TransportMaps.Algorithms.SequentialInference.LinearSequentialInference

Module Contents

Classes

LinearFilter	Perform the on-line filtering of a sequential linear Gaussian Hidden Markov chain.
LinearSmoother	Perform the on-line assimilation of a sequential linear Gaussian Hidden Markov chain.

class TransportMaps.Algorithms.SequentialInference.LinearSequentialInference.LinearFilter(ders=0, pi_hyper=None)

Bases: TransportMaps.Algorithms.SequentialInference.SequentialInferenceBase.Filter

Perform the on-line filtering of a sequential linear Gaussian Hidden Markov chain.

Aka: Kalman filter.

If the linear state-space model is parametric, i.e.

\[\begin{split}{\bf Z}_{k+1} = {\bf c}_k(\theta) + {\bf F}_k(\theta){\bf Z}_k + {\bf w}_k(\theta) \\ {\bf Y}_{k} = {\bf H}_k(\theta){\bf Z}_k + {\bf v}_k(\theta)\end{split}\]

then one can optionally compute the gradient (with respect to the parameters) of the filter.

Parameters:

• ders (int) – 0 no gradient is computed, 1 compute gradient

• pi_hyper (Distribution) – prior distribution on the hyper-parameters \(\pi(\Theta)\)

Todo

Square-root filter

property marginal_log_likelihood

Returns the marginal log-likelihood \(\log\pi\left({\bf Y}_{\Xi\leq k}\right)\)

Returns:

(float) – current marginal likelihood

property filtering_mean_list

Returns the means of all the filtering distributions

Returns:

(list of float) – means of

\(\pi\left({\bf Z}_k\middle\vert{\bf Y}_{\Xi\leq k}\right)\) for \(k\in \Lambda=0,\ldots,n\).

property filtering_covariance_list

Returns the covariances of all the filtering distributions

Returns:

(list of ndarray) – covariances of

\(\pi\left({\bf Z}_k\middle\vert{\bf Y}_{\Xi\leq k}\right)\) for \(k\in \Lambda=0,\ldots,n\).

property grad_marginal_log_likelihood

Returns the gradient of the marginal log-likelihood \(\nabla_\theta\log\pi\left({\bf Y}_{\Xi\leq k}\right)\)

Returns:

(float) – current marginal likelihood

property filtering_grad_mean_list

Returns the gradient of the means of all the filtering distributions

Returns:

(list of float) – gradient of the means of

\(\pi\left({\bf Z}_k\middle\vert{\bf Y}_{\Xi\leq k}\right)\) for \(k\in \Lambda=0,\ldots,n\).

property filtering_grad_covariance_list

Returns the gradient of the covariances of all the filtering distributions

Returns:

(list of ndarray) –

gradient of the covariances of \(\pi\left({\bf Z}_k\middle\vert{\bf Y}_{\Xi\leq k}\right)\) for \(k\in \Lambda=0,\ldots,n\).

_assimilation_step()

Assimilate one piece of Gaussian data \(\left( \pi\left({\bf Z}_{k+1} \middle\vert {\bf Z}_k \right), \log \mathcal{L}\left({\bf y}_{k+1}\middle\vert {\bf Z}_{k+1}\right) \right)\).

class TransportMaps.Algorithms.SequentialInference.LinearSequentialInference.LinearSmoother(lag=None)

Bases: LinearFilter, TransportMaps.Algorithms.SequentialInference.SequentialInferenceBase.Smoother

Perform the on-line assimilation of a sequential linear Gaussian Hidden Markov chain.

Parameters:

lag (numpy.float) – lag to be used in the backward updates of smoothing means and covariances. The default value None indicates infinite lag.

Todo

no hyper-parameter admitted right now.

property lag

property smoothing_mean_list

property smoothing_covariance_list

_assimilation_step()

Assimilate one piece of Gaussian data \(\left( \pi\left({\bf Z}_{k+1} \middle\vert {\bf Z}_k \right), \log \mathcal{L}\left({\bf y}_{k+1}\middle\vert {\bf Z}_{k+1}\right) \right)\).

_update_smoothing_mean_covariance_lists(nsteps, lag, smooth_mean_list, smooth_cov_list, CB_queue, CB2_queue, c, C, a=None, A=None, B=None)

offline_smoothing_mean_covariance_lists(lag=None)

Compute the mean and covariances with a fixed lag for a pre-assimilated density