Classes

Class Description
Builder [Abstract] Basis builder class.
KullbackLeiblerBuilder Basis builder through minimization of kl divergence
SequentialKullbackLeiblerBuilder Solve over a list of maps, using the former to warm start the next one
ToleranceSequentialKullbackLeiblerBuilder Solve over a list of maps, using the former to warm start the next one, until a target tolerance is met
FirstVariationKullbackLeiblerBuilder Adaptive builder based on the first variation of the kl divergence
L2RegressionBuilder Basis builder through $$\mathcal{L}^2$$ regression
ToleranceSequentialL2RegressionBuilder

Documentation

[Abstract] Basis builder class.

Provides a :fun:solve for constructing a transport map

class TransportMaps.Algorithms.Adaptivity.KullbackLeiblerBuilder(base_distribution, target_distribution, transport_map, solve_params, validator=None, callback=None, callback_kwargs={}, verbosity=0)[source]

Basis builder through minimization of kl divergence

Given distribution $$\nu_\rho$$ and $$\nu_\pi$$, and the parametric transport map $$T[{\bf a}]$$, provides the functionalities to solve the problem

$\arg\min_{\bf a}\mathcal{D}_{\rm KL}\left( T[{\bf a}]_\sharp\rho \Vert \pi\right)$

up to a chosen tolerance.

Parameters: base_distribution (Distribution) – distribution $$\nu_\rho$$ target_distribution (Distribution) – distribution $$\nu_\pi$$ transport_map (TransportMap) – transport map $$T$$ solve_params (dict) – dictionary of parameters for solution validator (Validator) – validator to be used to check stability of the solution callback (function) – function taking a map and optional additional arguments which is called whenever it is deemed necessary by the chosen algorithm (e.g. for storing purposes) callback_kwargs (dict) – additional arguments to be provided to the function callback. verbosity (int) – level of verbosity of the builder
Returns: (TransportMaps.Maps.TransportMap) – the transport map fitted.
class TransportMaps.Algorithms.Adaptivity.SequentialKullbackLeiblerBuilder(base_distribution, target_distribution, transport_map_list, solve_params_list, validator=None, regression_params_list=None, callback=None, callback_kwargs={}, verbosity=0)[source]

Solve over a list of maps, using the former to warm start the next one

Given distribution $$\nu_\rho$$ and $$\nu_\pi$$, and the list of parametric transport maps $$[T_1[{\bf a}_1,\ldots,T_n[{\bf a}_n]$$, provides the functionalities to solve the problems

$\arg\min_{{\bf a}_i}\mathcal{D}_{\rm KL}\left( T_i[{\bf a}_i]_\sharp\rho \Vert \pi\right)$

up to a chosen tolerance, where the numerical solution for map $$T_{i+1}$$ is started at $$T_i$$

Parameters: base_distribution (Distribution) – distribution $$\nu_\rho$$ target_distribution (Distribution) – distribution $$\nu_\pi$$ transport_map_list (list of TransportMap) – list of transports map $$T_i$$ solve_params_list (list of dict) – list of dictionaries of parameters for solution validator (Validator) – validator to be used to check stability of the solution regression_params_list (list of dict) – list of dictionaries of parameters for the regression between $$T_i$$ and $$T_{i+1}$$ verbosity (int) – level of verbosity of the builder
Returns: (TransportMaps.Maps.TransportMap) – the last transport map fitted.
class TransportMaps.Algorithms.Adaptivity.ToleranceSequentialKullbackLeiblerBuilder(base_distribution, target_distribution, transport_map_list, solve_params_list, validator=None, tol=0.01, var_diag_params=None, laplace_pull=False, callback=None, callback_kwargs={}, verbosity=0)[source]

Solve over a list of maps, using the former to warm start the next one, until a target tolerance is met

Given distribution $$\nu_\rho$$ and $$\nu_\pi$$, and the list of parametric transport maps $$[T_1[{\bf a}_1,\ldots,T_n[{\bf a}_n]$$, provides the functionalities to solve the problems

$\arg\min_{{\bf a}_i}\mathcal{D}_{\rm KL}\left( T_i[{\bf a}_i]_\sharp\rho \Vert \pi\right)$

up to a chosen tolerance, where the numerical solution for map $$T_{i+1}$$ is started at $$T_i$$

Parameters: base_distribution (Distribution) – distribution $$\nu_\rho$$ target_distribution (Distribution) – distribution $$\nu_\pi$$ transport_map_list (list of TransportMap) – list of transports map $$T_i$$ solve_params_list (list of dict) – list of dictionaries of parameters for solution regression_params_list (list of dict) – list of dictionaries of parameters for the regression between $$T_i$$ and $$T_{i+1}$$ validator (Validator) – validator to be used to check stability of the solution tol (float) – target variance diagnostic tolerance var_diag_params (dict) – parameters to be used in the variance diagnostic approximation callback (function) – function taking a map and optional additional arguments which is called whenever it is deemed necessary by the chosen algorithm (e.g. for storing purposes) callback_kwargs (dict) – additional arguments to be provided to the function callback. verbosity (int) – level of verbosity of the builder
Returns: (TransportMaps.Maps.TransportMap) – the last transport map fitted.
class TransportMaps.Algorithms.Adaptivity.FirstVariationKullbackLeiblerBuilder(base_distribution, target_distribution, transport_map, validator, eps_bull, regression_builder=None, solve_params={}, line_search_params={}, max_it=20, use_fv_hess=False, prune_trunc=0.01, avar_trunc=0.1, coeff_trunc=0.01, callback=None, callback_kwargs={}, verbosity=0)[source]

Adaptive builder based on the first variation of the kl divergence

Given distribution $$\nu_\rho$$ and $$\nu_\pi$$, and the parametric transport map $$T[{\bf a}]$$, provides the functionalities to solve the problem

$\arg\min_{\bf a}\mathcal{D}_{\rm KL}\left( T[{\bf a}]_\sharp\rho \Vert \pi\right) = \arg\min_{\bf a}\underbrace{\mathbb{E}_\rho\left[ -\log T[{\bf a}]^\sharp\pi \right]}_{ \mathcal{J}[T]({\bf x})}$

up to a chosen tolerance, by enriching the map using information from the first variation

$\nabla\mathcal{J}[T]({\bf x}) = (\nabla_{\bf x}T)^{-\top} \left(\log\frac{\rho({\bf x})}{T^\sharp\pi({\bf x})}\right)$
Parameters: base_distribution (Distribution) – distribution $$\nu_\rho$$ target_distribution (Distribution) – distribution $$\nu_\pi$$ transport_map (TransportMap) – starting transport map $$T$$ validator (Validator) – validator to be used to check stability of the solution eps_bull (float) – target tolerance of variance diagnostic solve_params (dict) – dictionary of parameters for solution callback (function) – function taking a map and optional additional arguments which is called whenever it is deemed necessary by the chosen algorithm (e.g. for storing purposes) callback_kwargs (dict) – additional arguments to be provided to the function callback. verbosity (int) – level of verbosity of the builder

Returns: (TransportMaps.Maps.TransportMap) – the transport map fitted.

Basis builder through $$\mathcal{L}^2$$ regression
Given a map $$M$$, fit a supplied parametric transport map $$T$$ through the solution of the $$\mathcal{L}^2$$ regression problem
$\arg\min_{\bf a}\left\Vert M - T \right\Vert_{\mathcal{L}^2} + \alpha \Vert {\bf a} \Vert_x$
where $$\alpha\Vert{\bf a}\Vert_x$$ is a regularization term, with respect to one of the available norms.