dodiscover.toporder.CAM

class dodiscover.toporder.CAM(alpha=0.05, prune=True, n_splines=10, splines_degree=3, pns=False, pns_num_neighbors=None, pns_threshold=1)

The CAM (Causal Additive Model) algorithm for causal discovery.

CAM [1] iteratively defines a topological ordering by leaf additions. Then it prunes the fully connected DAG consistent with the inferred topological order. The method assumes Additive Noise Model and Gaussianity of the noise terms.

Parameters:

alphafloat, optional

Alpha cutoff value for variable selection with hypothesis testing over regression coefficients, default is 0.05.

prunebool, optional

If True (default), apply CAM-pruning after finding the topological order.

n_splinesint, optional

Number of splines to use for the feature function, default is 10. Automatically decreased in case of insufficient samples

splines_degree: int, optional

Order of spline to use for the feature function, default is 3.

pnsbool, optional

If True, perform Preliminary Neighbour Search (PNS) before CAM pruning step, default is False. Allows scaling CAM pruning and ordering to large graphs.

pns_num_neighbors: int, optional

Number of neighbors to use for PNS. If None (default) use all variables.

pns_threshold: float, optional

Threshold to use for PNS, default is 1.

Notes

Prior knowledge about the included and excluded directed edges in the output DAG is supported. It is not possible to provide explicit constraints on the relative positions of nodes in the topological ordering. However, explicitly including a directed edge in the DAG defines an implicit constraint on the relative position of the nodes in the topological ordering (i.e. if directed edge (i,j) is encoded in the graph, node i will precede node j in the output order).

References

[1]

Peter Bühlmann, Jonas Peters, and Jan Ernest. Cam: causal additive models, high-dimensional order search and penalized regression. The Annals of Statistics, 42:, 10 2013. doi:10.1214/14-AOS1260.

Methods

learn_graph(data_df, context)	Fit topological order based causal discovery algorithm on input data.
prune(X, A_dense, G_included, G_excluded)	Prune the dense adjacency matrix A_dense from spurious edges.

learn_graph(data_df, context)

Fit topological order based causal discovery algorithm on input data.

Parameters:

data_dfpd.DataFrame

Datafame of the input data.

context: Context

The context of the causal discovery problem.

prune(X, A_dense, G_included, G_excluded)

Prune the dense adjacency matrix A_dense from spurious edges.

Use sparse regression over the matrix of the data X for variable selection over the edges in the dense (potentially fully connected) adjacency matrix A_dense

Parameters:

Xnp.ndarray of shape (n_samples, n_nodes)

Matrix of the data.

A_densenp.ndarray of shape (n_nodes, n_nodes)

Dense adjacency matrix to be pruned.

G_includednx.DiGraph

Graph with edges that are required to be included in the output. It encodes assumptions and prior knowledge about the causal graph.

G_excludednx.DiGraph

Graph with edges that are required to be excluded from the output. It encodes assumptions and prior knowledge about the causal graph.

Returns:

Anp.ndarray

The pruned adjacency matrix output of the causal discovery algorithm.