# copulas.multivariate package¶

## Module contents¶

class copulas.multivariate.Multivariate(random_seed=None)[source]

Bases: object

Abstract class for a multi-variate copula object.

cdf(X)[source]

Compute the cumulative distribution value for each point in X.

Parameters

X (pandas.DataFrame) – Values for which the cumulative distribution will be computed.

Returns

Cumulative distribution values for points in X.

Return type

numpy.ndarray

Raises

NotFittedError – if the model is not fitted.

check_fit()[source]

Check whether this model has already been fit to a random variable.

Raise a NotFittedError if it has not.

Raises

NotFittedError – if the model is not fitted.

cumulative_distribution(X)[source]

Compute the cumulative distribution value for each point in X.

Parameters

X (pandas.DataFrame) – Values for which the cumulative distribution will be computed.

Returns

Cumulative distribution values for points in X.

Return type

numpy.ndarray

Raises

NotFittedError – if the model is not fitted.

fit(X)[source]

Fit the model to table with values from multiple random variables.

Parameters

X (pandas.DataFrame) – Values of the random variables.

fitted = False
classmethod from_dict(params)[source]

Create a new instance from a parameters dictionary.

Parameters

params (dict) – Parameters of the distribution, in the same format as the one returned by the to_dict method.

Returns

Instance of the distribution defined on the parameters.

Return type

Multivariate

classmethod load(path)[source]

Load a Multivariate instance from a pickle file.

Parameters

path (str) – Path to the pickle file where the distribution has been serialized.

Returns

Return type

Multivariate

log_probability_density(X)[source]

Compute the log of the probability density for each point in X.

Parameters

X (pandas.DataFrame) – Values for which the log probability density will be computed.

Returns

Log probability density values for points in X.

Return type

numpy.ndarray

Raises

NotFittedError – if the model is not fitted.

pdf(X)[source]

Compute the probability density for each point in X.

Parameters

X (pandas.DataFrame) – Values for which the probability density will be computed.

Returns

Probability density values for points in X.

Return type

numpy.ndarray

Raises

NotFittedError – if the model is not fitted.

probability_density(X)[source]

Compute the probability density for each point in X.

Parameters

X (pandas.DataFrame) – Values for which the probability density will be computed.

Returns

Probability density values for points in X.

Return type

numpy.ndarray

Raises

NotFittedError – if the model is not fitted.

sample(num_rows=1)[source]

Sample values from this model.

Argument:
num_rows (int):

Number of rows to sample.

Returns

Array of shape (n_samples, *) with values randomly sampled from this model distribution.

Return type

numpy.ndarray

Raises

NotFittedError – if the model is not fitted.

save(path)[source]

Serialize this multivariate instance using pickle.

Parameters

path (str) – Path to where this distribution will be serialized.

to_dict()[source]

Return a dict with the parameters to replicate this object.

Returns

Parameters of this distribution.

Return type

dict

class copulas.multivariate.GaussianMultivariate(*args, **kwargs)[source]

Class for a multivariate distribution that uses the Gaussian copula.

Parameters

distribution (str or dict) – Fully qualified name of the class to be used for modeling the marginal distributions or a dictionary mapping column names to the fully qualified distribution names.

columns = None
covariance = None
cumulative_distribution(X)[source]

Compute the cumulative distribution value for each point in X.

Parameters

X (pandas.DataFrame) – Values for which the cumulative distribution will be computed.

Returns

Cumulative distribution values for points in X.

Return type

numpy.ndarray

Raises

NotFittedError – if the model is not fitted.

fit(X, *args, **kwargs)
classmethod from_dict(copula_dict)[source]

Create a new instance from a parameters dictionary.

Parameters

params (dict) – Parameters of the distribution, in the same format as the one returned by the to_dict method.

Returns

Instance of the distribution defined on the parameters.

Return type

Multivariate

probability_density(X)[source]

Compute the probability density for each point in X.

Parameters

X (pandas.DataFrame) – Values for which the probability density will be computed.

Returns

Probability density values for points in X.

Return type

numpy.ndarray

Raises

NotFittedError – if the model is not fitted.

sample(*args, **kwargs)
to_dict()[source]

Return a dict with the parameters to replicate this object.

Returns

Parameters of this distribution.

Return type

dict

univariates = None
class copulas.multivariate.VineCopula(*args, **kwargs)[source]

Vine copula model.

A $$vine$$ is a graphical representation of one factorization of the n-variate probability distribution in terms of $$n(n − 1)/2$$ bivariate copulas by means of the chain rule.

It consists of a sequence of levels and as many levels as variables. Each level consists of a tree (no isolated nodes and no loops) satisfying that if it has $$n$$ nodes there must be $$n − 1$$ edges.

Each node in tree $$T_1$$ is a variable and edges are couplings of variables constructed with bivariate copulas.

Each node in tree $$T_{k+1}$$ is a coupling in $$T_{k}$$, expressed by the copula of the variables; while edges are couplings between two vertices that must have one variable in common, becoming a conditioning variable in the bivariate copula. Thus, every level has one node less than the former. Once all the trees are drawn, the factorization is the product of all the nodes.

Parameters
• vine_type (str) – type of the vine copula, could be ‘center’,’direct’,’regular’

• random_seed (int) – Random seed to use.

model

Distribution to compute univariates.

Type

copulas.univariate.Univariate

u_matrix

Univariates.

Type

numpy.array

n_sample

Number of samples.

Type

int

n_var

Number of variables.

Type

int

columns

Names of the variables.

Type

pandas.Series

tau_mat

Kendall correlation parameters for data.

Type

numpy.array

truncated

Max level used to build the vine.

Type

int

depth

Vine depth.

Type

int

trees

List of trees used by this vine.

Type

list[Tree]

ppfs

percent point functions from the univariates used by this vine.

Type

list[callable]

fit(X, *args, **kwargs)
classmethod from_dict(vine_dict)[source]

Create a new instance from a parameters dictionary.

Parameters

params (dict) – Parameters of the Vine, in the same format as the one returned by the to_dict method.

Returns

Instance of the Vine defined on the parameters.

Return type

Vine

get_likelihood(uni_matrix)[source]

Compute likelihood of the vine.

sample(*args, **kwargs)
to_dict()[source]

Return a dict with the parameters to replicate this Vine.

Returns

Parameters of this Vine.

Return type

dict

train_vine(tree_type)[source]

Build the wine.

1. For the construction of the first tree $$T_1$$, assign one node to each variable and then couple them by maximizing the measure of association considered. Different vines impose different constraints on this construction. When those are applied different trees are achieved at this level.

2. Select the copula that best fits to the pair of variables coupled by each edge in $$T_1$$.

3. Let $$C_{ij}(u_i , u_j )$$ be the copula for a given edge $$(u_i, u_j)$$ in $$T_1$$. Then for every edge in $$T_1$$, compute either

${v^1}_{j|i} = \frac{\partial C_{ij}(u_i, u_j)}{\partial u_j}$

or similarly $${v^1}_{i|j}$$, which are conditional cdfs. When finished with all the edges, construct the new matrix with $$v^1$$ that has one less column u.

4. Set k = 2.

5. Assign one node of $$T_k$$ to each edge of $$T_ {k−1}$$. The structure of $$T_{k−1}$$ imposes a set of constraints on which edges of $$T_k$$ are realizable. Hence the next step is to get a linked list of the accesible nodes for every node in $$T_k$$.

6. As in step 1, nodes of $$T_k$$ are coupled maximizing the measure of association considered and satisfying the constraints impose by the kind of vine employed plus the set of constraints imposed by tree $$T_{k−1}$$.

7. Select the copula that best fit to each edge created in $$T_k$$.

8. Recompute matrix $$v_k$$ as in step 4, but taking $$T_k$$ and $$vk−1$$ instead of $$T_1$$ and u.

9. Set $$k = k + 1$$ and repeat from (5) until all the trees are constructed.

Parameters

tree_type (str or TreeTypes) – Type of trees to use.

class copulas.multivariate.Tree(random_seed=None)[source]

Helper class to instantiate a single tree in the vine model.

fit(index, n_nodes, tau_matrix, previous_tree, edges=None)[source]

Fit this tree object.

Parameters
• index (int) – index of the tree.

• n_nodes (int) – number of nodes in the tree.

• tau_matrix (numpy.array) – kendall’s tau matrix of the data, shape (n_nodes, n_nodes).

• previous_tree (Tree) – tree object of previous level.

fitted = False
classmethod from_dict(tree_dict, previous=None)[source]

Create a new instance from a parameters dictionary.

Parameters

params (dict) – Parameters of the Tree, in the same format as the one returned by the to_dict method.

Returns

Instance of the tree defined on the parameters.

Return type

Tree

get_adjacent_matrix()[source]

Returns

Return type

numpy.ndarray

get_likelihood(uni_matrix)[source]

Compute likelihood of the tree given an U matrix.

Parameters

uni_matrix (numpy.array) – univariate matrix to evaluate likelihood on.

Returns

likelihood of the current tree, next level conditional univariate matrix

Return type

tuple[float, numpy.array]

get_tau_matrix()[source]

Get tau matrix for adjacent pairs.

Returns

tau matrix for the current tree

Return type

tau (numpy.ndarray)

prepare_next_tree()[source]

Prepare conditional U matrix for next tree.

to_dict()[source]

Return a dict with the parameters to replicate this Tree.

Returns

Parameters of this Tree.

Return type

dict

tree_type = None
class copulas.multivariate.TreeTypes[source]

Bases: enum.Enum

An enumeration.

CENTER = 0
DIRECT = 1
REGULAR = 2