GPSat.models.multioutput package

Submodules

GPSat.models.multioutput.gpr module

class GPSat.models.multioutput.gpr.MultioutputGPR(data, kernel, num_latent_gps, mean_function=None, noise_variance=None, likelihood: LinearModelLikelihood = None)

Bases: GPR

log_marginal_likelihood() → Tensor

Computes the log marginal likelihood.

\[\log p(Y | \theta).\]
Returns:

  • return has shape [].

predict_f(Xnew, full_cov: bool = False, full_output_cov: bool = False)

For backwards compatibility, GPR’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, …)

Parameters:

Xnew –

  • Xnew has shape [batch…, N, D].

Returns:

  • return[0] has shape [batch…, N, P].

  • return[1] has shape [batch…, N, P, N, P] if full_cov and full_output_cov.

  • return[1] has shape [batch…, N, P, P] if (not full_cov) and full_output_cov.

  • return[1] has shape [batch…, N, P] if (not full_cov) and (not full_output_cov).

  • return[1] has shape [batch…, P, N, N] if full_cov and (not full_output_cov).

class GPSat.models.multioutput.gpr.MultioutputSVGP(kernel: LinearCoregionalization, likelihood: ForwardModelLikelihood, inducing_variable: InducingVariables | Tensor | ndarray[Any, Any], *, mean_function: MeanFunction | None = None, q_diag: bool = False, q_mu: Tensor | None = None, q_sqrt: Tensor | None = None, num_data: Tensor | None = None)

Bases: SVGP

elbo(data) → Tensor

This gives a variational bound (the evidence lower bound or ELBO) on the log marginal likelihood of the model.

Returns:

  • return has shape [].

GPSat.models.multioutput.likelihoods module

class GPSat.models.multioutput.likelihoods.ForwardModelLikelihood(variance: Tensor, *args, **kwargs)

Bases: ABC

Base class for likelihoods defined via a measurement model y = h(x) + noise This requires a) a forward model h(x) and b) a measurement error covariance R

abstract get_model(*args, **kwargs) → ForwardModel

Returns a ForwardModel object defining h(x)

class GPSat.models.multioutput.likelihoods.LinearModelLikelihood(input_dim: int, variance: Tensor, forward_model: Tensor | LinearForwardModel)

Bases: Likelihood, ForwardModelLikelihood

Implements likelihood of form y = Hx + noise for a linear operator H

get_model(input_dim, forward_model)

Returns a ForwardModel object defining h(x)

predict_log_density(X, Fmu, Fcov, Y)

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:

  • X –

    • X has shape [broadcast batch…, input_dim].

    input tensor

  • Fmu –

    • Fmu has shape [broadcast batch…, latent_dim].

    mean function evaluation tensor

  • Fvar –

    • Fvar has shape [broadcast batch…, latent_dim].

    variance of function evaluation tensor

  • Y –

    • Y has shape [broadcast batch…, observation_dim].

    observation tensor

Returns:

  • return has shape [batch…].

log predictive density

predict_mean_and_var(X, Fmu, Fcov)

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:

  • X –

    • X has shape [broadcast batch…, input_dim].

    input tensor

  • Fmu –

    • Fmu has shape [broadcast batch…, latent_dim].

    mean function evaluation tensor

  • Fvar –

    • Fvar has shape [broadcast batch…, latent_dim].

    variance of function evaluation tensor

Returns:

  • return[0] has shape [batch…, observation_dim].

  • return[1] has shape [batch…, observation_dim].

mean and variance

variance_at(X) → Tensor
variational_expectations(X, Fmu, Fcov, Y)

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:

  • X –

    • X has shape [broadcast batch…, input_dim].

    input tensor

  • Fmu –

    • Fmu has shape [broadcast batch…, latent_dim].

    mean function evaluation tensor

  • Fvar –

    • Fvar has shape [broadcast batch…, latent_dim].

    variance of function evaluation tensor

  • Y –

    • Y has shape [broadcast batch…, observation_dim].

    observation tensor

Returns:

  • return has shape [batch…].

expected log density of the data given q(F)

class GPSat.models.multioutput.likelihoods.NonlinearModelLikelihood(forward_model: ForwardModel, variance: Tensor, num_samples: int = 100)

Bases: MonteCarloLikelihood, ForwardModelLikelihood

Implements likelihood of form y = h(x) + noise for a nonlinear operator h The variational expectation ∫log p(y|f)q(f)df is computed using Monte-Carlo method

get_model(forward_model)

Returns a ForwardModel object defining h(x)

variational_expectations(X, Fmu, Fcov, Y)

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:

  • X –

    • X has shape [broadcast batch…, input_dim].

    input tensor

  • Fmu –

    • Fmu has shape [broadcast batch…, latent_dim].

    mean function evaluation tensor

  • Fvar –

    • Fvar has shape [broadcast batch…, latent_dim].

    variance of function evaluation tensor

  • Y –

    • Y has shape [broadcast batch…, observation_dim].

    observation tensor

Returns:

  • return has shape [batch…].

expected log density of the data given q(F)

GPSat.models.multioutput.models module

GPSat.models.multioutput.utils module

class GPSat.models.multioutput.utils.ForwardModel(input_dim: int, latent_dim: int, observation_dim: int, *args, **kwargs)

Bases: ABC

class GPSat.models.multioutput.utils.LinearForwardModel(input_dim: int, latent_dim: int, observation_dim: int, H: Tensor | ndarray)

Bases: ForwardModel

Class for linear forward models y = Hx where H is a P x L matrix

propagate_cov(Fcov: Tensor)

Computes the second moment ∫ (H(x-μ))’(H(x-μ)) p(x)dx = HΣH’ where Σ is the covariance of x

propagate_mean(Fmu: Tensor)

Computes the first moment ∫ Hx p(x)dx = Hμ where μ is the mean of x

GPSat.models.multioutput.utils.add_likelihood_noise_cov(K, R)
GPSat.models.multioutput.utils.multioutput_conditional(Kmn: Tensor, Kmm: Tensor, Knn: Tensor, f: Tensor, H: Tensor, R: Tensor, *, full_cov=False)
GPSat.models.multioutput.utils.multivariate_gaussian_log_density(x, mu, cov) → Tensor

Module contents