TransportMaps.Distributions.FactorizedDistributionBase

Module Contents

Classes

FactorizedDistribution

Distribution \(\nu_\pi\) defiened by its conditional factors.

class TransportMaps.Distributions.FactorizedDistributionBase.FactorizedDistribution(factors)

Bases: TransportMaps.Distributions.DistributionBase.Distribution

Distribution \(\nu_\pi\) defiened by its conditional factors.

The density of the distribution \(\nu_\pi\) is defined by

\[\pi({\bf x}) = \prod_{({\bf i},{\bf k}) \in \mathcal{I}} \pi({\bf x}_{\bf i},{\bf x}_{\bf k})`\]

Parameters:

factors (list of tuple) – each tuple contains a factor (ConditionalDistribution and/or Distribution), and two lists containing the list of marginal variables and conditioning variables

Example

Let \(\pi(x_0,x_1,x_2) = \pi_1(x_2|x_1,x_0) \pi_2(x_0|x_1) \pi_3(x_1)\).

>>> factors = [(p1, [2], [1,0] ),
>>>            (p2, [0], [1]  ),
>>>            (p3, [1], []    )]
>>> pi = FactorizedDistribution(factors)

property var_to_factor_map

property n_factors

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()

append(factor)

Add a new factor to the distribution

Parameters:

factor (tuple) – tuple containing a factor (ConditionalDistribution and/or Distribution), and two tuples with the list of marginal variables and conditioning variables

Example

Let \(\pi(x_0,x_1,x_2) = \pi_1(x_2|x_1,x_0) \pi_2(x_0|x_1) \pi_3(x_1)\) and let’s add the factor \(\pi_4(x_3|x_0,x_1,x_2)\), obtaining:

\[\pi(x_0,x_1,x_2,x_3) = \pi_4(x_3|x_0,x_1,x_2)\pi_1(x_2|x_1,x_0) \pi_2(x_0|x_1) \pi_3(x_1)\]

>>> factor = (pi4, [3], [0,1,2])
>>> pi.append(factor)

update_var_to_factor_map()

rvs(m, *args, **kwargs)

[Abstract] Generate \(m\) samples from the distribution.

Parameters:

m (int) – number of samples to generate

Returns:

(ndarray [\(m,d\)]) – \(m\)

\(d\)-dimensional samples

Raises:

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

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

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

Parameters:

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

• 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, params=None, idxs_slice=slice(None, None, None), cache=None)

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

Parameters:

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

• 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.

tuple_grad_x_log_pdf(x, params=None, idxs_slice=slice(None, None, None), cache=None)

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

Parameters:

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

• 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:

(tuple) – function and gradient evaluation

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

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

Parameters:

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

• 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 [\(m,d,d\)]) – values of

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

action_hess_x_log_pdf(x, dx, params=None, idxs_slice=slice(None, None, None), cache=None)

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

Parameters:

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

• dx (ndarray [\(m,d\)]) – 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].

• cache (dict) – cache

Returns:

(ndarray [\(m,d,d\)]) – values of

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