TransportMaps.Maps.Decomposable.SequentialInferenceMaps

Module Contents

Classes

LiftedTransportMap	Given a map \(T\) of dimension \(d_\theta + 2 d_{\bf x}\), where \(d_\theta\) is the number of hyper-parameters and \(d_{\bf x}\) is the state dimension, lift it to a \(\hat{d}\) state dimensional map.
SequentialMarkovChainTransportMap	Compose the lower triangular 1-lag smoothing maps into the smoothing map

class TransportMaps.Maps.Decomposable.SequentialInferenceMaps.LiftedTransportMap(idx, tm, dim, hyper_dim)

Bases: TransportMaps.Maps.TransportMap

Given a map \(T\) of dimension \(d_\theta + 2 d_{\bf x}\), where \(d_\theta\) is the number of hyper-parameters and \(d_{\bf x}\) is the state dimension, lift it to a \(\hat{d}\) state dimensional map.

Let

\[\begin{split}T(\Theta, {\bf x}) = \begin{bmatrix} T^{(0)}(\Theta) \\ T^{(1)}(\Theta, {\bf x}) \\ \end{bmatrix}\end{split}\]

be the map to be lifted at index \(i\) into a \(\hat{d}\) dimensional map.

\[\begin{split}T_{\rm lift}(\Theta, {\bf x}) = \left[ \begin{array}{c} T^{(0)}(\theta) \\ x_{1} \\ \; \vdots \\ x_{i-1} \\ T^{(1)}(\theta, x_{i}, \ldots, x_{i+2 d_{\bf x}}) \\ x_{i+2d_{\bf x}+1} \\ \; \vdots \\ x_{\hat{d}} \end{array} \right]\end{split}\]

Parameters:

• idx (int) – index where to lift \(T\)

• tm (TransportMap) – transport map \(T\)

• dim (int) – total dimension \(\hat{d}\)

• hyper_dim (int) – number of hyper-parameters \(d_\theta\)

property n_coeffs

Returns the total number of coefficients.

Returns:

(int) – total number \(N\) of

coefficients characterizing the map.

property coeffs

Returns the actual value of the coefficients.

Returns:

(ndarray [\(N\)]) – coefficients.

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()

evaluate(x, precomp=None, idxs_slice=slice(None), cache=None)

[Abstract] Evaluate the map \(T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m,d_y\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

inverse(x, *args, **kwargs)

[Abstract] Compute: \(T^{-1}({\bf x})\)

Parameters:

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

• precomp (dict) – precomputed values

• 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 [\(m,d\)]) – \(T^{-1}({\bf x})\) for every evaluation point

grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)

[Abstract] Evaluate the gradient \(\nabla_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m,d_y,d_x\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

hess_x(x, precomp=None, idxs_slice=slice(None), cache=None)

[Abstract] Evaluate the Hessian \(\nabla^2_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m,d_y,d_x,d_x\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

grad_x_inverse(x, *args, **kwargs)

[Abstract] Compute \(\nabla_{\bf x} T^{-1}({\bf x})\).

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m,d,d\)]) – gradient matrices for every evaluation point.

Raises:

NotImplementedError – to be implemented in subclasses

hess_x_inverse(x, *args, **kwargs)

[Abstract] Compute \(\nabla_{\bf x}^2 T^{-1}({\bf x})\).

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m,d,d\)]) – Hessian tensors for every evaluation point.

Raises:

NotImplementedError – to be implemented in subclasses

log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)

[Abstract] Compute: \(\log \det \nabla_{\bf x} T({\bf x}, {\bf a})\).

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m\)]) – \(\log \det \nabla_{\bf x} T({\bf x}, {\bf a})\) at every evaluation point

grad_x_log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)

[Abstract] Compute: \(\nabla_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\)

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m,d\)]) – \(\nabla_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\) at every evaluation point

See also

log_det_grad_x().

hess_x_log_det_grad_x(x, precomp=None, idxs_slice=slice(None), cache=None)

[Abstract] Compute: \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\)

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m,d,d\)]) – \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T({\bf x}, {\bf a})\) at every evaluation point

See also

log_det_grad_x() and grad_x_log_det_grad_x().

log_det_grad_x_inverse(x, *args, **kwargs)

[Abstract] Compute: \(\log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})\).

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m\)]) – \(\log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})\) at every evaluation point

grad_x_log_det_grad_x_inverse(x, *args, **kwargs)

[Abstract] Compute: \(\nabla_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})\)

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m,d\)]) – \(\nabla_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})\) at every evaluation point

See also

log_det_grad_x().

hess_x_log_det_grad_x_inverse(x, *args, **kwargs)

[Abstract] Compute: \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})\)

Parameters:

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

• precomp (dict) – dictionary of precomputed values

• 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 [\(m,d,d\)]) – \(\nabla^2_{\bf x} \log \det \nabla_{\bf x} T^{-1}({\bf x}, {\bf a})\) at every evaluation point

See also

log_det_grad_x() and grad_x_log_det_grad_x().

class TransportMaps.Maps.Decomposable.SequentialInferenceMaps.SequentialMarkovChainTransportMap(tm_list, hyper_dim)

Bases: TransportMaps.Maps.ListCompositeTransportMap

Compose the lower triangular 1-lag smoothing maps into the smoothing map

Parameters:

• tm_list (list) – list of 1-lag smoothing lower triangular transport maps

• hyper_dim (int) – number of hyper-parameters

Warning

this works only for one dimensional states! It will be extended for higher dimensional states in the future.