DirectLiNGAM in Python
DirectLiNGAM (with bootstrapping) in Python
Notes & memorandums
table of contents
◆ Introduction ◆ Environment ◆ Procedure ◆ 3 variables --Preparation --Data generation --Bootstrap --Confirmation of orientation --Confirmation of DAG ◆ 7 variables --Preparation --Data generation --Bootstrap --Confirmation of orientation --Confirmation of DAG ◆ Reference
Introduction
I estimated the simulation data using the lingam package implemented last time.
LiNGAM in Python https://qiita.com/kumalpha/items/f05bd031cf9daac464a0
environment
OS: Mojave (version; 10.14.6) Python: 3.7.6 JupyterLab: 1.2.6
procedure
- Preparation
- Data generation
- Bootstrap
- Confirmation of orientation
- Confirmation of DAG
3 variables
Preparation
# DirectLiNGAM
# Import and sets
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)
['1.18.1', '1.0.1', '0.13.2', '1.2.1']
Data generation
# Create test data
x0 = np.random.uniform(size=10000)
x1 = 3.0*x0 + np.random.uniform(size=10000)
x2 = 5.0*x0 + 0.5*x1 + np.random.uniform(size=10000)
X = pd.DataFrame(np.array([x0, x1, x2]).T,columns=['x0', 'x1', 'x2'])
X.head()
x0 x1 x2
0 0.758125 2.643633 5.420089
1 0.503319 1.721282 3.439239
2 0.177017 1.007955 2.377846
3 0.832537 2.579844 6.171695
4 0.516825 1.788134 4.235760
# Visualize the test data
m = np.array([[0.0, 0.0, 0.0],
[3.0, 0.0, 0.0],
[5.0, 0.5, 0.0]])
make_dot(m)
This causal relationship will be estimated using the bootstrap method.
Bootstrap
model = lingam.DirectLiNGAM()
result = model.bootstrap(X, 3000) # Number of bootstrapping samples
cdc = result.get_causal_direction_counts(n_directions=10, min_causal_effect=0.1)
Confirmation of orientation
from lingam.utils import print_causal_directions
print_causal_directions(cdc, 3000)
x1 <--- x0 (100.0%)
x2 <--- x0 (100.0%)
x2 <--- x1 (100.0%)
Since this time is simple data, the causal relationship is clear at this point.
Confirmation of DAG
In the previous stage, we were just looking at the one-to-one relationship between variables. This time, we will integrate them into a DAG.
dagc = result.get_directed_acyclic_graph_counts(n_dags=5, min_causal_effect=0.1)
from lingam.utils import print_dagc
print_dagc(dagc, 3000)
DAG[0]: 100.0%
x1 <--- x0
x2 <--- x0
x2 <--- x1
I was able to estimate the orientation well. I had set it to output up to 5 DAG candidates, but probably because it was 100.0%, the rest were not output.
# Get the probability of bootstrapping.
prob = result.get_probabilities(min_causal_effect=0.1)
print(prob)
[[0. 0. 0.]
[1. 0. 0.]
[1. 1. 0.]]
The probability was also output as 1.
7 variables
This causal relationship was estimated with some complexity.
Preparation
# DirectLiNGAM
# Import and sets
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)
['1.18.1', '1.0.1', '0.13.2', '1.2.1']
Data generation
# Create test data
x0 = np.random.uniform(size=10000)
x6 = np.random.uniform(size=10000)
x1 = -5.0*x0 + np.random.uniform(size=10000)
x2 = -2.5*x0 + 3.0*x1 + np.random.uniform(size=10000)
x5 = 6.0*x6 + np.random.uniform(size=10000)
x3 = 4.0*x2 + 7.0*x5 + np.random.uniform(size=10000)
x4 = 1.0*x1 + 2.0*x2 + 8.0*x6 +np.random.uniform(size=10000)
X = pd.DataFrame(np.array([x0, x1, x2, x3, x4, x5, x6]).T,columns=['x0', 'x1', 'x2', 'x3', 'x4', 'x5', 'x6'])
X.head()
x0 x1 x2 x3 x4 x5 x6
0 0.548814 -2.351895 -7.669592 3.641327 -10.776980 4.858864 0.748268
1 0.715189 -3.534790 -11.889026 -38.446302 -24.968283 1.292542 0.180203
2 0.602763 -2.090516 -7.601441 -9.739672 -13.753596 2.811044 0.389023
3 0.544883 -2.318181 -7.484214 -27.062919 -16.475002 0.307835 0.037600
4 0.423655 -1.173992 -4.064288 -13.340880 -8.625065 0.308386 0.011788
# Visualize the test data
m = np.array([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[-5.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[-2.5, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 4.0, 0.0, 0.0, 7.0, 0.0],
[0.0, 1.0, 2.0, 0.0, 0.0, 0.0, 8.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]])
make_dot(m)
This causal relationship will be estimated using the bootstrap method.
Bootstrap
model = lingam.DirectLiNGAM()
result = model.bootstrap(X, 3000) # Number of bootstrapping samples
cdc = result.get_causal_direction_counts(n_directions=10, min_causal_effect=0.1)
Confirmation of orientation
from lingam.utils import print_causal_directions
print_causal_directions(cdc, 3000)
x1 <--- x0 (100.0%)
x2 <--- x0 (100.0%)
x2 <--- x1 (100.0%)
x3 <--- x5 (100.0%)
x4 <--- x1 (100.0%)
x4 <--- x2 (100.0%)
x5 <--- x6 (100.0%)
x4 <--- x6 (97.4%)
x3 <--- x2 (96.1%)
x3 <--- x4 (4.8%)
Confirmation of DAG
dagc = result.get_directed_acyclic_graph_counts(n_dags=5, min_causal_effect=0.1)
from lingam.utils import print_dagc
print_dagc(dagc, 3000)
DAG[0]: 88.5%
x1 <--- x0
x2 <--- x0
x2 <--- x1
x3 <--- x2
x3 <--- x5
x4 <--- x1
x4 <--- x2
x4 <--- x6
x5 <--- x6
DAG[1]: 3.9%
x1 <--- x0
x2 <--- x0
x2 <--- x1
x3 <--- x4
x3 <--- x5
x4 <--- x1
x4 <--- x2
x4 <--- x6
x5 <--- x6
DAG[2]: 2.7%
x1 <--- x0
x2 <--- x0
x2 <--- x1
x3 <--- x2
x3 <--- x5
x4 <--- x0
x4 <--- x1
x4 <--- x2
x4 <--- x6
x5 <--- x6
DAG[3]: 2.6%
x1 <--- x0
x2 <--- x0
x2 <--- x1
x3 <--- x2
x3 <--- x5
x4 <--- x1
x4 <--- x2
x4 <--- x3
x5 <--- x6
DAG[4]: 0.9%
x1 <--- x0
x2 <--- x0
x2 <--- x1
x3 <--- x2
x3 <--- x4
x3 <--- x5
x4 <--- x1
x4 <--- x2
x4 <--- x6
x5 <--- x6
An accurate causal relationship could be estimated at 88.5%.
prob = result.get_probabilities(min_causal_effect=0.1)
print(prob)
[[0. 0. 0. 0. 0. 0. 0. ]
[1. 0. 0. 0. 0. 0. 0. ]
[1. 1. 0. 0. 0. 0. 0. ]
[0.006 0. 0.961 0. 0.048 1. 0.007]
[0.027 1. 1. 0.026 0. 0. 0.974]
[0. 0. 0. 0. 0. 0. 1. ]
[0. 0. 0. 0. 0. 0. 0. ]]
reference
・ LiNGAM (ICA version) to understand with mathematical formulas and Python https://qiita.com/k-kotera/items/6d7f5598464e18afaa7c ・ Causal reasoning by structural equation model: Recent developments in causal structure search https://www.slideshare.net/sshimizu2006/bsj2012-tutorial-finalweb ・ LiNGAM in Python https://qiita.com/kumalpha/items/f05bd031cf9daac464a0 ・ LiNGAM docs https://lingam.readthedocs.io/en/latest/index.html ・ Lingam GitHub (examples) https://github.com/cdt15/lingam/tree/master/examples
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