torchvinecopulib package¶

Subpackages¶

Module contents¶

class torchvinecopulib.BiCop(num_step_grid: int = 128)[source]¶

Bases: Module

cdf(obs: Tensor) → Tensor[source]¶

Evaluate the copula CDF at given points. For independent copula, returns u₁·u₂.

Parameters:: obs (torch.Tensor) – Points in [0,1]² where to evaluate the CDF (rows are (u₁,u₂)), shape (n,2).
Returns:: CDF values at each observation, shape (n,1).
Return type:: torch.Tensor

property device: device¶

Get the device of the bicop model (all internal buffers).

Returns:: The device on which the registered buffers reside.
Return type:: torch.device

property dtype: dtype¶

Get the data type of the bicop model (all internal buffers). Should be torch.float64.

Returns:: The data type of the registered buffers.
Return type:: torch.dtype

fit(obs: Tensor, mtd_kde: str = 'tll', mtd_tll: str = 'constant', num_iter_max: int = 17, is_tau_est: bool = False) → None[source]¶

Estimate and cache PDF/CDF/h-function grids from bivariate copula observations.

This method computes KDE-based bicopula densities on a uniform [0,1]² grid and populates internal buffers (_pdf_grid, _cdf_grid, _hfunc_l_grid, _hfunc_r_grid, negloglik).

Nagler, T., Schellhase, C., & Czado, C. (2017). Nonparametric estimation of simplified vine copula models: comparison of methods. Dependence Modeling, 5(1), 99-120.
O’Brien, T. A., Kashinath, K., Cavanaugh, N. R., Collins, W. D. & O’Brien, J. P. A fast and objective multidimensional kernel density estimation method: fastKDE. Comput. Stat. Data Anal. 101, 148–160 (2016). http://dx.doi.org/10.1016/j.csda.2016.02.014
O’Brien, T. A., Collins, W. D., Rauscher, S. A. & Ringler, T. D. Reducing the computational cost of the ECF using a nuFFT: A fast and objective probability density estimation method. Comput. Stat. Data Anal. 79, 222–234 (2014). http://dx.doi.org/10.1016/j.csda.2014.06.002

Parameters:

obs (torch.Tensor) – shape (n, 2) bicop obs in [0, 1]².
mtd_kde (str, optional) – Method for estimating the copula density. One of (“tll”, “fastKDE”). Defaults to “tll”.
mtd_tll (str, optional) – fit method for the transformation local-likelihood (TLL) nonparametric family, used only when mtd_kde="tll", one of (“constant”, “linear”, or “quadratic”). Defaults to “constant”.
num_iter_max (int, optional) – num of Sinkhorn/IPF iters for grid normalization, used only when mtd_kde="fastKDE". Defaults to 17.
is_tau_est (bool, optional) – If True, compute and store Kendall’s τ. Defaults to False.

hfunc_l(obs: Tensor) → Tensor[source]¶

Evaluate the left h-function at given points. Computes H(u₂ | u₁):= ∂/∂u₁ C(u₁,u₂) for the fitted copula. For independent copula, returns u₂.

Parameters:: obs (torch.Tensor) – Points in [0,1]² where to evaluate the left h-function (rows are (u₁,u₂)), shape (n,2).
Returns:: Left h-function values at each observation, shape (n,1).
Return type:: torch.Tensor

hfunc_r(obs: Tensor) → Tensor[source]¶

Evaluate the right h-function at given points. Computes H(u₁ | u₂):= ∂/∂u₂ C(u₁,u₂) for the fitted copula. For independent copula, returns u₁.

Parameters:: obs (torch.Tensor) – Points in [0,1]² where to evaluate the right h-function (rows are (u₁,u₂)), shape (n,2).
Returns:: Right h-function values at each observation, shape (n,1).
Return type:: torch.Tensor

hinv_l(obs: Tensor) → Tensor[source]¶

Invert the left h‐function via root‐finding: find u₂ given (u₁, p). Solves H(u₂ | u₁) = p by ITP between 0 and 1.

Parameters:: obs (torch.Tensor) – Points in [0,1]² where to evaluate the left h-function (rows are (u₁,u₂)), shape (n,2).
Returns:: Solutions u₂ ∈ [0,1], shape (n,1).
Return type:: torch.Tensor

hinv_r(obs: Tensor) → Tensor[source]¶

Invert the right h‐function via root‐finding: find u₁ given (u₂, p). Solves H(u₁ | u₂) = p by ITP between 0 and 1.

Parameters:: obs (torch.Tensor) – Points in [0,1]² where to evaluate the right h-function (rows are (u₁,u₂)), shape (n,2).
Returns:: Solutions u₁ ∈ [0,1], shape (n,1).
Return type:: torch.Tensor

imshow(is_log_pdf: bool = False, ax: Axes | None = None, cmap: str = 'inferno', xlabel: str = '$u_{left}$', ylabel: str = '$u_{right}$', title: str = 'Estimated bivariate copula density', colorbartitle: str = 'Density', **imshow_kwargs: dict) → tuple[Figure, Axes][source]¶

Display the (log-)PDF grid as a heatmap.

Parameters:

is_log_pdf (bool, optional) – If True, plot log-PDF. Defaults to False.
ax (plt.Axes, optional) – Matplotlib Axes object to plot on. If None, a new figure and axes are created. Defaults to None.
cmap (str, optional) – Colormap for the plot. Defaults to “inferno”.
xlabel (str, optional) – X-axis label. Defaults to r”$u_{left}$”.
ylabel (str, optional) – Y-axis label. Defaults to r”$u_{right}$”.
title (str, optional) – Plot title. Defaults to “Estimated bivariate copula density”.
colorbartitle (str, optional) – Colorbar title. Defaults to “Density”.
**imshow_kwargs – Additional keyword arguments for imshow.

Returns:

The figure and axes objects.

Return type:

tuple[plt.Figure, plt.Axes]

log_pdf(obs: Tensor) → Tensor[source]¶

Evaluate the copula log-PDF at given points, with safe handling of inf/nan. For independent copula, returns 0.

Parameters:: obs (torch.Tensor) – Points in [0,1]² where to evaluate the log-PDF (rows are (u₁,u₂)), shape (n,2).
Returns:: log-PDF values at each observation, shape (n,1).
Return type:: torch.Tensor

pdf(obs: Tensor) → Tensor[source]¶

Evaluate the copula PDF at given points. For independent copula, returns 1.

Parameters:: obs (torch.Tensor) – Points in [0,1]² where to evaluate the PDF (rows are (u₁,u₂)), shape (n,2).
Returns:: PDF values at each observation, shape (n,1).
Return type:: torch.Tensor

plot(plot_type: str = 'surface', margin_type: str = 'unif', xylim: tuple[float, float] | None = None, grid_size: int | None = None) → tuple[Figure, Axes][source]¶

Plot the bivariate copula density.

Parameters:

plot_type (str, optional) – Type of plot, either “contour” or “surface”. Defaults to “surface”.
margin_type (str, optional) – Type of margin, either “unif” or “norm”. Defaults to “unif”.
xylim (tuple[float, float], optional) – Limits for x and y axes. Defaults to None.
grid_size (int, optional) – Size of the grid for the plot. Defaults to None.

Returns:

The figure and axes objects.

Return type:

tuple[plt.Figure, plt.Axes]

reset() → None[source]¶

Reinitialize state and zero all statistics and precomputed grids.

Sets the bicop back to independent bicop and clears accumulated metrics (tau, num_obs, negloglik) as well as all grid buffers (_pdf_grid, _cdf_grid, _hfunc_l_grid, _hfunc_r_grid).

sample(num_sample: int = 100, seed: int = 42, is_sobol: bool = False) → Tensor[source]¶

Sample from the copula by inverse Rosenblatt transform. Uses Sobol sequence if is_sobol=True, otherwise uniform RNG. For independent copula, returns uniform samples in [0,1]².

Parameters:

num_sample (int, optional) – number of samples to generate. Defaults to 100.
seed (int, optional) – random seed for reproducibility. Defaults to 42.
is_sobol (bool, optional) – If True, use Sobol sampling. Defaults to False.

Returns:

Generated samples, shape (num_sample, 2).

Return type:

torch.Tensor

class torchvinecopulib.VineCop(num_dim: int, is_cop_scale: bool = False, num_step_grid: int = 128)[source]¶

Bases: Module

cdf(obs: Tensor, num_sample: int = 10007, seed: int = 42) → Tensor[source]¶

Estimate the multivariate CDF via Monte Carlo of the vine copula. Approximates C(u) = P(U ≤ u) by drawing num_sample Sobol samples in copula scale and computing the proportion that lie below obs.

Parameters:

obs (torch.Tensor) – Points at which to evaluate the CDF. Shape (num_obs, num_dim).
num_sample (int, optional) – number of samples to draw for approx. Defaults to 10007.
seed (int, optional) – random seed for Sobol engine. Defaults to 0.

Returns:

Estimated CDF values at the given observations. Shape (num_obs, 1).

Return type:

torch.Tensor

property device¶: Device of internal buffers.

draw_dag(sample_order: tuple[int, ...] = None, title: str = 'Vine comp graph', font_size_vertex: int = 8, f_path: Path = None, fig_size: tuple = None) → tuple[source]¶

Draw the computational graph (DAG) of the vine copula. Creates a directed graph where edges flow from upstream pseudo‐obs and bicop modules to downstream pseudo‐obs, laid out by vine levels.

Parameters:

sample_order (tuple[int, ...], optional) – Variable sampling order. Defaults to self.sample_order.
title (str, optional) – Title of the plot. Defaults to “Vine comp graph”.
font_size_vertex (int, optional) – Font size for vertex labels. Defaults to 8.
f_path (Path, optional) – Path to save the figure. If provided, the figure will be saved. Defaults to None.
fig_size (tuple, optional) – Figure size. Defaults to None.

Raises:

ImportError – If matplotlib or networkx is not installed.

Returns:

Figure, axis, graph object, and file path (if saved).

Return type:

tuple

draw_lv(lv: int = 0, is_bcp: bool = True, title: str | None = None, num_digit: int = 2, font_size_vertex: int = 8, font_size_edge: int = 7, f_path: Path = None, fig_size: tuple = None) → tuple[source]¶

Draw the weighted undirected graph at a single level of the vine copula. Constructs a NetworkX graph of bivariate‐copula edges at level lv, where nodes represent either raw variables (lv=0), parent‐copula modules, or pseudo‐observations, and edge widths encode dependence strength.

Parameters:

lv (int, optional) – Level to draw. Defaults to 0.
is_bcp (bool, optional) – If True, nodes are parent‐bicop “l,r;s”. Otherwise, nodes are pseudo‐obs “v|s”. Defaults to True.
title (str | None, optional) – Title of the plot. Defaults to f"Vine level {lv}".
num_digit (int, optional) – Number of decimal digits for edge weights. Defaults to 2.
font_size_vertex (int, optional) – Font size for vertex labels. Defaults to 8.
font_size_edge (int, optional) – Font size for edge labels. Defaults to 7.
f_path (Path, optional) – Path to save the figure. Defaults to None.
fig_size (tuple, optional) – Figure size. Defaults to None.

Raises:

ImportError – If matplotlib or networkx is not installed.

Returns:

Figure, axis, graph object, and file path (if saved).

Return type:

tuple

property dtype¶: Data type of internal buffers.

fit(obs: Tensor, is_dissmann: bool = True, matrix: Tensor = None, first_tree_vertex: tuple = (), mtd_vine: str = 'rvine', mtd_bidep: str = 'chatterjee_xi', thresh_trunc: None | float = 0.01, mtd_kde: str = 'fastKDE', mtd_tll: str = 'constant', num_iter_max: int = 17, is_tau_est: bool = False, num_step_grid_kde1d: int = None, **kde_kwargs) → None[source]¶

Fit the VineCop object to multivariate data. Learns both the vine structure (via Dissmann’s greedy MST or a provided matrix) and fits all bivariate copulas and 1D marginals (if needed).

Parameters:

obs (torch.Tensor) – observations of shape (num_obs, num_dim). If is_cop_scale=False, raw data; otherwise assumed already uniform.
is_dissmann (bool, optional) – if True, use Dissmann’s algorithm to learn the vine structure. Otherwise, use the provided matrix. Defaults to True.
matrix (torch.Tensor, optional) – matrix representation of the vine structure. Defaults to None.
first_tree_vertex (tuple, optional) – vertices of the first tree (set of conditioning variables). Defaults to ().
mtd_vine (str, optional) – method for vine structure. One of “cvine”, “dvine”, “rvine”. Defaults to “rvine”.
mtd_bidep (str, optional) – method for bivariate dependence. One of “chatterjee_xi”, “ferreira_tail_dep_coeff”, “kendall_tau”, “mutual_info”, “spearman_rho”. Defaults to “chatterjee_xi”.
thresh_trunc (None | float, optional) – threshold for truncating bivariate copulas using p-val from Kendall’s tau stats test. Defaults to 0.01.
mtd_kde (str, optional) – method for bicop KDE. One of “fastKDE” or “tll”. Defaults to “fastKDE”.
mtd_tll (str, optional) – fit method for the transformation local-likelihood (TLL) nonparametric family, one of (“constant”, “linear”, or “quadratic”). Defaults to “constant”.
num_iter_max (int, optional) – num of Sinkhorn/IPF iters for grid normalization, used only when mtd_kde is “fastKDE”. Defaults to 17.
is_tau_est (bool, optional) – If True, compute and store Kendall’s τ inside BiCop. Defaults to False.
num_step_grid_kde1d (int, optional) – Grid resolution for each marginal KDE. Defaults to None.
**kde_kwargs – additional keyword arguments for kdeCDFPPF1D.

Raises:

ValueError – if mtd_vine is not one of “cvine”, “dvine”, or “rvine”.

forward(x: Tensor) → Tensor[source]¶

Neg average log-likelihood function for the given observations.

Parameters:: x (torch.Tensor) – Points at which to evaluate. Shape (num_obs, num_dim).
Returns:: scalar loss value.
Return type:: torch.Tensor

log_pdf(obs: Tensor) → Tensor[source]¶

Compute the log-density function of the vine copula at the given observations (including marginals).

Parameters:: obs (torch.Tensor) – Points at which to evaluate the log-density function. Shape (num_obs, num_dim).
Returns:: Log-density function values at the given observations. Shape (num_obs, 1).
Return type:: torch.Tensor

property matrix: Tensor¶

Matrix representation of the vine. Diagonal elements form the sampling order.: Read in row-wise: a row of (0,1,3,4,2) indicates a source vertex (0|1,2,3,4) and bicops (fix the leftmost, move ; from right to left) including (0,2;), (0,4;2), (0,3;2,4), and (0,1;2,3,4).

Returns:: Matrix representation of the vine.
Return type:: torch.Tensor

static ref_count_hfunc(num_dim: int, struct_obs: list, sample_order: tuple) → tuple[dict, list, int][source]¶

Count references of pseudo-obs, identify source vertices, and count number of hfuncs.

Parameters:

num_dim (int) – number of dimensions in the vine.
struct_obs (list) – structure of pseudo observations. (parents)
sample_order (tuple) – sampling order.

Returns:

reference counts of pseudo-obs, list of source vertices, and number of hfuncs.

Return type:

tuple[dict, list, int]

reset() → None[source]¶: Reset the VineCop object to its initial state.

rosenblatt(obs: Tensor, sample_order: tuple | None = None) → Tensor[source]¶

Compute the Rosenblatt transform of observations.

Maps input obs into uniform pseudo‐observations via successive conditional CDFs (Rosenblatt). # TODO, needs grad as residuals

sample(num_sample: int = 1000, seed: int = 42, is_sobol: bool = False, sample_order: tuple[int, ...] | None = None, dct_v_s_obs: dict[tuple[int, ...], Tensor] | None = None) → Tensor[source]¶

Draw random samples from the fitted vine copula via inverse Rosenblatt.

Generates num_sample joint samples in original or copula scale by (1) sampling independent uniforms for each “source” pseudo-obs, (2) recursively applying h-functions and their inverses following the vine structure, and (3) optionally transforming back through 1D marginal PPFs.

Parameters:

num_sample (int, optional) – number of samples to draw. Defaults to 1000.
seed (int, optional) – random seed for RNG or Sobol engine. Defaults to 42.
is_sobol (bool, optional) – if True, use Sobol engine for quasi-random sampling. Defaults to False.
sample_order (tuple[int, ...] | None, optional) – custom sampling order. Defaults to None and uses self.sample_order.
dct_v_s_obs (dict[tuple[int, ...], torch.Tensor] | None, optional) – dict mapping tuple(idx|conding set)->pseudo-obs. Defaults to None. User-provided pseudo-obs to initialize the sampling process. Notice if is_cop_scale=False, CDF/PPF will only be applied to the top level marginals. Pseudo-obs at deeper levels are assumed to be in copula scale [0,1].

Returns:

sampled observations in original scale if self.is_cop_scale=False, otherwise in [0,1]^d.

Return type:

torch.Tensor