vineknockoffs.vine_copulas.DVineCopula#

class vineknockoffs.vine_copulas.DVineCopula(copulas)#

Methods

`compute_pits`(u)	Compute probability integral transforms (PITs) from a simplified D-vine copula.
`compute_pits_d_par`(which_tree, which_cop, u)	Compute probability integral transforms (PITs) and their derivative with respect to a parameter \(\theta_{k,l}\).
`compute_pits_par_jacobian`(u)
`compute_pits_par_jacobian_fast`(u[, return_w])
`cop_select`(u[, families, rotations, indep_test])
`get_par_vec`([from_tree])
`get_par_vec_w_info`([from_tree])
`ll`(u)
`set_par_vec`(par_vec[, from_tree, ...])
`sim`([n_obs, w])	Simulate random observations from a simplified D-vine copula.
`sim_d_par`(which_tree, which_cop[, n_obs, w])	Simulate random observations from a simplified D-vine copula and compute the derivative with respect to a parameter \(\theta_{k,l}\).
`sim_par_jacobian`([n_obs, w])
`sim_par_jacobian_fast`([n_obs, w, ...])

Attributes

`copulas`
`n_pars`
`n_vars`

DVineCopula.compute_pits(u)#

Compute probability integral transforms (PITs) from a simplified D-vine copula.

Parameters#

unumpy.ndarray: Array of copula observations.

Returns#

resnumpy.ndarray: Result array.

Notes#

Implements Algorithm 1 from Kurz (2022) to compute the probability integral transforms

\[ \begin{align}\begin{aligned}W_{1:d} &:= \big( U_1, U_{2|1}, U_{3|1:2}, \ldots, U_{d|1:d-1}\big)\\&:= \big( F_1(U_1), F_{2|1}(U_2|U_1), F_{3|1:2}(U_3|U_{1:2}), \ldots, F_{d|1:d-1}(U_d|U_{1:d-1}) \big).\end{aligned}\end{align} \]

References#

Kurz, M. S. (2022), Vine copula based knockoff generation for high-dimensional controlled variable selection. arXiv:2210.11196 [stat.ME].

DVineCopula.compute_pits_d_par(which_tree, which_cop, u, return_w=False)#

Compute probability integral transforms (PITs) and their derivative with respect to a parameter \(\theta_{k,l}\).

Parameters#

which_treeint: Determines \(\theta_{k,l}\) (copula in which tree?)
which_copint: Determines \(\theta_{k,l}\) (which copula within the tree?)
unumpy.ndarray: Array of copula observations.
return_wboolean: Whether the PITs should also be returned (in addition to the derivatives).

Returns#

resnumpy.ndarray: Result array(s).

Notes#

Implements Algorithm 5 from Kurz (2022) to compute the probability integral transforms and their derivative with respect to a parameter \(\theta_{k,l}\)

\[ \begin{align}\begin{aligned}W_{1:d} &:= \big( U_1, U_{2|1}, U_{3|1:2}, \ldots, U_{d|1:d-1}\big),\\\check{W}_{1:d} &:= \big( \partial_{\theta_{k,l}} U_{1}, \partial_{\theta_{k,l}} U_{2|1}, \partial_{\theta_{k,l}} U_{3|1:2}, \ldots, \partial_{\theta_{k,l}} U_{d|1:d-1} \big)\end{aligned}\end{align} \]

References#

Kurz, M. S. (2022), Vine copula based knockoff generation for high-dimensional controlled variable selection. arXiv:2210.11196 [stat.ME].

DVineCopula.compute_pits_par_jacobian(u)#

DVineCopula.compute_pits_par_jacobian_fast(u, return_w=False)#

classmethod DVineCopula.cop_select(u, families='all', rotations=True, indep_test=True)#

DVineCopula.get_par_vec(from_tree=1)#

DVineCopula.get_par_vec_w_info(from_tree=1)#

DVineCopula.ll(u)#

DVineCopula.set_par_vec(par_vec, from_tree=1, assert_to_bounds=False)#

DVineCopula.sim(n_obs=100, w=None)#

Simulate random observations from a simplified D-vine copula.

Parameters#

n_obs :: The number of observations to simulate. Default is 100.
wNone or numpy.ndarray: Array of iid standard uniform observations. If None, iid standard uniform observations are drawn. Default is None.

Returns#

resnumpy.ndarray: Result array.

Notes#

Implements Algorithm 2 from Kurz (2022) to simulate from a simplified D-vine copula based on standard uniform random variables.

References#

Kurz, M. S. (2022), Vine copula based knockoff generation for high-dimensional controlled variable selection. arXiv:2210.11196 [stat.ME].

DVineCopula.sim_d_par(which_tree, which_cop, n_obs=100, w=None)#

Simulate random observations from a simplified D-vine copula and compute the derivative with respect to a parameter \(\theta_{k,l}\).

Parameters#

which_treeint: Determines \(\theta_{k,l}\) (copula in which tree?)
which_copint: Determines \(\theta_{k,l}\) (which copula within the tree?)
n_obs :: The number of observations to simulate. Default is 100.
wNone or numpy.ndarray: Array of iid standard uniform observations. If None, iid standard uniform observations are drawn. Default is None.

Returns#

resnumpy.ndarray: Result array(s).

Notes#

Implements Algorithm 6 from Kurz (2022) to simulate from a simplified D-vine copula and compute the derivative with respect to a parameter \(\theta_{k,l}\).

\[ \begin{align}\begin{aligned}U_{1:d} &\sim C_{1:d},\\\check{U}_{1:d} &:= \big(\partial_{\theta_{k,l}}U_1, \ldots, \partial_{\theta_{k,l}}U_d)\end{aligned}\end{align} \]

References#

Kurz, M. S. (2022), Vine copula based knockoff generation for high-dimensional controlled variable selection. arXiv:2210.11196 [stat.ME].

DVineCopula.sim_par_jacobian(n_obs=100, w=None)#

DVineCopula.sim_par_jacobian_fast(n_obs=100, w=None, w_jacobian=None, from_tree=1, return_u=False)#