_output_cov=full_output_cov)
[docs]@conditional._gpflow_internal_register(object, object, Kernel, object) @check_shapes( "Xnew: [batch..., N, D]", "X: [M, D]", "f: [M, R]", "return[0]: [batch..., N, R]", "return[1]: [batch..., N, R] if (not full_cov) and (not full_output_cov)", "return[1]: [batch..., R, N, N] if full_cov and (not full_output_cov)", "return[1]: [batch..., N, R, R] if (not full_cov) and full_output_cov", "return[1]: [batch..., N, R, N, R] if full_cov and full_output_cov", ) def _dense_conditional( Xnew: tf.Tensor, X: tf.Tensor, kernel: Kernel, f: tf.Tensor, *, full_cov: bool = False, full_output_cov: bool = False, q_sqrt: Optional[tf.Tensor] = None, white: bool = False, ) -> MeanAndVariance: """ Given f, representing the GP at the points X, produce the mean and (co-)variance of the GP at the points Xnew. Additionally, there may be Gaussian uncertainty about f as represented by q_sqrt. In this case `f` represents the mean of the distribution and q_sqrt the square-root of the covariance. Additionally, the GP may have been centered (whitened) so that:: p(v) = ๐’ฉ(๐ŸŽ, ๐ˆ) f = ๐‹v thus:: p(f) = ๐’ฉ(๐ŸŽ, ๐‹๐‹แต€) = ๐’ฉ(๐ŸŽ, ๐Š). In this case `f` represents the values taken by v. The method can either return the diagonals of the covariance matrix for each output (default) or the full covariance matrix (full_cov=True). We assume R independent GPs, represented by the columns of f (and the first dimension of q_sqrt). :param Xnew: data matrix. Evaluate the GP at these new points :param X: data points. :param kernel: GPflow kernel. :param f: data matrix, representing the function values at X, for R functions. :param q_sqrt: matrix of standard-deviations or Cholesky matrices, size [M, R] or [R, M, M]. :param white: boolean of whether to use the whitened representation as described above. :return: mean and variance """ posterior = VGPPosterior( kernel=kernel, X=X, q_mu=f, q_sqrt=q_sqrt, white=white, precompute_cache=None, ) return posterior.fused_predict_f(Xnew, full_cov=full_cov, full_output_cov=full_output_cov)