gpflow.likelihoods¶

gpflow.likelihoods.Bernoulli¶

class gpflow.likelihoods.Bernoulli(invlink=<function inv_probit>, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.ScalarLikelihood

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

invlink (Callable[[Tensor], Tensor]) –
kwargs (Any) –

gpflow.likelihoods.Beta¶

class gpflow.likelihoods.Beta(invlink=<function inv_probit>, scale=1.0, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.ScalarLikelihood

This uses a reparameterisation of the Beta density. We have the mean of the Beta distribution given by the transformed process:

m = invlink(f)

and a scale parameter. The familiar α, β parameters are given by

m = α / (α + β) scale = α + β

so:: α = scale * m β = scale * (1-m)

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

invlink (Callable[[Tensor], Tensor]) –
scale (float) –
kwargs (Any) –

gpflow.likelihoods.Exponential¶

class gpflow.likelihoods.Exponential(invlink=<function exp>, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.ScalarLikelihood

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

invlink (Callable[[Tensor], Tensor]) –
kwargs (Any) –

gpflow.likelihoods.Gamma¶

class gpflow.likelihoods.Gamma(invlink=<function exp>, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.ScalarLikelihood

Use the transformed GP to give the scale (inverse rate) of the Gamma

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

invlink (Callable[[Tensor], Tensor]) –
kwargs (Any) –

gpflow.likelihoods.Gaussian¶

class gpflow.likelihoods.Gaussian(variance=1.0, variance_lower_bound=1e-06, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.ScalarLikelihood

The Gaussian likelihood is appropriate where uncertainties associated with the data are believed to follow a normal distribution, with constant variance.

Very small uncertainties can lead to numerical instability during the optimization process. A lower bound of 1e-6 is therefore imposed on the likelihood variance by default.

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

variance (float) –
variance_lower_bound (float) –
kwargs (Any) –

gpflow.likelihoods.GaussianMC¶

class gpflow.likelihoods.GaussianMC(*args, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.MonteCarloLikelihood, gpflow.likelihoods.scalar_continuous.Gaussian

Stochastic version of Gaussian likelihood for demonstration purposes only.

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

args (Any) –
kwargs (Any) –

gpflow.likelihoods.HeteroskedasticTFPConditional¶

class gpflow.likelihoods.HeteroskedasticTFPConditional(distribution_class=<class 'tensorflow_probability.python.distributions.normal.Normal'>, scale_transform=None, **kwargs)[source]¶

Bases: gpflow.likelihoods.multilatent.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.

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

distribution_class (Type[Distribution]) –
scale_transform (Optional[Bijector]) –
kwargs (Any) –

gpflow.likelihoods.Likelihood¶

class gpflow.likelihoods.Likelihood(latent_dim, observation_dim)[source]¶

Bases: gpflow.base.Module

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

latent_dim (Optional[int]) –
observation_dim (Optional[int]) –

conditional_mean(F)[source]¶

The conditional mean of Y|F: [E[Y₁|F], …, E[Yₖ|F]] where K = observation_dim

Parameters: F (Union[ndarray, Tensor, Variable, Parameter]) – function evaluation Tensor, with shape […, latent_dim]
Return type: Tensor
Returns: mean […, observation_dim]

conditional_variance(F)[source]¶

The conditional marginal variance of Y|F: [var(Y₁|F), …, var(Yₖ|F)] where K = observation_dim

Parameters: F (Union[ndarray, Tensor, Variable, Parameter]) – function evaluation Tensor, with shape […, latent_dim]
Return type: Tensor
Returns: variance […, observation_dim]

log_prob(F, Y)[source]¶

The log probability density log p(Y|F)

Parameters

F (Union[ndarray, Tensor, Variable, Parameter]) – function evaluation Tensor, with shape […, latent_dim]
Y (Union[ndarray, Tensor, Variable, Parameter]) – observation Tensor, with shape […, observation_dim]:

Return type

Tensor

Returns

log pdf, with shape […]

predict_density(Fmu, Fvar, Y)[source]¶

Deprecated: see predict_log_density

Parameters

Fmu (Union[ndarray, Tensor, Variable, Parameter]) –
Fvar (Union[ndarray, Tensor, Variable, Parameter]) –
Y (Union[ndarray, Tensor, Variable, Parameter]) –

Return type

Tensor

predict_log_density(Fmu, Fvar, Y)[source]¶

Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,

i.e. if: q(F) = N(Fmu, Fvar)

and this object represents

p(y|F)

then this method computes the predictive density

log ∫ p(y=Y|F)q(F) df

Parameters

Fmu (Union[ndarray, Tensor, Variable, Parameter]) – mean function evaluation Tensor, with shape […, latent_dim]
Fvar (Union[ndarray, Tensor, Variable, Parameter]) – variance of function evaluation Tensor, with shape […, latent_dim]
Y (Union[ndarray, Tensor, Variable, Parameter]) – observation Tensor, with shape […, observation_dim]:

Return type

Tensor

Returns

log predictive density, with shape […]

predict_mean_and_var(Fmu, Fvar)[source]¶

Given a Normal distribution for the latent function, return the mean and marginal variance of Y,

i.e. if: q(f) = N(Fmu, Fvar)

and this object represents

p(y|f)

then this method computes the predictive mean

∫∫ y p(y|f)q(f) df dy

and the predictive variance

∫∫ y² p(y|f)q(f) df dy - [ ∫∫ y p(y|f)q(f) df dy ]²

Parameters

Fmu (Union[ndarray, Tensor, Variable, Parameter]) – mean function evaluation Tensor, with shape […, latent_dim]
Fvar (Union[ndarray, Tensor, Variable, Parameter]) – variance of function evaluation Tensor, with shape […, latent_dim]

Return type

Tuple[Tensor, Tensor]

Returns

mean and variance, both with shape […, observation_dim]

variational_expectations(Fmu, Fvar, Y)[source]¶

Compute the expected log density of the data, given a Gaussian distribution for the function values,

i.e. if: q(f) = N(Fmu, Fvar)

and this object represents

p(y|f)

then this method computes

∫ log(p(y=Y|f)) q(f) df.

This only works if the broadcasting dimension of the statistics of q(f) (mean and variance) are broadcastable with that of the data Y.

Parameters

Fmu (Union[ndarray, Tensor, Variable, Parameter]) – mean function evaluation Tensor, with shape […, latent_dim]
Fvar (Union[ndarray, Tensor, Variable, Parameter]) – variance of function evaluation Tensor, with shape […, latent_dim]
Y (Union[ndarray, Tensor, Variable, Parameter]) – observation Tensor, with shape […, observation_dim]:

Return type

Tensor

Returns

expected log density of the data given q(F), with shape […]

gpflow.likelihoods.MonteCarloLikelihood¶

class gpflow.likelihoods.MonteCarloLikelihood(*args, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.Likelihood

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

args (Any) –
kwargs (Any) –

gpflow.likelihoods.MultiClass¶

class gpflow.likelihoods.MultiClass(num_classes, invlink=None, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.Likelihood

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

num_classes (int) –
invlink (Optional[RobustMax]) –
kwargs (Any) –

gpflow.likelihoods.MultiLatentLikelihood¶

class gpflow.likelihoods.MultiLatentLikelihood(latent_dim, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.QuadratureLikelihood

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.

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

latent_dim (int) –
kwargs (Any) –

gpflow.likelihoods.MultiLatentTFPConditional¶

class gpflow.likelihoods.MultiLatentTFPConditional(latent_dim, conditional_distribution, **kwargs)[source]¶

Bases: gpflow.likelihoods.multilatent.MultiLatentLikelihood

MultiLatent likelihood where the conditional distribution is given by a TensorFlow Probability Distribution.

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

latent_dim (int) –
conditional_distribution (Callable[..., Distribution]) –
kwargs (Any) –

gpflow.likelihoods.Ordinal¶

class gpflow.likelihoods.Ordinal(bin_edges, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.ScalarLikelihood

A likelihood for doing ordinal regression.

The data are integer values from 0 to k, and the user must specify (k-1) ‘bin edges’ which define the points at which the labels switch. Let the bin edges be [a₀, a₁, … aₖ₋₁], then the likelihood is

p(Y=0|F) = ɸ((a₀ - F) / σ) p(Y=1|F) = ɸ((a₁ - F) / σ) - ɸ((a₀ - F) / σ) p(Y=2|F) = ɸ((a₂ - F) / σ) - ɸ((a₁ - F) / σ) … p(Y=K|F) = 1 - ɸ((aₖ₋₁ - F) / σ)

where ɸ is the cumulative density function of a Gaussian (the inverse probit function) and σ is a parameter to be learned. A reference is:

@article{chu2005gaussian,: title={Gaussian processes for ordinal regression}, author={Chu, Wei and Ghahramani, Zoubin}, journal={Journal of Machine Learning Research}, volume={6}, number={Jul}, pages={1019–1041}, year={2005}

}

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

bin_edges (ndarray) –
kwargs (Any) –

gpflow.likelihoods.Poisson¶

class gpflow.likelihoods.Poisson(invlink=<function exp>, binsize=1.0, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.ScalarLikelihood

Poisson likelihood for use with count data, where the rate is given by the (transformed) GP.

let g(.) be the inverse-link function, then this likelihood represents

p(yᵢ | fᵢ) = Poisson(yᵢ | g(fᵢ) * binsize)

Note:binsize For use in a Log Gaussian Cox process (doubly stochastic model) where the rate function of an inhomogeneous Poisson process is given by a GP. The intractable likelihood can be approximated via a Riemann sum (with bins of size ‘binsize’) and using this Poisson likelihood.

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

invlink (Callable[[Tensor], Tensor]) –
binsize (float) –
kwargs (Any) –

gpflow.likelihoods.QuadratureLikelihood¶

class gpflow.likelihoods.QuadratureLikelihood(latent_dim, observation_dim, *, quadrature=None)[source]¶

Bases: gpflow.likelihoods.base.Likelihood

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

latent_dim (Optional[int]) –
observation_dim (Optional[int]) –
quadrature (Optional[GaussianQuadrature]) –

gpflow.likelihoods.RobustMax¶

class gpflow.likelihoods.RobustMax(num_classes, epsilon=0.001, **kwargs)[source]¶

Bases: gpflow.base.Module

This class represent a multi-class inverse-link function. Given a vector f=[f_1, f_2, … f_k], the result of the mapping is

y = [y_1 … y_k]

with

y_i = (1-epsilon) i == argmax(f): epsilon/(k-1) otherwise

where k is the number of classes.

Attributes

eps_k1
name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`__call__`(F)	Call self as a function.
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

prob_is_largest
safe_sqrt

Parameters

num_classes (int) –
epsilon (float) –
kwargs (Any) –

gpflow.likelihoods.ScalarLikelihood¶

class gpflow.likelihoods.ScalarLikelihood(**kwargs)[source]¶

Bases: gpflow.likelihoods.base.QuadratureLikelihood

A likelihood class that helps with scalar likelihood functions: likelihoods where each scalar latent function is associated with a single scalar observation variable.

If there are multiple latent functions, then there must be a corresponding number of data: we check for this.

The Likelihood class contains methods to compute marginal statistics of functions of the latents and the data ϕ(y,f):

variational_expectations: ϕ(y,f) = log p(y|f)

predict_log_density: ϕ(y,f) = p(y|f)

Those statistics are computed after having first marginalized the latent processes f under a multivariate normal distribution q(f) that is fully factorized.

Some univariate integrals can be done by quadrature: we implement quadrature routines for 1D integrals in this class, though they may be overwritten by inheriting classes where those integrals are available in closed form.

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters: kwargs (Any) –

gpflow.likelihoods.Softmax¶

class gpflow.likelihoods.Softmax(num_classes, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.MonteCarloLikelihood

The soft-max multi-class likelihood. It can only provide a stochastic Monte-Carlo estimate of the variational expectations term, but this added variance tends to be small compared to that due to mini-batching (when using the SVGP model).

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

num_classes (int) –
kwargs (Any) –

gpflow.likelihoods.StudentT¶

class gpflow.likelihoods.StudentT(scale=1.0, df=3.0, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.ScalarLikelihood

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

scale (float) –
df (float) –
kwargs (Any) –

gpflow.likelihoods.SwitchedLikelihood¶

class gpflow.likelihoods.SwitchedLikelihood(likelihood_list, **kwargs)[source]¶

Bases: gpflow.likelihoods.base.ScalarLikelihood

Attributes

name: Returns the name of this module as passed or determined in the ctor.
name_scope: Returns a tf.name_scope instance for this class.
non_trainable_variables: Sequence of non-trainable variables owned by this module and its submodules.
num_gauss_hermite_points
parameters
submodules: Sequence of all sub-modules.
trainable_parameters
trainable_variables: Sequence of trainable variables owned by this module and its submodules.
variables: Sequence of variables owned by this module and its submodules.

Methods

`conditional_mean`(F)	The conditional mean of Y\|F: [E[Y₁\|F], ..., E[Yₖ\|F]] where K = observation_dim
`conditional_variance`(F)	The conditional marginal variance of Y\|F: [var(Y₁\|F), ..., var(Yₖ\|F)] where K = observation_dim
`log_prob`(F, Y)	The log probability density log p(Y\|F)
`predict_density`(Fmu, Fvar, Y)	Deprecated: see predict_log_density
`predict_log_density`(Fmu, Fvar, Y)	Given a Normal distribution for the latent function, and a datum Y, compute the log predictive density of Y,
`predict_mean_and_var`(Fmu, Fvar)	Given a Normal distribution for the latent function, return the mean and marginal variance of Y,
`variational_expectations`(Fmu, Fvar, Y)	Compute the expected log density of the data, given a Gaussian distribution for the function values,
`with_name_scope`(method)	Decorator to automatically enter the module name scope.

Parameters

likelihood_list (Iterable[ScalarLikelihood]) –
kwargs (Any) –

gpflow.likelihoods.utils¶

gpflow.likelihoods.utils