twodlearn.bayesnet.gaussian_process module¶

class twodlearn.bayesnet.gaussian_process.BasisBase(**kargs)[source]¶

Bases: twodlearn.core.common.TdlModel

class Basis(value)[source]¶

Bases: object

matmul(mat)[source]¶: Evaluate basis over the given matrix.

matvec(vec)[source]¶: Evaluate basis over the given vectors.

basis_fn(inputs)[source]¶

basis_shape[source]¶

input_shape[source]¶

kernel[source]¶

prior[source]¶

tolerance[source]¶

units[source]¶

class twodlearn.bayesnet.gaussian_process.ExplicitVGP(**kargs)[source]¶

Bases: twodlearn.core.common.TdlModel

class EVGPInference(**kargs)[source]¶

Bases: twodlearn.core.common.TdlModel

property basis[source]¶

basis_m[source]¶

basis_x[source]¶

cov_residuals[source]¶

expected_residuals[source]¶: Kxm @ inv(Kmm) @ fm.loc

property fm[source]¶

inputs[source]¶

property kernel[source]¶

kmm[source]¶

kmx[source]¶

model[source]¶: ExplicitVGP model

property xm[source]¶

y_scale[source]¶: linear operation for y_scale

class EVGPPrediction(**kargs)[source]¶

Bases: twodlearn.bayesnet.gaussian_process.EVGPInference, twodlearn.bayesnet.distributions.MVN

covariance[source]¶

loc[source]¶

neg_elbo(labels, dataset_size=None)[source]¶

with_noise()[source]¶: return the posterior with noise

class VariationalLoss(**kargs)[source]¶

Bases: twodlearn.core.common.TdlModel

batch_size[source]¶

dataset_size[source]¶: number of samples in the entire dataset

elbo[source]¶

property inputs[source]¶

labels[source]¶

property model[source]¶

posterior[source]¶

value[source]¶: negative variational lower bound

basis[source]¶

batch_shape[source]¶: Number of output dimensions.

fm[source]¶: Inducing points for the model.

input_shape[source]¶

kernel[source]¶: Autoinit with arguments [‘l_scale’, ‘f_scale’]

m[source]¶: number of inducing points

neg_elbo(inputs, labels, dataset_size=None)[source]¶

predict(inputs, tolerance=None)[source]¶

tolerance[source]¶

xm[source]¶: inducing input points for the model

y_scale[source]¶: Measurement scale y sim N(g, y_scale**2 I)

class twodlearn.bayesnet.gaussian_process.GPNegLogEvidence(cov, cov_inv=None, labels=None, loc=None, name=None)[source]¶

Bases: twodlearn.losses.EmpiricalLoss

Negative log evidence for a Gaussian Process with training covariance cov = K(train, train).

The loss takes the following form

loss = 0.5(y^T inv(cov) y + log(|cov|) + n log(2 pi))

if conv_inv can be provided when instiating the loss to prevent computing the inverse multiple times

define_fit_loss(cov, cov_inv, labels, loc)[source]¶

labels[source]¶

class twodlearn.bayesnet.gaussian_process.GaussianProcess(xm, ym, y_scale=0.1, kernel=None, options=None, name=None, **kargs)[source]¶

Bases: twodlearn.core.common.TdlModel

Gaussian process with zero mean.

The covariance kernel takes by default the following form

# X1 is a matrix, whose rows represent samples
# X2 is a matrix, whose rows represent samples
K(i,j) = (f_scale**2) exp(-0.5 (x1(i)-x2(j))^T (l**-2)I (x1(i)-x2(j)) )

By default, when float values of l_scale, f_scale and y_scale are provided, a trainable variable is created. If want them fixed, you can provide a kernel with parameters as tf.Variable(value, trainable=False)

class GPPosterior(**kargs)[source]¶

Bases: twodlearn.bayesnet.gaussian_process.GpOutput, twodlearn.bayesnet.distributions.MVN

Compute the posterior distribution for p(f*| x*, ym, Xm) where {ym, Xm} is the training dataset of the GP model.

covariance[source]¶

loc[source]¶

with_noise()[source]¶: return the posterior with noise

class GpOutput(**kargs)[source]¶

Bases: twodlearn.core.common.OutputModel

inputs[source]¶

k11[source]¶

k12[source]¶

k22[source]¶

model[source]¶: GP model

property xm[source]¶

y_scale[source]¶

property ym[source]¶

kernel[source]¶

m[source]¶

marginal_likelihood(*args, **kargs)[source]¶

predict(inputs)[source]¶

Compute the posterior distribution for p(f*| x*, y, X) where {y, X} is the training dataset of the GP model. :param inputs: matrix with test inputs x*. :type inputs: tf.Tensor, TdlModel

Returns

TdlModel with the value of p(f*| x*, y, X).: loc: mean for f* scale: scale for f* posterior: distributions for y* and f*

Return type

GpOutput

tolerance[source]¶

xm[source]¶

y_scale[source]¶

y sim N(f, y_scale**2 I)

Type: Measurement scale

ym[source]¶

class twodlearn.bayesnet.gaussian_process.GpWithExplicitMean(gp_model, prior_scale=None, explicit_basis=None, **kargs)[source]¶

Bases: twodlearn.core.common.TdlModel

class EGPPosterior(**kargs)[source]¶

Bases: twodlearn.bayesnet.gaussian_process.EGpOutput, twodlearn.bayesnet.distributions.MVN

covariance[source]¶

loc[source]¶

class EGpOutput(**kargs)[source]¶

Bases: twodlearn.core.common.TdlModel

basis[source]¶

beta_mean[source]¶

beta_r[source]¶

property gp_model[source]¶

gp_output[source]¶

ht_k11inv_h[source]¶

inputs[source]¶

property k11[source]¶

property k12[source]¶

model[source]¶

property tolerance[source]¶

class MarginalOutput(**kargs)[source]¶

Bases: twodlearn.core.common.OutputModel

A[source]¶

basis[source]¶

gp_marginal[source]¶

property gp_model[source]¶

k11[source]¶

property prior_scale[source]¶

yCy[source]¶

explicit_basis[source]¶

gp_model[source]¶

marginal_likelihood(*args, **kargs)[source]¶

predict(inputs)[source]¶

Compute the posterior distribution for p(f*| x*, y, X) where {y, X} is the training dataset of the GP model. :param inputs: matrix with test inputs x*. :type inputs: tf.Tensor, TdlModel

Returns