Generalized-Score-Functions-for-Causal-Discovery

Copyright (c) 2017-2018 Biwei Huang

Causal structure learning by greedy equivalence search with generalized score functions (which is applicable to mixed continuous and discrete data, data with Gaussian or non-Gaussian distributions, linear or nonlinear causal mechanisms, and variables with multi-dimensionalities.)

IMPORTANT FUNCTIONS:

function [Record] = GES(X,score_type,multi_sign,maxP,parameters)

• INPUT:

  • X: Data with T*D dimensions
  • score_type: the score function you want to use

    • score_type = 1: cross-validated likelihood
      

    • score_type = 2: marginal likelihood
      

  • multi_sign: 1: if are multi-dimensional variables; 0: otherwise
  • maxP: allowed maximum number of parents when searching the graph
  • parameters:
    • when using CV likelihood,

    •  parameters.kfold: k-fold cross validation
      

    •  parameters.lambda: regularization parameter
      

    • parameters.dlabel: for variables with multi-dimensions, indicate which dimensions belong to the i-th variable.

• OUTPUT:

  • Record.G: learned causal graph

    •  G(i,j) = 1: i->j (the edge is from i to j)
      

    •  G(i,j) = -1: i-j (the direction between i and j is not determined)
      

    •  G(i,j) = 0:  i j (no causal edge between i and j)
      

  • Record.update1: each update (Insert operator) in the forward step
  • Record.update2: each update (Delete operator) in the backward step
  • Record.G_step1: learned graph at each step in the forward step
  • Record.G_step2: learned graph at each step in the backward step
  • Record.score: the score of the learned graph

EXAMPLE:

see example1.m and example2.m (for data with multi-variate dimensions)

CITATION:

Biwei Huang ,Kun Zhang , Yizhu Lin, Bernhard Scholkopf, Clark Glymour. Generalized Score Functions for Causal Discovery. KDD, 2018.