Algorithm Introduction

Perform Peter-Clark algorithm for causal discovery on the augmented data set that captures the unobserved changing factors (CD-NOD, 1).


from import cdnod
G = cdnod(data, c_indx, alpha, indep_test, stable, uc_rule, uc_priority, mvcdnod,
      correction_name, background_knowledge, verbose, show_progress)

# visualization using pydot
# note that the last node is the c_indx

Visualization using pydot is recommended. If specific label names are needed, please refer to this usage example (e.g., ‘cg.draw_pydot_graph(labels=[“A”, “B”, “C”])’ or ‘GraphUtils.to_pydot(cg.G, labels=[“A”, “B”, “C”])’).


data: numpy.ndarray, shape (n_samples, n_features). Data, where n_samples is the number of samples and n_features is the number of features.

c_indx: time index or domain index that captures the unobserved changing factors.

alpha: desired significance level (float) in (0, 1). Default: 0.05.

indep_test: Independence test method function. Default: ‘fisherz’.
  • fisherz”: Fisher’s Z conditional independence test.

  • chisq”: Chi-squared conditional independence test.

  • gsq”: G-squared conditional independence test.

  • kci”: kernel-based conditional independence test. (As a kernel method, its complexity is cubic in the sample size, so it might be slow if the same size is not small.)

  • mv_fisherz”: Missing-value Fisher’s Z conditional independence test.

stable: run stabilized skeleton discovery if True. Default: True.

uc_rule: how unshielded colliders are oriented. Default: 0.
  • 0: run uc_sepset.

  • 1: run maxP 2. Orient an unshielded triple X-Y-Z as a collider with an additional CI test.

  • 2: run definiteMaxP 2. Orient only the definite colliders in the skeleton and keep track of all the definite non-colliders as well.

uc_priority: rule of resolving conflicts between unshielded colliders. Default: 2.
  • -1: whatever is default in uc_rule.

  • 0: overwrite.

  • 1: orient bi-directed.

  • 2: prioritize existing colliders.

  • 3: prioritize stronger colliders.

  • 4: prioritize stronger* colliders.

mvpc: use missing-value PC or not. Default (and suggested for CDNOD): False.

correction_name: Missing value correction if using missing-value PC. Default: ‘MV_Crtn_Fisher_Z’

background_knowledge: class BackgroundKnowledge. Add prior edges according to assigned causal connections. Default: Nnoe. For detailed usage, please kindly refer to its usage example.

verbose: True iff verbose output should be printed. Default: False.

show_progress: True iff the algorithm progress should be show in console. Default: True.


cg : a CausalGraph object, where cg.G.graph[j,i]=1 and cg.G.graph[i,j]=-1 indicate i –> j; cg.G.graph[i,j] = cg.G.graph[j,i] = -1 indicates i — j; cg.G.graph[i,j] = cg.G.graph[j,i] = 1 indicates i <-> j.


Huang, B., Zhang, K., Zhang, J., Ramsey, J. D., Sanchez-Romero, R., Glymour, C., & Schölkopf, B. (2020). Causal Discovery from Heterogeneous/Nonstationary Data. J. Mach. Learn. Res., 21(89), 1-53.


Ramsey, J. (2016). Improving accuracy and scalability of the pc algorithm by maximizing p-value. arXiv preprint arXiv:1610.00378.