.. _fci:

FCI
=====

Algorithm Introduction
--------------------------------------

Causal Discovery with Fast Causal Inference (FCI [1]_).


Usage
----------------------------
.. code-block:: python

    from causallearn.search.ConstraintBased.FCI import fci

    # default parameters
    G, edges = fci(data)

    # or customized parameters
    G, edges = fci(data, independence_test_method, alpha, depth, max_path_length,
        verbose, background_knowledge, cache_variables_map)

    # visualization
    from causallearn.utils.GraphUtils import GraphUtils

    pdy = GraphUtils.to_pydot(G)
    pdy.write_png('simple_test.png')

Visualization using pydot is recommended. If specific label names are needed, please refer to this `usage example <https://github.com/cmu-phil/causal-learn/blob/main/tests/TestGraphVisualization.py>`_.


Parameters
-------------------
**dataset**: numpy.ndarray, shape (n_samples, n_features). Data, where n_samples is the number of samples
and n_features is the number of features.

**independence_test_method**: Independence test method function. Default: 'fisherz'.
       - ":ref:`fisherz <Fisher-z test>`": Fisher's Z conditional independence test.
       - ":ref:`chisq <Chi-Square test>`": Chi-squared conditional independence test.
       - ":ref:`gsq <G-Square test>`": G-squared conditional independence test.
       - ":ref:`kci <Kernel-based conditional independence (KCI) test and independence test>`": 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.)
       - ":ref:`mv_fisherz <Missing-value Fisher-z test>`": Missing-value Fisher's Z conditional independence test.

**alpha**: Significance level of individual partial correlation tests. Default: 0.05.

**depth**: The depth for the fast adjacency search, or -1 if unlimited. Default: -1.

**max_path_length**: the maximum length of any discriminating path, or -1 if unlimited. Default: -1.

**verbose**: True is verbose output should be printed or logged. Default: False.

**background_knowledge**: class BackgroundKnowledge. Add prior edges according to assigned causal connections. Default: None.
For detailed usage, please kindly refer to its `usage example <https://github.com/cmu-phil/causal-learn/blob/main/tests/TestBackgroundKnowledge.py>`_.

**cache_variables_map**: This variable a map which contains the variables relate with cache. If it is not None, it should contain 'data_hash_key' 、'ci_test_hash_key' and 'cardinalities'. Default: None.


Returns
-------------------
**G**: a CausalGraph object, where G is a PAG and the illustration of its end nodes is as follows:

.. image:: pag.png
  :width: 500


**edges**: list. Contains graph's edges properties.
       - If edge.properties have the Property 'nl', then there is no latent confounder. Otherwise, there are possibly latent confounders.
       - If edge.properties have the Property 'dd', then it is definitely direct. Otherwise, it is possibly direct.
       - If edge.properties have the Property 'pl', then there are possibly latent confounders. Otherwise, there is no latent confounder.
       - If edge.properties have the Property 'pd', then it is possibly direct. Otherwise, it is definitely direct.


.. [1] Spirtes, P., Meek, C., & Richardson, T. (1995, August). Causal inference in the presence of latent variables and selection bias. In Proceedings of the Eleventh conference on Uncertainty in artificial intelligence (pp. 499-506).
