TransportMaps.Distributions.ConditionalDistributions

Module Contents

Classes

ConditionallyNormalDistribution	Multivariate Gaussian distribution \(\pi({\bf x}\vert{\bf y}) \sim \mathcal{N}(\mu({\bf y}), \Sigma({\bf y}))\)
MeanConditionallyNormalDistribution	Multivariate Gaussian distribution \(\pi({\bf x}\vert{\bf y}) \sim \mathcal{N}(\mu({\bf y}), \Sigma)\)

Attributes

ConditionallyGaussianDistribution
MeanConditionallyGaussianDistribution

class TransportMaps.Distributions.ConditionalDistributions.ConditionallyNormalDistribution(mu, sigma=None, precision=None, coeffs=None)

Bases: TransportMaps.Distributions.ConditionalDistributionBase.ConditionalDistribution

Multivariate Gaussian distribution \(\pi({\bf x}\vert{\bf y}) \sim \mathcal{N}(\mu({\bf y}), \Sigma({\bf y}))\)

Parameters:

• mu (Map) – mean vector map

• sigma (Map) – covariance matrix map

• precision (Map) – precision matrix map

• coeffs (ndarray) – fix the coefficients \({\bf y}\)

property pi

property mu

property sigma

property precision

property muMap

property sigmaMap

property precisionMap

property coeffs

property grad_a_mu

property grad_a_sigma

property grad_a_precision

get_ncalls_tree(indent='')

get_nevals_tree(indent='')

get_teval_tree(indent='')

update_ncalls_tree(obj)

update_nevals_tree(obj)

update_teval_tree(obj)

reset_counters()

rvs(m, y=None, **kwargs)

Generate \(m\) samples from the distribution.

Parameters:

• m (int) – number of samples to generate

• y (ndarray [\(d_y\)]) – conditioning values \({\bf Y}={\bf y}\)

Returns:

(ndarray [\(m,d\)]) – \(m\)

\(d\)-dimensional samples

Raises:

NotImplementedError – the method needs to be defined in the sub-classes

log_pdf(x, y, params=None, idxs_slice=slice(None, None, None), cache=None)

Evaluate \(\log \pi({\bf x}\vert{\bf y})\)

Parameters:

• x (ndarray [\(m,d\)]) – evaluation points

• y (ndarray [\(m,d_y\)] or ndarray [\(d_y\)]) – conditioning values \({\bf Y}={\bf y}\). In the second case one conditioning value is used for all the \(m\) points \({\bf x}\)

• params (dict) – parameters

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(ndarray [\(m\)]) – values of \(\log\pi\)

at the x points.

grad_x_log_pdf(x, y, params=None, idxs_slice=slice(None, None, None), cache=None)

Evaluate \(\nabla_{\bf x,y} \log \pi({\bf x}\vert{\bf y})\)

Parameters:

• x (ndarray [\(m,d\)]) – evaluation points

• y (ndarray [\(m,d_y\)]) – conditioning values \({\bf Y}={\bf y}\)

• params (dict) – parameters

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(ndarray [\(m,d\)]) – values of

\(\nabla_x\log\pi\) at the x points.

TransportMaps.Distributions.ConditionalDistributions.ConditionallyGaussianDistribution

class TransportMaps.Distributions.ConditionalDistributions.MeanConditionallyNormalDistribution(mu, sigma=None, precision=None, coeffs=None)

Bases: TransportMaps.Distributions.ConditionalDistributionBase.ConditionalDistribution

Multivariate Gaussian distribution \(\pi({\bf x}\vert{\bf y}) \sim \mathcal{N}(\mu({\bf y}), \Sigma)\)

Parameters:

• mu (Map) – mean vector map

• sigma (ndarray) – covariance matrix map

• precision (ndarray) – precision matrix map

• coeffs (ndarray) – fix the coefficients \({\bf y}\)

property pi

property mu

property sigma

property precision

property muMap

property coeffs

property grad_a_mu

get_ncalls_tree(indent='')

get_nevals_tree(indent='')

get_teval_tree(indent='')

update_ncalls_tree(obj)

update_nevals_tree(obj)

update_teval_tree(obj)

reset_counters()

rvs(m, y=None, **kwargs)

Generate \(m\) samples from the distribution.

Parameters:

• m (int) – number of samples to generate

• y (ndarray [\(d_y\)]) – conditioning values \({\bf Y}={\bf y}\)

Returns:

(ndarray [\(m,d\)]) – \(m\)

\(d\)-dimensional samples

Raises:

NotImplementedError – the method needs to be defined in the sub-classes

log_pdf(x, y, params=None, idxs_slice=slice(None, None, None), cache=None)

Evaluate \(\log \pi({\bf x}\vert{\bf y})\)

Parameters:

• x (ndarray [\(m,d\)]) – evaluation points

• y (ndarray [\(m,d_y\)] or ndarray [\(d_y\)]) – conditioning values \({\bf Y}={\bf y}\). In the second case one conditioning value is used for all the \(m\) points \({\bf x}\)

• params (dict) – parameters

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(ndarray [\(m\)]) – values of \(\log\pi\)

at the x points.

grad_x_log_pdf(x, y, params=None, idxs_slice=slice(None, None, None), cache=None)

Evaluate \(\nabla_{\bf x,y} \log \pi({\bf x}\vert{\bf y})\)

Parameters:

• x (ndarray [\(m,d\)]) – evaluation points

• y (ndarray [\(m,d_y\)]) – conditioning values \({\bf Y}={\bf y}\)

• params (dict) – parameters

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(ndarray [\(m,d\)]) – values of

\(\nabla_x\log\pi\) at the x points.

hess_x_log_pdf(x, y, params=None, idxs_slice=slice(None, None, None), cache=None)

Evaluate \(\nabla^2_{\bf x,y} \log \pi({\bf x}\vert{\bf y})\)

Parameters:

• x (ndarray [\(m,d\)]) – evaluation points

• y (ndarray [\(m,d_y\)]) – conditioning values \({\bf Y}={\bf y}\)

• params (dict) – parameters

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(ndarray [\(m,d\)]) – values of

\(\nabla^2_x\log\pi\) at the x points.

TransportMaps.Distributions.ConditionalDistributions.MeanConditionallyGaussianDistribution