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HighDimDirectLiNGAM

Import and settings

In this example, we need to import numpy, pandas, and graphviz in addition to lingam.

import numpy as np
import pandas as pd
import graphviz
import lingam
from lingam import HighDimDirectLiNGAM
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(100)
['1.24.4', '2.0.3', '0.20.1', '1.8.3']

Test data

We create test data consisting of 6 variables.

m = np.array([
    [ 0.000,  0.000,  0.000,  0.895,  0.000,  0.000],
    [ 0.565,  0.000,  0.377,  0.000,  0.000,  0.000],
    [ 0.000,  0.000,  0.000,  0.895,  0.000,  0.000],
    [ 0.000,  0.000,  0.000,  0.000,  0.000,  0.000],
    [ 0.991,  0.000, -0.124,  0.000,  0.000,  0.000],
    [ 0.895,  0.000,  0.000,  0.000,  0.000,  0.000]
])

generate_error = lambda p: np.random.uniform(-p, p, size=1000)

error_vars = [0.2, 0.2, 0.2, 1.0, 0.2, 0.2]
params = [0.5 * np.sqrt(12 * v) for v in error_vars]
e = np.array([generate_error(p) for p in params])

X = np.linalg.pinv(np.eye(len(m)) - m) @ e
X = pd.DataFrame(X.T)

display(make_dot(m))

X.head()

.dataframe tbody tr th:only-of-type { vertical-align: middle; } .dataframe tbody tr th { vertical-align: top; } .dataframe thead th { text-align: right; }
0 1 2 3 4 5
0 -1.245034 -2.070303 -1.684946 -1.466231 -0.607202 -1.208680
1 -0.129694 -0.453755 -0.525306 0.238720 -0.770446 0.214530
2 -0.426608 0.434575 -0.070464 -0.346001 -0.891935 0.060805
3 -0.058363 -0.412667 0.134419 -0.661997 -0.661361 0.382801
4 0.560928 0.631961 1.636429 1.484039 0.757059 0.526978

Causal Discovery

To run causal discovery, we create a HighDimDirectLiNGAM object and call the fit method.

model = HighDimDirectLiNGAM()
model.fit(X)
<lingam.high_dim_direct_lingam.HighDimDirectLiNGAM at 0x7f47d61bcc10>

Using the causal_order_ properties, we can see the causal ordering as a result of the causal discovery.

model.causal_order_
[3, 2, 0, 4, 1, 5]

Also, using the adjacency_matrix_ properties, we can see the adjacency matrix as a result of the causal discovery.

model.adjacency_matrix_
array([[ 0.   ,  0.   ,  0.   ,  0.87 ,  0.   ,  0.   ],
       [ 0.535,  0.   ,  0.411,  0.   ,  0.   ,  0.   ],
       [ 0.   ,  0.   ,  0.   ,  0.894,  0.   ,  0.   ],
       [ 0.   ,  0.   ,  0.   ,  0.   ,  0.   ,  0.   ],
       [ 0.937,  0.   , -0.103,  0.   ,  0.   ,  0.   ],
       [ 0.875,  0.   ,  0.   ,  0.   ,  0.   ,  0.   ]])

We can draw a causal graph by utility funciton.

make_dot(model.adjacency_matrix_)