Source code for gpflow.likelihoods.multilatent

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from typing import Any, Callable, Optional, Type

import tensorflow as tf
import tensorflow_probability as tfp
from check_shapes import check_shapes, inherit_check_shapes

from ..base import TensorType
from ..utilities import positive
from .base import QuadratureLikelihood


[docs] class MultiLatentLikelihood(QuadratureLikelihood): r""" A Likelihood which assumes that a single dimensional observation is driven by multiple latent GPs. Note that this implementation does not allow for taking into account covariance between outputs. """ def __init__(self, latent_dim: int, **kwargs: Any) -> None: super().__init__( input_dim=None, latent_dim=latent_dim, observation_dim=1, **kwargs, )
[docs] class MultiLatentTFPConditional(MultiLatentLikelihood): """ MultiLatent likelihood where the conditional distribution is given by a TensorFlow Probability Distribution. """ def __init__( self, latent_dim: int, conditional_distribution: Callable[..., tfp.distributions.Distribution], **kwargs: Any, ): """ :param latent_dim: number of arguments to the `conditional_distribution` callable :param conditional_distribution: function from F to a tfp Distribution, where F has shape [..., latent_dim] """ super().__init__(latent_dim, **kwargs) self.conditional_distribution = conditional_distribution @inherit_check_shapes def _log_prob(self, X: TensorType, F: TensorType, Y: TensorType) -> tf.Tensor: """ The log probability density log p(Y|F) :param F: function evaluation Tensor, with shape [..., latent_dim] :param Y: observation Tensor, with shape [..., 1]: :returns: log pdf, with shape [...] """ return tf.squeeze(self.conditional_distribution(F).log_prob(Y), -1) @inherit_check_shapes def _conditional_mean(self, X: TensorType, F: TensorType) -> tf.Tensor: """ The conditional marginal mean of Y|F: [E(Y₁|F)] :param F: function evaluation Tensor, with shape [..., latent_dim] :returns: mean [..., 1] """ return self.conditional_distribution(F).mean() @inherit_check_shapes def _conditional_variance(self, X: TensorType, F: TensorType) -> tf.Tensor: """ The conditional marginal variance of Y|F: [Var(Y₁|F)] :param F: function evaluation Tensor, with shape [..., latent_dim] :returns: variance [..., 1] """ return self.conditional_distribution(F).variance()
[docs] class HeteroskedasticTFPConditional(MultiLatentTFPConditional): """ Heteroskedastic Likelihood where the conditional distribution is given by a TensorFlow Probability Distribution. The `loc` and `scale` of the distribution are given by a two-dimensional multi-output GP. """ def __init__( self, distribution_class: Type[tfp.distributions.Distribution] = tfp.distributions.Normal, scale_transform: Optional[tfp.bijectors.Bijector] = None, **kwargs: Any, ) -> None: """ :param distribution_class: distribution class parameterized by `loc` and `scale` as first and second argument, respectively. :param scale_transform: callable/bijector applied to the latent function modelling the scale to ensure its positivity. Typically, `tf.exp` or `tf.softplus`, but can be any function f: R -> R^+. Defaults to exp if not explicitly specified. """ if scale_transform is None: scale_transform = positive(base="exp") self.scale_transform = scale_transform @check_shapes( "F: [batch..., 2]", ) def conditional_distribution(F: TensorType) -> tfp.distributions.Distribution: loc = F[..., :1] scale = self.scale_transform(F[..., 1:]) return distribution_class(loc, scale) super().__init__( latent_dim=2, conditional_distribution=conditional_distribution, **kwargs, )