TransportMaps.Distributions.ConditionalDistributionBase

Module Contents

Classes

ConditionalDistribution

Abstract distribution \(\pi_{{\bf X}\vert{\bf Y}}\).

class TransportMaps.Distributions.ConditionalDistributionBase.ConditionalDistribution(dim, dim_y)

Bases: TransportMaps.Distributions.DistributionBase.Distribution

Abstract distribution \(\pi_{{\bf X}\vert{\bf Y}}\).

Parameters:

• dim (int) – input dimension of the distribution

• dim_y (int) – dimension of the conditioning variables

property dim_y

abstract rvs(m, y, *args, **kwargs)

[Abstract] 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

abstract quadrature(qtype, qparams, y, mass, *args, **kwargs)

[Abstract] Generate quadrature points and weights.

Parameters:

• qtype (int) – quadrature type number. The different types are defined in the associated sub-classes.

• qparams (object) – inputs necessary to the generation of the selected quadrature

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

• mass (float) – total mass of the quadrature (1 for probability measures)

Returns:

(tuple (ndarray [\(m,d\)],

ndarray [\(m\)])) – list of quadrature points and weights

Raises:

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

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

Evaluate \(\pi({\bf x})\)

Parameters:

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

• y (ndarray [\(d_y\)]) – 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 (dist) – cache

Returns:

(ndarray [\(m\)]) – values of \(\pi\)

at the x points.

Raises:

NotImplementedError – the method calls :fun:`log_pdf`

abstract log_pdf(x, y, params=None, idxs_slice=slice(None, None, None), **kwargs)

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

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].

Returns:

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

at the x points.

Raises:

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

abstract grad_x_log_pdf(x, y, params=None, idxs_slice=slice(None, None, None), **kwargs)

[Abstract] 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].

Returns:

(ndarray [\(m,d\)]) – values of

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

Raises:

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

tuple_grad_x_log_pdf(x, y, params=None, idxs_slice=slice(None, None, None), cache=None, **kwargs)

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

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 (dist) – cache

Returns:

(tuple) – containing

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

Raises:

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

abstract hess_x_log_pdf(x, y, params=None, idxs_slice=slice(None, None, None), **kwargs)

[Abstract] 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].

Returns:

(ndarray [\(m,d,d\)]) – values of

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

Raises:

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

abstract action_hess_x_log_pdf(x, y, dx, dy, params=None, idxs_slice=slice(None, None, None), **kwargs)

[Abstract] Evaluate \(\langle\nabla^2_{\bf x,y} \log \pi({\bf x}\vert{\bf y}), [\delta{\bf x},\delta{\bf y}]\rangle\)

Parameters:

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

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

• dx (ndarray [\(m,d\)]) – x direction on which to evaluate the Hessian

• dy (ndarray [\(m,d_y\)]) – y direction on which to evaluate the Hessian

• 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].

Returns:

(ndarray [\(m,d,d\)]) – values of

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

Raises:

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

abstract mean_log_pdf(y)

[Abstract] Evaluate \(\mathbb{E}_{\pi}[\log \pi]\)

Parameters:

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

Returns:

(float) – \(\mathbb{E}_{\pi}[\log \pi]\)

Raises:

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