# CD-NOD

## Algorithm Introduction

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

## Usage

```
from causallearn.search.ConstraintBased.CDNOD import cdnod
cg = 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
cg.draw_pydot_graph()
# or save the graph
from causallearn.utils.GraphUtils import GraphUtils
pyd = GraphUtils.to_pydot(cg.G)
pyd.write_png('simple_test.png')
```

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”])’).

## Parameters

**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.**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.

## Returns

**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.

- 1
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.

- 2(1,2)
Ramsey, J. (2016). Improving accuracy and scalability of the pc algorithm by maximizing p-value. arXiv preprint arXiv:1610.00378.