2.5.1. pywhy_graphs.functional.make_graph_linear_gaussian

pywhy_graphs.functional.make_graph_linear_gaussian(G: DiGraph, node_mean_lims: List[float] | None = None, node_std_lims: List[float] | None = None, edge_functions: List[Callable[[float], float]] | None = None, edge_weight_lims: List[float] | None = None, random_state=None) → DiGraph

Convert an existing DAG to a linear Gaussian graphical model.

All nodes are sampled from a normal distribution with parametrizations defined uniformly at random between the limits set by the input parameters. The edges apply then a weight and a function based on the inputs in an additive fashion. For node \(X_i\), we have:

\[\begin{split}X_i = \\sum_{j \in parents} w_j f_j(X_j) + \\epsilon_i\end{split}\]

where:

• \(\\epsilon_i \sim N(\mu_i, \sigma_i)\), where \(\mu_i\) is sampled

  uniformly at random from node_mean_lims and \(\sigma_i\) is sampled uniformly at random from node_std_lims.

• \(w_j \sim U(\\text{edge_weight_lims})\)

• \(f_j\) is a function sampled uniformly at random

  from edge_functions

Parameters:

GNetworkX DiGraph

The graph to sample data from. The graph will be modified in-place to get the weights and functions of the edges.

node_mean_limsOptional[List[float]], optional

The lower and upper bounds of the mean of the Gaussian random variable, by default None, which defaults to a mean of 0.

node_std_limsOptional[List[float]], optional

The lower and upper bounds of the std of the Gaussian random variable, by default None, which defaults to a std of 1.

edge_functionsList[Callable[float]], optional

The set of edge functions that take in an iid sample from the parent and computes a transformation (possibly nonlinear), such as (lambda x: x**2, lambda x: x), by default None, which defaults to the identity function lambda x: x.

edge_weight_limsOptional[List[float]], optional

The lower and upper bounds of the edge weight, by default None, which defaults to a weight of 1.

random_stateint, optional

Random seed, by default None.

Returns:

GNetworkX DiGraph

NetworkX graph with the edge weights and functions set with node attributes set with 'parent_function', and 'gaussian_noise_function'. Moreover the graph attribute 'linear_gaussian' is set to True.