def sample_transition_within_subspace(model, state, hyperparams):
    """
    MCMC iteration (Gibbs sampling) for transition matrix and covariance
    within the constrained subspace
    """

    # Calculate sufficient statistics
    suffStats = smp.evaluate_transition_sufficient_statistics(state)

    # Convert to Givens factorisation form
    U, D = model.convert_to_givens_form()

    # Sample a new projected transition matrix and transition covariance
    rank = model.parameters['rank'][0]
    nu0 = rank
    Psi0 = rank * hyperparams['rPsi0']
    nu, Psi, M, V = smp.hyperparam_update_degenerate_mniw_transition(
        suffStats, U, nu0, Psi0, hyperparams['M0'], hyperparams['V0'])
    D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
    FU = smp.sample_matrix_normal(M, D, V)

    # Project out
    Fold = model.parameters['F']
    F = smp.project_degenerate_transition_matrix(Fold, FU, U)
    model.parameters['F'] = F

    # Convert back to eigen-decomposition form
    model.update_from_givens_form(U, D)

    return model
def sample_transition_within_subspace(model, state, hyperparams):
    """
    MCMC iteration (Gibbs sampling) for transition matrix and covariance
    within the constrained subspace
    """

    # Calculate sufficient statistics
    suffStats = smp.evaluate_transition_sufficient_statistics(state)

    # Convert to Givens factorisation form
    U,D = model.convert_to_givens_form()

    # Sample a new projected transition matrix and transition covariance
    rank = model.parameters['rank'][0]
    nu0 = rank
    Psi0 = rank*hyperparams['rPsi0']
    nu,Psi,M,V = smp.hyperparam_update_degenerate_mniw_transition(
                                                suffStats, U,
                                                nu0,
                                                Psi0,
                                                hyperparams['M0'],
                                                hyperparams['V0'])
    D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
    FU = smp.sample_matrix_normal(M, D, V)

    # Project out
    Fold = model.parameters['F']
    F = smp.project_degenerate_transition_matrix(Fold, FU, U)
    model.parameters['F'] = F

    # Convert back to eigen-decomposition form
    model.update_from_givens_form(U, D)

    return model
def sample_transition_within_subspace(model, state, hyperparams, pseudo_dof=None, pseudo_sd=None):
    """
    MCMC iteration (Gibbs sampling) for transition matrix and covariance
    within the constrained subspace
    """

    # Calculate sufficient statistics
    suffStats = smp.evaluate_transition_sufficient_statistics(state)

    # Convert to Givens factorisation form
    U,D = model.convert_to_givens_form()

    # Sampke a pseudo-observation to constrain the size of move
    if pseudo_dof is not None:
        extra_nu = pseudo_dof
        extra_Psi = smp.sample_wishart(pseudo_dof, D)
    else:
        extra_nu = 0
        extra_Psi = 0

    # Sample a new projected transition matrix and transition covariance
    rank = model.parameters['rank'][0]
    nu0 = rank + extra_nu
    Psi0 = rank*hyperparams['rPsi0'] + np.dot(U, np.dot(extra_Psi, U.T))
    nu,Psi,M,V = smp.hyperparam_update_degenerate_mniw_transition(
                                                suffStats, U,
                                                nu0,
                                                Psi0,
                                                hyperparams['M0'],
                                                hyperparams['V0'])
    D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
    FU = smp.sample_matrix_normal(M, D, V)

    # Project out
    Fold = model.parameters['F']
    F = smp.project_degenerate_transition_matrix(Fold, FU, U)
    model.parameters['F'] = F

    # Convert back to eigen-decomposition form
    model.update_from_givens_form(U, D)

    return model
示例#4
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def sample_transition_within_subspace(model,
                                      state,
                                      hyperparams,
                                      pseudo_dof=None,
                                      pseudo_sd=None):
    """
    MCMC iteration (Gibbs sampling) for transition matrix and covariance
    within the constrained subspace
    """

    # Calculate sufficient statistics
    suffStats = smp.evaluate_transition_sufficient_statistics(state)

    # Convert to Givens factorisation form
    U, D = model.convert_to_givens_form()

    # Sampke a pseudo-observation to constrain the size of move
    if pseudo_dof is not None:
        extra_nu = pseudo_dof
        extra_Psi = smp.sample_wishart(pseudo_dof, D)
    else:
        extra_nu = 0
        extra_Psi = 0

    # Sample a new projected transition matrix and transition covariance
    rank = model.parameters['rank'][0]
    nu0 = rank + extra_nu
    Psi0 = rank * hyperparams['rPsi0'] + np.dot(U, np.dot(extra_Psi, U.T))
    nu, Psi, M, V = smp.hyperparam_update_degenerate_mniw_transition(
        suffStats, U, nu0, Psi0, hyperparams['M0'], hyperparams['V0'])
    D = la.inv(smp.sample_wishart(nu, la.inv(Psi)))
    FU = smp.sample_matrix_normal(M, D, V)

    # Project out
    Fold = model.parameters['F']
    F = smp.project_degenerate_transition_matrix(Fold, FU, U)
    model.parameters['F'] = F

    # Convert back to eigen-decomposition form
    model.update_from_givens_form(U, D)

    return model