Draw Causal Graph

Import and settings

In this example, we need to import numpy, pandas, and graphviz in addition to lingam. And to draw the causal graph, we need to import make_dot method from lingam.utils.

import numpy as np
import pandas as pd
import graphviz
import lingam
from lingam.utils import make_dot

print([np.__version__, pd.__version__, graphviz.__version__, lingam.__version__])

np.set_printoptions(precision=3, suppress=True)
np.random.seed(0)

['1.16.2', '0.24.2', '0.11.1', '1.3.1']

Draw the result of LiNGAM

First, we can draw a simple graph that is the result of LiNGAM.

x3 = np.random.uniform(size=10000)
x0 = 3.0*x3 + np.random.uniform(size=10000)
x2 = 6.0*x3 + np.random.uniform(size=10000)
x1 = 3.0*x0 + 2.0*x2 + np.random.uniform(size=10000)
x5 = 4.0*x0 + np.random.uniform(size=10000)
x4 = 8.0*x0 - 1.0*x2 + np.random.uniform(size=10000)
X = pd.DataFrame(np.array([x0, x1, x2, x3, x4, x5]).T ,columns=['x0', 'x1', 'x2', 'x3', 'x4', 'x5'])

model = lingam.DirectLiNGAM()
model.fit(X)
make_dot(model.adjacency_matrix_)
../_images/draw_graph1.svg

If we want to change the variable name, we can use labels.

labels = [f'var{i}' for i in range(X.shape[1])]
make_dot(model.adjacency_matrix_, labels=labels)
../_images/draw_graph2.svg

Save graph

The created dot data can be saved as an image file in addition to being displayed in Jupyter Notebook.

dot = make_dot(model.adjacency_matrix_, labels=labels)

# Save pdf
dot.render('dag')

# Save png
dot.format = 'png'
dot.render('dag')

'dag.png'

Draw the result of LiNGAM with prediction model

For example, we create a linear regression model with x0 as the target variable.

from sklearn.linear_model import LinearRegression

target = 0
features = [i for i in range(X.shape[1]) if i != target]
reg = LinearRegression()

reg.fit(X.iloc[:, features], X.iloc[:, target])

LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,
         normalize=False)

By specify prediction_feature_indices and prediction_coefs that can be obtained from the prediction model, we can draw the prediction model with the causal structure.

make_dot(model.adjacency_matrix_, prediction_feature_indices=features, prediction_coefs=reg.coef_)
../_images/draw_graph3.svg

Also, we can change the label of the target variable by prediction_target_label, omit the coefficient of prediction model without prediction_coefs, and change the color by prediction_line_color.

make_dot(model.adjacency_matrix_, prediction_feature_indices=features, prediction_target_label='Target', prediction_line_color='#0000FF')
../_images/draw_graph4.svg

In addition to the above, we can use prediction_feature_importance to draw the importance of the prediction model as an edge label.

import lightgbm as lgb

target = 0
features = [i for i in range(X.shape[1]) if i != target]
reg = lgb.LGBMRegressor(random_state=0)
reg.fit(X.iloc[:, features], X.iloc[:, target])
reg.feature_importances_

array([619, 205, 310, 957, 909])

make_dot(model.adjacency_matrix_, prediction_feature_indices=features, prediction_feature_importance=reg.feature_importances_)
../_images/draw_graph5.svg