copulas.multivariate package

Submodules

Module contents

Multivariate copulas module.

class copulas.multivariate.GaussianMultivariate(distribution=<class 'copulas.univariate.base.Univariate'>, random_state=None)[source]

Bases: Multivariate

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

correlation = 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)[source]

Compute the distribution for each variable and then its correlation matrix.

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

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(num_rows=1, conditions=None)[source]

Sample values from this model.

Argument:

num_rows (int):: Number of rows to sample.
conditions (dict or pd.Series):: Mapping of the column names and column values to condition on.

Returns:: Array of shape (n_samples, *) with values randomly sampled from this model distribution. If conditions have been given, the output array also contains the corresponding columns populated with the given values.
Return type:: numpy.ndarray
Raises:: NotFittedError – if the model is not fitted.

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.Multivariate(random_state=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:: Loaded instance.
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.

set_random_state(random_state)[source]

Set the random state.

Parameters:: random_state (int, np.random.RandomState, or None) – Seed or RandomState for the random generator.

to_dict()[source]

Return a dict with the parameters to replicate this object.

Returns:: Parameters of this distribution.
Return type:: dict

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

Bases: Multivariate

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]

Get adjacency matrix.

Returns:: adjacency matrix
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(*values)[source]

Bases: Enum

The available types of trees.

CENTER = 0

DIRECT = 1

REGULAR = 2

class copulas.multivariate.VineCopula(vine_type, random_state=None)[source]

Bases: Multivariate

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_state (int or np.random.RandomState) – Random seed or RandomState 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, truncated=3)[source]

Fit a vine model to the data.

1. Transform all the variables by means of their marginals. In other words, compute

\[u_i = F_i(x_i), i = 1, ..., n\]

and compose the matrix \(u = u_1, ..., u_n,\) where \(u_i\) are their columns.

Parameters:

X (numpy.ndarray) – Data to be fitted to.
truncated (int) – Max level to build the vine.

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(num_rows)[source]

Sample new rows.

Parameters:: num_rows (int) – Number of rows to sample
Returns:: sampled rows.
Return type:: pandas.DataFrame

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 vine.

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.
Select the copula that best fits to the pair of variables coupled by each edge in \(T_1\).
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

\[\begin{split}{v^1}_{j|i} = \\frac{\\partial C_{ij}(u_i, u_j)}{\\partial u_j}\end{split}\]

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.
Set k = 2.
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 \(T_k\).
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 \(T_{k−1}\).
Select the copula that best fit to each edge created in \(T_k\).
Recompute matrix \(v_k\) as in step 4, but taking \(T_k\) and \(vk−1\) instead of \(T_1\) and u.
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.