TransportMaps.Maps.Functionals.ProductDistributionParametricPullbackComponentFunctionBase

Module Contents

Classes

ProductDistributionParametricPullbackComponentFunction

Parametric function \(f[{\bf a}](x_{1:k}) = \log\pi\circ T_k[{\bf a}](x_{1:k}) + \log\partial_{x_k}T_k[{\bf a}](x_{1:k})\)

class TransportMaps.Maps.Functionals.ProductDistributionParametricPullbackComponentFunctionBase.ProductDistributionParametricPullbackComponentFunction(transport_map_component, base_distribution)

Bases: TransportMaps.Maps.Functionals.ParametricFunctionalBase.ParametricFunctional

Parametric function \(f[{\bf a}](x_{1:k}) = \log\pi\circ T_k[{\bf a}](x_{1:k}) + \log\partial_{x_k}T_k[{\bf a}](x_{1:k})\)

Parameters:

• transport_map_component (MonotonicFunctionApproximation) – component \(T_k\) of monotone map \(T\)

• base_distribution (Distribution) – distribution \(\pi\)

property coeffs

Get the coefficients \({\bf a}\) of the function

See also

ParametricFunctionApproximation.coeffs()

property n_coeffs

Get the number \(N\) of coefficients

See also

ParametricFunctionApproximation.n_coeffs()

evaluate(x, params={}, idxs_slice=slice(None), cache=None)

Evaluate \(f[{\bf a}](x_{1:k})\)

Parameters:

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

• params (dict) – parameters with keys params_pi, params_t

• 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) – cached values

Returns:

(ndarray [\(m,1\)]) – evaluations

grad_a(x, params={}, idxs_slice=slice(None), cache=None)

Evaluate \(\nabla_{\bf a}f[{\bf a}](x_{1:k})\)

Parameters:

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

• params (dict) – parameters with keys params_pi, params_t

• 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) – cached values

Returns:

(ndarray [\(m,1,n\)]) – evaluations

hess_a(x, params={}, idxs_slice=slice(None), cache=None)

Evaluate \(\nabla^2_{\bf a}f[{\bf a}](x_{1:k})\)

Parameters:

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

• params (dict) – parameters with keys params_pi, params_t

• 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) – cached values

Returns:

(ndarray [\(m,1,n,n\)]) – evaluations

grad_x(x, params={}, idxs_slice=slice(None))

Evaluate \(\nabla_{\bf x} \log T_{k}^\sharp \pi({\bf x_{1:k}})\)

Parameters:

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

• params (dict) – parameters with keys params_pi, params_t

• 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 [\(m,1,k\)]) – values of

\(\nabla_{\bf x} \log T_{k}^\sharp \pi\) at the x points.

hess_x(x, params={}, idxs_slice=slice(None))

Evaluate \(\nabla^2_{\bf x} \log T_{k}^\sharp \pi({\bf x_{1:k}})\)

Parameters:

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

• params (dict) – parameters with keys params_pi, params_t

• 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 [\(m,1,k,k\)]) – values of

\(\nabla^2_{\bf x} \log T_{k}^\sharp \pi\) at the x points.

grad_a_hess_x(x, params={}, idxs_slice=slice(None))

Evaluate \(\nabla_{\bf a} \nabla^2_{\bf x} \log T_{k}^\sharp \pi({\bf x_{1:k}})\)

Parameters:

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

• params (dict) – parameters with keys params_pi, params_t

• 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 [\(m,1,n,k,k\)]) – values of

\(\nabla^2_{\bf x} \log T_{k}^\sharp \pi\) at the x points.