Note
Go to the end to download the full example code.
Random forest#
A RandomForestRegressor is a random forest model
based on scikit-learn.
from __future__ import annotations
from matplotlib import pyplot as plt
from numpy import array
from gemseo import configure_logger
from gemseo import create_design_space
from gemseo import create_discipline
from gemseo import sample_disciplines
from gemseo.mlearning import create_regression_model
configure_logger()
<RootLogger root (INFO)>
Problem#
In this example,
we represent the function \(f(x)=(6x-2)^2\sin(12x-4)\) [FSK08]
by the AnalyticDiscipline
discipline = create_discipline(
"AnalyticDiscipline",
name="f",
expressions={"y": "(6*x-2)**2*sin(12*x-4)"},
)
and seek to approximate it over the input space
input_space = create_design_space()
input_space.add_variable("x", lower_bound=0.0, upper_bound=1.0)
To do this, we create a training dataset with 6 equispaced points:
training_dataset = sample_disciplines(
[discipline], input_space, "y", algo_name="PYDOE_FULLFACT", n_samples=6
)
WARNING - 20:35:13: No coupling in MDA, switching chain_linearize to True.
INFO - 20:35:13: *** Start Sampling execution ***
INFO - 20:35:13: Sampling
INFO - 20:35:13: Disciplines: f
INFO - 20:35:13: MDO formulation: MDF
INFO - 20:35:13: Running the algorithm PYDOE_FULLFACT:
INFO - 20:35:13: 17%|█▋ | 1/6 [00:00<00:00, 638.01 it/sec]
INFO - 20:35:13: 33%|███▎ | 2/6 [00:00<00:00, 1049.63 it/sec]
INFO - 20:35:13: 50%|█████ | 3/6 [00:00<00:00, 1373.38 it/sec]
INFO - 20:35:13: 67%|██████▋ | 4/6 [00:00<00:00, 1657.83 it/sec]
INFO - 20:35:13: 83%|████████▎ | 5/6 [00:00<00:00, 1902.52 it/sec]
INFO - 20:35:13: 100%|██████████| 6/6 [00:00<00:00, 2113.53 it/sec]
INFO - 20:35:13: *** End Sampling execution ***
Basics#
Training#
Then, we train an random forest regression model from these samples:
model = create_regression_model("RandomForestRegressor", training_dataset)
model.learn()
Prediction#
Once it is built, we can predict the output value of \(f\) at a new input point:
input_value = {"x": array([0.65])}
output_value = model.predict(input_value)
output_value
{'y': array([-0.88837697])}
but cannot predict its Jacobian value:
try:
model.predict_jacobian(input_value)
except NotImplementedError:
print("The derivatives are not available for RandomForestRegressor.")
The derivatives are not available for RandomForestRegressor.
Plotting#
You can see that the random forest model is pretty good on the left, but bad on the right:
test_dataset = sample_disciplines(
[discipline], input_space, "y", algo_name="PYDOE_FULLFACT", n_samples=100
)
input_data = test_dataset.get_view(variable_names=model.input_names).to_numpy()
reference_output_data = test_dataset.get_view(variable_names="y").to_numpy().ravel()
predicted_output_data = model.predict(input_data).ravel()
plt.plot(input_data.ravel(), reference_output_data, label="Reference")
plt.plot(input_data.ravel(), predicted_output_data, label="Regression - Basics")
plt.grid()
plt.legend()
plt.show()
WARNING - 20:35:13: No coupling in MDA, switching chain_linearize to True.
INFO - 20:35:13: *** Start Sampling execution ***
INFO - 20:35:13: Sampling
INFO - 20:35:13: Disciplines: f
INFO - 20:35:13: MDO formulation: MDF
INFO - 20:35:13: Running the algorithm PYDOE_FULLFACT:
INFO - 20:35:13: 1%| | 1/100 [00:00<00:00, 2922.86 it/sec]
INFO - 20:35:13: 2%|▏ | 2/100 [00:00<00:00, 2861.05 it/sec]
INFO - 20:35:13: 3%|▎ | 3/100 [00:00<00:00, 3126.19 it/sec]
INFO - 20:35:13: 4%|▍ | 4/100 [00:00<00:00, 3357.46 it/sec]
INFO - 20:35:13: 5%|▌ | 5/100 [00:00<00:00, 3481.33 it/sec]
INFO - 20:35:13: 6%|▌ | 6/100 [00:00<00:00, 3614.22 it/sec]
INFO - 20:35:13: 7%|▋ | 7/100 [00:00<00:00, 3739.19 it/sec]
INFO - 20:35:13: 8%|▊ | 8/100 [00:00<00:00, 3842.70 it/sec]
INFO - 20:35:13: 9%|▉ | 9/100 [00:00<00:00, 3923.99 it/sec]
INFO - 20:35:13: 10%|█ | 10/100 [00:00<00:00, 3936.47 it/sec]
INFO - 20:35:13: 11%|█ | 11/100 [00:00<00:00, 3994.23 it/sec]
INFO - 20:35:13: 12%|█▏ | 12/100 [00:00<00:00, 4058.35 it/sec]
INFO - 20:35:13: 13%|█▎ | 13/100 [00:00<00:00, 4118.90 it/sec]
INFO - 20:35:13: 14%|█▍ | 14/100 [00:00<00:00, 4128.83 it/sec]
INFO - 20:35:13: 15%|█▌ | 15/100 [00:00<00:00, 4132.05 it/sec]
INFO - 20:35:13: 16%|█▌ | 16/100 [00:00<00:00, 4163.60 it/sec]
INFO - 20:35:13: 17%|█▋ | 17/100 [00:00<00:00, 4198.26 it/sec]
INFO - 20:35:13: 18%|█▊ | 18/100 [00:00<00:00, 4234.53 it/sec]
INFO - 20:35:13: 19%|█▉ | 19/100 [00:00<00:00, 4246.15 it/sec]
INFO - 20:35:13: 20%|██ | 20/100 [00:00<00:00, 4270.53 it/sec]
INFO - 20:35:13: 21%|██ | 21/100 [00:00<00:00, 4289.07 it/sec]
INFO - 20:35:13: 22%|██▏ | 22/100 [00:00<00:00, 4313.72 it/sec]
INFO - 20:35:13: 23%|██▎ | 23/100 [00:00<00:00, 4338.22 it/sec]
INFO - 20:35:13: 24%|██▍ | 24/100 [00:00<00:00, 4346.80 it/sec]
INFO - 20:35:13: 25%|██▌ | 25/100 [00:00<00:00, 4369.25 it/sec]
INFO - 20:35:13: 26%|██▌ | 26/100 [00:00<00:00, 4393.18 it/sec]
INFO - 20:35:13: 27%|██▋ | 27/100 [00:00<00:00, 4411.45 it/sec]
INFO - 20:35:13: 28%|██▊ | 28/100 [00:00<00:00, 4427.71 it/sec]
INFO - 20:35:13: 29%|██▉ | 29/100 [00:00<00:00, 4416.66 it/sec]
INFO - 20:35:13: 30%|███ | 30/100 [00:00<00:00, 4433.26 it/sec]
INFO - 20:35:13: 31%|███ | 31/100 [00:00<00:00, 4447.98 it/sec]
INFO - 20:35:13: 32%|███▏ | 32/100 [00:00<00:00, 4354.47 it/sec]
INFO - 20:35:13: 33%|███▎ | 33/100 [00:00<00:00, 4346.16 it/sec]
INFO - 20:35:13: 34%|███▍ | 34/100 [00:00<00:00, 4359.18 it/sec]
INFO - 20:35:13: 35%|███▌ | 35/100 [00:00<00:00, 4371.80 it/sec]
INFO - 20:35:13: 36%|███▌ | 36/100 [00:00<00:00, 4386.58 it/sec]
INFO - 20:35:13: 37%|███▋ | 37/100 [00:00<00:00, 4391.32 it/sec]
INFO - 20:35:13: 38%|███▊ | 38/100 [00:00<00:00, 4401.64 it/sec]
INFO - 20:35:13: 39%|███▉ | 39/100 [00:00<00:00, 4415.30 it/sec]
INFO - 20:35:13: 40%|████ | 40/100 [00:00<00:00, 4428.81 it/sec]
INFO - 20:35:13: 41%|████ | 41/100 [00:00<00:00, 4441.74 it/sec]
INFO - 20:35:13: 42%|████▏ | 42/100 [00:00<00:00, 4444.91 it/sec]
INFO - 20:35:13: 43%|████▎ | 43/100 [00:00<00:00, 4455.41 it/sec]
INFO - 20:35:13: 44%|████▍ | 44/100 [00:00<00:00, 4467.86 it/sec]
INFO - 20:35:13: 45%|████▌ | 45/100 [00:00<00:00, 4478.65 it/sec]
INFO - 20:35:13: 46%|████▌ | 46/100 [00:00<00:00, 4490.58 it/sec]
INFO - 20:35:13: 47%|████▋ | 47/100 [00:00<00:00, 4488.54 it/sec]
INFO - 20:35:13: 48%|████▊ | 48/100 [00:00<00:00, 4496.91 it/sec]
INFO - 20:35:13: 49%|████▉ | 49/100 [00:00<00:00, 4506.44 it/sec]
INFO - 20:35:13: 50%|█████ | 50/100 [00:00<00:00, 4517.87 it/sec]
INFO - 20:35:13: 51%|█████ | 51/100 [00:00<00:00, 4528.24 it/sec]
INFO - 20:35:13: 52%|█████▏ | 52/100 [00:00<00:00, 4529.20 it/sec]
INFO - 20:35:13: 53%|█████▎ | 53/100 [00:00<00:00, 4536.23 it/sec]
INFO - 20:35:13: 54%|█████▍ | 54/100 [00:00<00:00, 4545.76 it/sec]
INFO - 20:35:13: 55%|█████▌ | 55/100 [00:00<00:00, 4554.17 it/sec]
INFO - 20:35:13: 56%|█████▌ | 56/100 [00:00<00:00, 4562.48 it/sec]
INFO - 20:35:13: 57%|█████▋ | 57/100 [00:00<00:00, 4561.90 it/sec]
INFO - 20:35:13: 58%|█████▊ | 58/100 [00:00<00:00, 4568.53 it/sec]
INFO - 20:35:13: 59%|█████▉ | 59/100 [00:00<00:00, 4577.58 it/sec]
INFO - 20:35:13: 60%|██████ | 60/100 [00:00<00:00, 4583.94 it/sec]
INFO - 20:35:13: 61%|██████ | 61/100 [00:00<00:00, 4588.87 it/sec]
INFO - 20:35:13: 62%|██████▏ | 62/100 [00:00<00:00, 4588.23 it/sec]
INFO - 20:35:13: 63%|██████▎ | 63/100 [00:00<00:00, 4594.22 it/sec]
INFO - 20:35:13: 64%|██████▍ | 64/100 [00:00<00:00, 4601.46 it/sec]
INFO - 20:35:13: 65%|██████▌ | 65/100 [00:00<00:00, 4599.72 it/sec]
INFO - 20:35:13: 66%|██████▌ | 66/100 [00:00<00:00, 4606.59 it/sec]
INFO - 20:35:13: 67%|██████▋ | 67/100 [00:00<00:00, 4603.09 it/sec]
INFO - 20:35:13: 68%|██████▊ | 68/100 [00:00<00:00, 4609.27 it/sec]
INFO - 20:35:13: 69%|██████▉ | 69/100 [00:00<00:00, 4616.62 it/sec]
INFO - 20:35:13: 70%|███████ | 70/100 [00:00<00:00, 4624.15 it/sec]
INFO - 20:35:13: 71%|███████ | 71/100 [00:00<00:00, 4631.06 it/sec]
INFO - 20:35:13: 72%|███████▏ | 72/100 [00:00<00:00, 4628.06 it/sec]
INFO - 20:35:13: 73%|███████▎ | 73/100 [00:00<00:00, 4632.70 it/sec]
INFO - 20:35:13: 74%|███████▍ | 74/100 [00:00<00:00, 4638.82 it/sec]
INFO - 20:35:13: 75%|███████▌ | 75/100 [00:00<00:00, 4644.72 it/sec]
INFO - 20:35:13: 76%|███████▌ | 76/100 [00:00<00:00, 4649.80 it/sec]
INFO - 20:35:13: 77%|███████▋ | 77/100 [00:00<00:00, 4646.73 it/sec]
INFO - 20:35:13: 78%|███████▊ | 78/100 [00:00<00:00, 4651.79 it/sec]
INFO - 20:35:13: 79%|███████▉ | 79/100 [00:00<00:00, 4655.17 it/sec]
INFO - 20:35:13: 80%|████████ | 80/100 [00:00<00:00, 4659.56 it/sec]
INFO - 20:35:13: 81%|████████ | 81/100 [00:00<00:00, 4660.59 it/sec]
INFO - 20:35:13: 82%|████████▏ | 82/100 [00:00<00:00, 4663.12 it/sec]
INFO - 20:35:13: 83%|████████▎ | 83/100 [00:00<00:00, 4667.59 it/sec]
INFO - 20:35:13: 84%|████████▍ | 84/100 [00:00<00:00, 4666.94 it/sec]
INFO - 20:35:13: 85%|████████▌ | 85/100 [00:00<00:00, 4669.86 it/sec]
INFO - 20:35:13: 86%|████████▌ | 86/100 [00:00<00:00, 4652.64 it/sec]
INFO - 20:35:13: 87%|████████▋ | 87/100 [00:00<00:00, 4650.42 it/sec]
INFO - 20:35:13: 88%|████████▊ | 88/100 [00:00<00:00, 4652.35 it/sec]
INFO - 20:35:13: 89%|████████▉ | 89/100 [00:00<00:00, 4655.22 it/sec]
INFO - 20:35:13: 90%|█████████ | 90/100 [00:00<00:00, 4658.32 it/sec]
INFO - 20:35:13: 91%|█████████ | 91/100 [00:00<00:00, 4654.37 it/sec]
INFO - 20:35:13: 92%|█████████▏| 92/100 [00:00<00:00, 4656.63 it/sec]
INFO - 20:35:13: 93%|█████████▎| 93/100 [00:00<00:00, 4658.39 it/sec]
INFO - 20:35:13: 94%|█████████▍| 94/100 [00:00<00:00, 4660.23 it/sec]
INFO - 20:35:13: 95%|█████████▌| 95/100 [00:00<00:00, 4658.81 it/sec]
INFO - 20:35:13: 96%|█████████▌| 96/100 [00:00<00:00, 4656.89 it/sec]
INFO - 20:35:13: 97%|█████████▋| 97/100 [00:00<00:00, 4660.12 it/sec]
INFO - 20:35:13: 98%|█████████▊| 98/100 [00:00<00:00, 4663.03 it/sec]
INFO - 20:35:13: 99%|█████████▉| 99/100 [00:00<00:00, 4666.26 it/sec]
INFO - 20:35:13: 100%|██████████| 100/100 [00:00<00:00, 4665.42 it/sec]
INFO - 20:35:13: *** End Sampling execution ***
Settings#
Number of estimators#
The main hyperparameter of random forest regression is the number of trees in the forest (default: 100). Here is a comparison when increasing and decreasing this number:
model = create_regression_model(
"RandomForestRegressor", training_dataset, n_estimators=10
)
model.learn()
predicted_output_data_1 = model.predict(input_data).ravel()
model = create_regression_model(
"RandomForestRegressor", training_dataset, n_estimators=1000
)
model.learn()
predicted_output_data_2 = model.predict(input_data).ravel()
plt.plot(input_data.ravel(), reference_output_data, label="Reference")
plt.plot(input_data.ravel(), predicted_output_data, label="Regression - Basics")
plt.plot(input_data.ravel(), predicted_output_data_1, label="Regression - 10 trees")
plt.plot(input_data.ravel(), predicted_output_data_2, label="Regression - 1000 trees")
plt.grid()
plt.legend()
plt.show()
Others#
The RandomForestRegressor class of scikit-learn has a lot of settings
(read more),
and we have chosen to exhibit only n_estimators.
However,
any argument of RandomForestRegressor can be set
using the dictionary parameters.
For example,
we can impose a minimum of two samples per leaf:
model = create_regression_model(
"RandomForestRegressor", training_dataset, parameters={"min_samples_leaf": 2}
)
model.learn()
predicted_output_data_ = model.predict(input_data).ravel()
plt.plot(input_data.ravel(), reference_output_data, label="Reference")
plt.plot(input_data.ravel(), predicted_output_data, label="Regression - Basics")
plt.plot(input_data.ravel(), predicted_output_data_, label="Regression - 2 samples")
plt.grid()
plt.legend()
plt.show()
Total running time of the script: (0 minutes 0.950 seconds)