Note

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Calibration of a polynomial regression#

from __future__ import annotations

import matplotlib.pyplot as plt
from matplotlib.tri import Triangulation

from gemseo.algos.design_space import DesignSpace
from gemseo.mlearning.core.calibration import MLAlgoCalibration
from gemseo.mlearning.regression.quality.mse_measure import MSEMeasure
from gemseo.problems.dataset.rosenbrock import create_rosenbrock_dataset

Load the dataset#

dataset = create_rosenbrock_dataset(opt_naming=False, n_samples=25)

Define the measure#

test_dataset = create_rosenbrock_dataset(opt_naming=False)
measure_evaluation_method_name = "TEST"
measure_options = {"test_data": test_dataset}

Calibrate the degree of the polynomial regression#

Define and execute the calibration#

calibration_space = DesignSpace()
calibration_space.add_variable("degree", 1, "integer", 1, 10, 1)
calibration = MLAlgoCalibration(
    "PolynomialRegressor",
    dataset,
    ["degree"],
    calibration_space,
    MSEMeasure,
    measure_evaluation_method_name=measure_evaluation_method_name,
    measure_options=measure_options,
)
calibration.execute(algo_name="PYDOE_FULLFACT", n_samples=10)
x_opt = calibration.optimal_parameters
f_opt = calibration.optimal_criterion
degree = x_opt["degree"][0]
f"optimal degree = {degree}; optimal criterion = {f_opt}"

    INFO - 16:21:23: *** Start DOEScenario execution ***
    INFO - 16:21:23: DOEScenario
    INFO - 16:21:23:    Disciplines: MLAlgoAssessor
    INFO - 16:21:23:    MDO formulation: DisciplinaryOpt
    INFO - 16:21:23: Optimization problem:
    INFO - 16:21:23:    minimize criterion(degree)
    INFO - 16:21:23:    with respect to degree
    INFO - 16:21:23:    over the design space:
    INFO - 16:21:23:       +--------+-------------+-------+-------------+---------+
    INFO - 16:21:23:       | Name   | Lower bound | Value | Upper bound | Type    |
    INFO - 16:21:23:       +--------+-------------+-------+-------------+---------+
    INFO - 16:21:23:       | degree |      1      |   1   |      10     | integer |
    INFO - 16:21:23:       +--------+-------------+-------+-------------+---------+
    INFO - 16:21:23: Solving optimization problem with algorithm PYDOE_FULLFACT:
    INFO - 16:21:23:     10%|█         | 1/10 [00:00<00:00, 23.89 it/sec, feas=True, obj=5.89e+5]
    INFO - 16:21:23:     20%|██        | 2/10 [00:00<00:00, 41.45 it/sec, feas=True, obj=1.73e+5]
    INFO - 16:21:23:     30%|███       | 3/10 [00:00<00:00, 55.14 it/sec, feas=True, obj=3e+4]
    INFO - 16:21:23:     40%|████      | 4/10 [00:00<00:00, 66.03 it/sec, feas=True, obj=1.1e-24]
    INFO - 16:21:23:     50%|█████     | 5/10 [00:00<00:00, 74.94 it/sec, feas=True, obj=0.11]
    INFO - 16:21:23:     60%|██████    | 6/10 [00:00<00:00, 82.31 it/sec, feas=True, obj=1.18e+3]
    INFO - 16:21:23:     70%|███████   | 7/10 [00:00<00:00, 88.50 it/sec, feas=True, obj=6.9e+3]
    INFO - 16:21:23:     80%|████████  | 8/10 [00:00<00:00, 93.75 it/sec, feas=True, obj=1.36e+4]
    INFO - 16:21:23:     90%|█████████ | 9/10 [00:00<00:00, 98.29 it/sec, feas=True, obj=9.18e+4]
    INFO - 16:21:24:    100%|██████████| 10/10 [00:00<00:00, 102.10 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24: Optimization result:
    INFO - 16:21:24:    Optimizer info:
    INFO - 16:21:24:       Status: None
    INFO - 16:21:24:       Message: None
    INFO - 16:21:24:    Solution:
    INFO - 16:21:24:       Objective: 1.0957626812742524e-24
    INFO - 16:21:24:       Design space:
    INFO - 16:21:24:          +--------+-------------+-------+-------------+---------+
    INFO - 16:21:24:          | Name   | Lower bound | Value | Upper bound | Type    |
    INFO - 16:21:24:          +--------+-------------+-------+-------------+---------+
    INFO - 16:21:24:          | degree |      1      |   4   |      10     | integer |
    INFO - 16:21:24:          +--------+-------------+-------+-------------+---------+
    INFO - 16:21:24: *** End DOEScenario execution ***

'optimal degree = 4; optimal criterion = 1.0957626812742524e-24'

Get the history#

calibration.dataset
GROUP inputs outputs
VARIABLE degree criterion learning
COMPONENT 0 0 0
0 1 5.888317e+05 8.200828e+05
1 2 1.732475e+05 2.404571e+05
2 3 3.001292e+04 1.645714e+04
3 4 1.095763e-24 1.703801e-24
4 5 1.097877e-01 1.391092e-23
5 6 1.183264e+03 2.332471e-24
6 7 6.895919e+03 1.401963e-23
7 8 1.356307e+04 5.192192e-23
8 9 9.180547e+04 8.964290e-23
9 10 1.625259e+05 8.767875e-23


Visualize the results#

degree = calibration.get_history("degree")
criterion = calibration.get_history("criterion")
learning = calibration.get_history("learning")

plt.plot(degree, criterion, "-o", label="test", color="red")
plt.plot(degree, learning, "-o", label="learning", color="blue")
plt.xlabel("polynomial degree")
plt.ylabel("quality")
plt.axvline(x_opt["degree"], color="red", ls="--")
plt.legend()
plt.show()
plot calibration

Calibrate the ridge penalty of the polynomial regression#

Define and execute the calibration#

calibration_space = DesignSpace()
calibration_space.add_variable("penalty_level", 1, "float", 0.0, 100.0, 0.0)
calibration = MLAlgoCalibration(
    "PolynomialRegressor",
    dataset,
    ["penalty_level"],
    calibration_space,
    MSEMeasure,
    measure_evaluation_method_name=measure_evaluation_method_name,
    measure_options=measure_options,
    degree=10,
)
calibration.execute(algo_name="PYDOE_FULLFACT", n_samples=10)
x_opt = calibration.optimal_parameters
f_opt = calibration.optimal_criterion
x_opt["penalty_level"][0], f_opt

    INFO - 16:21:24: *** Start DOEScenario execution ***
    INFO - 16:21:24: DOEScenario
    INFO - 16:21:24:    Disciplines: MLAlgoAssessor
    INFO - 16:21:24:    MDO formulation: DisciplinaryOpt
    INFO - 16:21:24: Optimization problem:
    INFO - 16:21:24:    minimize criterion(penalty_level)
    INFO - 16:21:24:    with respect to penalty_level
    INFO - 16:21:24:    over the design space:
    INFO - 16:21:24:       +---------------+-------------+-------+-------------+-------+
    INFO - 16:21:24:       | Name          | Lower bound | Value | Upper bound | Type  |
    INFO - 16:21:24:       +---------------+-------------+-------+-------------+-------+
    INFO - 16:21:24:       | penalty_level |      0      |   0   |     100     | float |
    INFO - 16:21:24:       +---------------+-------------+-------+-------------+-------+
    INFO - 16:21:24: Solving optimization problem with algorithm PYDOE_FULLFACT:
    INFO - 16:21:24:     10%|█         | 1/10 [00:00<00:00, 118.67 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     20%|██        | 2/10 [00:00<00:00, 133.35 it/sec, feas=True, obj=3.25e+4]
    INFO - 16:21:24:     30%|███       | 3/10 [00:00<00:00, 140.87 it/sec, feas=True, obj=1.78e+4]
    INFO - 16:21:24:     40%|████      | 4/10 [00:00<00:00, 144.74 it/sec, feas=True, obj=1.72e+4]
    INFO - 16:21:24:     50%|█████     | 5/10 [00:00<00:00, 147.69 it/sec, feas=True, obj=2e+4]
    INFO - 16:21:24:     60%|██████    | 6/10 [00:00<00:00, 149.49 it/sec, feas=True, obj=2.35e+4]
    INFO - 16:21:24:     70%|███████   | 7/10 [00:00<00:00, 150.67 it/sec, feas=True, obj=2.7e+4]
    INFO - 16:21:24:     80%|████████  | 8/10 [00:00<00:00, 151.77 it/sec, feas=True, obj=3.03e+4]
    INFO - 16:21:24:     90%|█████████ | 9/10 [00:00<00:00, 152.63 it/sec, feas=True, obj=3.33e+4]
    INFO - 16:21:24:    100%|██████████| 10/10 [00:00<00:00, 152.88 it/sec, feas=True, obj=3.59e+4]
    INFO - 16:21:24: Optimization result:
    INFO - 16:21:24:    Optimizer info:
    INFO - 16:21:24:       Status: None
    INFO - 16:21:24:       Message: None
    INFO - 16:21:24:    Solution:
    INFO - 16:21:24:       Objective: 17189.52649297074
    INFO - 16:21:24:       Design space:
    INFO - 16:21:24:          +---------------+-------------+-------------------+-------------+-------+
    INFO - 16:21:24:          | Name          | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:24:          +---------------+-------------+-------------------+-------------+-------+
    INFO - 16:21:24:          | penalty_level |      0      | 33.33333333333333 |     100     | float |
    INFO - 16:21:24:          +---------------+-------------+-------------------+-------------+-------+
    INFO - 16:21:24: *** End DOEScenario execution ***

(np.float64(33.33333333333333), np.float64(17189.52649297074))

Get the history#

calibration.dataset
GROUP inputs outputs
VARIABLE penalty_level criterion learning
COMPONENT 0 0 0
0 0.000000 162525.860760 8.767875e-23
1 11.111111 32506.221289 1.087801e+03
2 22.222222 17820.599507 1.982580e+03
3 33.333333 17189.526493 2.690007e+03
4 44.444444 19953.420378 3.251453e+03
5 55.555556 23493.269988 3.703714e+03
6 66.666667 27024.053276 4.074147e+03
7 77.777778 30303.486633 4.382362e+03
8 88.888889 33272.062306 4.642448e+03
9 100.000000 35934.745536 4.864667e+03


Visualize the results#

penalty_level = calibration.get_history("penalty_level")
criterion = calibration.get_history("criterion")
learning = calibration.get_history("learning")

plt.plot(penalty_level, criterion, "-o", label="test", color="red")
plt.plot(penalty_level, learning, "-o", label="learning", color="blue")
plt.axvline(x_opt["penalty_level"], color="red", ls="--")
plt.xlabel("ridge penalty")
plt.ylabel("quality")
plt.legend()
plt.show()
plot calibration

Calibrate the lasso penalty of the polynomial regression#

Define and execute the calibration#

calibration_space = DesignSpace()
calibration_space.add_variable("penalty_level", 1, "float", 0.0, 100.0, 0.0)
calibration = MLAlgoCalibration(
    "PolynomialRegressor",
    dataset,
    ["penalty_level"],
    calibration_space,
    MSEMeasure,
    measure_evaluation_method_name=measure_evaluation_method_name,
    measure_options=measure_options,
    degree=10,
    l2_penalty_ratio=0.0,
)
calibration.execute(algo_name="PYDOE_FULLFACT", n_samples=10)
x_opt = calibration.optimal_parameters
f_opt = calibration.optimal_criterion
x_opt["penalty_level"][0], f_opt

    INFO - 16:21:24: *** Start DOEScenario execution ***
    INFO - 16:21:24: DOEScenario
    INFO - 16:21:24:    Disciplines: MLAlgoAssessor
    INFO - 16:21:24:    MDO formulation: DisciplinaryOpt
    INFO - 16:21:24: Optimization problem:
    INFO - 16:21:24:    minimize criterion(penalty_level)
    INFO - 16:21:24:    with respect to penalty_level
    INFO - 16:21:24:    over the design space:
    INFO - 16:21:24:       +---------------+-------------+-------+-------------+-------+
    INFO - 16:21:24:       | Name          | Lower bound | Value | Upper bound | Type  |
    INFO - 16:21:24:       +---------------+-------------+-------+-------------+-------+
    INFO - 16:21:24:       | penalty_level |      0      |   0   |     100     | float |
    INFO - 16:21:24:       +---------------+-------------+-------+-------------+-------+
    INFO - 16:21:24: Solving optimization problem with algorithm PYDOE_FULLFACT:
    INFO - 16:21:24:     10%|█         | 1/10 [00:00<00:00, 115.40 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     20%|██        | 2/10 [00:00<00:00, 117.18 it/sec, feas=True, obj=1.58e+4]
    INFO - 16:21:24:     30%|███       | 3/10 [00:00<00:00, 119.52 it/sec, feas=True, obj=3.15e+4]
    INFO - 16:21:24:     40%|████      | 4/10 [00:00<00:00, 121.01 it/sec, feas=True, obj=4.74e+4]
    INFO - 16:21:24:     50%|█████     | 5/10 [00:00<00:00, 122.31 it/sec, feas=True, obj=5.94e+4]
    INFO - 16:21:24:     60%|██████    | 6/10 [00:00<00:00, 123.27 it/sec, feas=True, obj=6.27e+4]
    INFO - 16:21:24:     70%|███████   | 7/10 [00:00<00:00, 123.92 it/sec, feas=True, obj=6.63e+4]
    INFO - 16:21:24:     80%|████████  | 8/10 [00:00<00:00, 124.46 it/sec, feas=True, obj=6.93e+4]
    INFO - 16:21:24:     90%|█████████ | 9/10 [00:00<00:00, 121.63 it/sec, feas=True, obj=7.25e+4]
    INFO - 16:21:24:    100%|██████████| 10/10 [00:00<00:00, 122.13 it/sec, feas=True, obj=7.57e+4]
    INFO - 16:21:24: Optimization result:
    INFO - 16:21:24:    Optimizer info:
    INFO - 16:21:24:       Status: None
    INFO - 16:21:24:       Message: None
    INFO - 16:21:24:    Solution:
    INFO - 16:21:24:       Objective: 15775.989581125898
    INFO - 16:21:24:       Design space:
    INFO - 16:21:24:          +---------------+-------------+-------------------+-------------+-------+
    INFO - 16:21:24:          | Name          | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:24:          +---------------+-------------+-------------------+-------------+-------+
    INFO - 16:21:24:          | penalty_level |      0      | 11.11111111111111 |     100     | float |
    INFO - 16:21:24:          +---------------+-------------+-------------------+-------------+-------+
    INFO - 16:21:24: *** End DOEScenario execution ***

(np.float64(11.11111111111111), np.float64(15775.989581125898))

Get the history#

calibration.dataset
GROUP inputs outputs
VARIABLE penalty_level criterion learning
COMPONENT 0 0 0
0 0.000000 162525.860760 8.767875e-23
1 11.111111 15775.989581 1.814382e+03
2 22.222222 31529.584354 4.057302e+03
3 33.333333 47420.249503 5.792299e+03
4 44.444444 59358.207437 7.169565e+03
5 55.555556 62656.171431 7.278397e+03
6 66.666667 66256.259889 7.410137e+03
7 77.777778 69336.190346 7.540731e+03
8 88.888889 72457.378777 7.675963e+03
9 100.000000 75749.793494 7.816545e+03


Visualize the results#

penalty_level = calibration.get_history("penalty_level")
criterion = calibration.get_history("criterion")
learning = calibration.get_history("learning")

plt.plot(penalty_level, criterion, "-o", label="test", color="red")
plt.plot(penalty_level, learning, "-o", label="learning", color="blue")
plt.axvline(x_opt["penalty_level"], color="red", ls="--")
plt.xlabel("lasso penalty")
plt.ylabel("quality")
plt.legend()
plt.show()
plot calibration

Calibrate the elasticnet penalty of the polynomial regression#

Define and execute the calibration#

calibration_space = DesignSpace()
calibration_space.add_variable("penalty_level", 1, "float", 0.0, 40.0, 0.0)
calibration_space.add_variable("l2_penalty_ratio", 1, "float", 0.0, 1.0, 0.5)
calibration = MLAlgoCalibration(
    "PolynomialRegressor",
    dataset,
    ["penalty_level", "l2_penalty_ratio"],
    calibration_space,
    MSEMeasure,
    measure_evaluation_method_name=measure_evaluation_method_name,
    measure_options=measure_options,
    degree=10,
)
calibration.execute(algo_name="PYDOE_FULLFACT", n_samples=100)
x_opt = calibration.optimal_parameters
f_opt = calibration.optimal_criterion
x_opt["penalty_level"][0], x_opt["l2_penalty_ratio"][0], f_opt

    INFO - 16:21:24: *** Start DOEScenario execution ***
    INFO - 16:21:24: DOEScenario
    INFO - 16:21:24:    Disciplines: MLAlgoAssessor
    INFO - 16:21:24:    MDO formulation: DisciplinaryOpt
    INFO - 16:21:24: Optimization problem:
    INFO - 16:21:24:    minimize criterion(penalty_level, l2_penalty_ratio)
    INFO - 16:21:24:    with respect to l2_penalty_ratio, penalty_level
    INFO - 16:21:24:    over the design space:
    INFO - 16:21:24:       +------------------+-------------+-------+-------------+-------+
    INFO - 16:21:24:       | Name             | Lower bound | Value | Upper bound | Type  |
    INFO - 16:21:24:       +------------------+-------------+-------+-------------+-------+
    INFO - 16:21:24:       | penalty_level    |      0      |   0   |      40     | float |
    INFO - 16:21:24:       | l2_penalty_ratio |      0      |  0.5  |      1      | float |
    INFO - 16:21:24:       +------------------+-------------+-------+-------------+-------+
    INFO - 16:21:24: Solving optimization problem with algorithm PYDOE_FULLFACT:
    INFO - 16:21:24:      1%|          | 1/100 [00:00<00:00, 116.45 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:      2%|▏         | 2/100 [00:00<00:00, 119.30 it/sec, feas=True, obj=4.14e+3]
    INFO - 16:21:24:      3%|▎         | 3/100 [00:00<00:00, 120.67 it/sec, feas=True, obj=1.34e+4]
    INFO - 16:21:24:      4%|▍         | 4/100 [00:00<00:00, 120.51 it/sec, feas=True, obj=1.79e+4]
    INFO - 16:21:24:      5%|▌         | 5/100 [00:00<00:00, 121.18 it/sec, feas=True, obj=2.39e+4]
    INFO - 16:21:24:      6%|▌         | 6/100 [00:00<00:00, 121.74 it/sec, feas=True, obj=3.15e+4]
    INFO - 16:21:24:      7%|▋         | 7/100 [00:00<00:00, 122.24 it/sec, feas=True, obj=3.91e+4]
    INFO - 16:21:24:      8%|▊         | 8/100 [00:00<00:00, 122.76 it/sec, feas=True, obj=4.5e+4]
    INFO - 16:21:24:      9%|▉         | 9/100 [00:00<00:00, 123.03 it/sec, feas=True, obj=4.95e+4]
    INFO - 16:21:24:     10%|█         | 10/100 [00:00<00:00, 123.47 it/sec, feas=True, obj=5.42e+4]
    INFO - 16:21:24:     11%|█         | 11/100 [00:00<00:00, 126.01 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     12%|█▏        | 12/100 [00:00<00:00, 125.52 it/sec, feas=True, obj=1.35e+4]
    INFO - 16:21:24:     13%|█▎        | 13/100 [00:00<00:00, 125.29 it/sec, feas=True, obj=2.44e+4]
    INFO - 16:21:24:     14%|█▍        | 14/100 [00:00<00:00, 125.08 it/sec, feas=True, obj=3.28e+4]
    INFO - 16:21:24:     15%|█▌        | 15/100 [00:00<00:00, 124.95 it/sec, feas=True, obj=4.19e+4]
    INFO - 16:21:24:     16%|█▌        | 16/100 [00:00<00:00, 124.79 it/sec, feas=True, obj=4.76e+4]
    INFO - 16:21:24:     17%|█▋        | 17/100 [00:00<00:00, 124.70 it/sec, feas=True, obj=5.16e+4]
    INFO - 16:21:24:     18%|█▊        | 18/100 [00:00<00:00, 124.63 it/sec, feas=True, obj=5.52e+4]
    INFO - 16:21:24:     19%|█▉        | 19/100 [00:00<00:00, 124.68 it/sec, feas=True, obj=5.78e+4]
    INFO - 16:21:24:     20%|██        | 20/100 [00:00<00:00, 124.78 it/sec, feas=True, obj=5.98e+4]
    INFO - 16:21:24:     21%|██        | 21/100 [00:00<00:00, 126.09 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     22%|██▏       | 22/100 [00:00<00:00, 125.86 it/sec, feas=True, obj=1.97e+4]
    INFO - 16:21:24:     23%|██▎       | 23/100 [00:00<00:00, 125.56 it/sec, feas=True, obj=3.17e+4]
    INFO - 16:21:24:     24%|██▍       | 24/100 [00:00<00:00, 125.36 it/sec, feas=True, obj=4.02e+4]
    INFO - 16:21:24:     25%|██▌       | 25/100 [00:00<00:00, 125.28 it/sec, feas=True, obj=4.59e+4]
    INFO - 16:21:24:     26%|██▌       | 26/100 [00:00<00:00, 125.17 it/sec, feas=True, obj=4.97e+4]
    INFO - 16:21:24:     27%|██▋       | 27/100 [00:00<00:00, 125.12 it/sec, feas=True, obj=5.3e+4]
    INFO - 16:21:24:     28%|██▊       | 28/100 [00:00<00:00, 125.03 it/sec, feas=True, obj=5.6e+4]
    INFO - 16:21:24:     29%|██▉       | 29/100 [00:00<00:00, 125.04 it/sec, feas=True, obj=5.89e+4]
    INFO - 16:21:24:     30%|███       | 30/100 [00:00<00:00, 125.04 it/sec, feas=True, obj=6.18e+4]
    INFO - 16:21:24:     31%|███       | 31/100 [00:00<00:00, 125.88 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     32%|███▏      | 32/100 [00:00<00:00, 125.71 it/sec, feas=True, obj=2.43e+4]
    INFO - 16:21:24:     33%|███▎      | 33/100 [00:00<00:00, 125.58 it/sec, feas=True, obj=3.58e+4]
    INFO - 16:21:24:     34%|███▍      | 34/100 [00:00<00:00, 125.49 it/sec, feas=True, obj=4.29e+4]
    INFO - 16:21:24:     35%|███▌      | 35/100 [00:00<00:00, 125.39 it/sec, feas=True, obj=4.77e+4]
    INFO - 16:21:24:     36%|███▌      | 36/100 [00:00<00:00, 125.32 it/sec, feas=True, obj=5.12e+4]
    INFO - 16:21:24:     37%|███▋      | 37/100 [00:00<00:00, 125.27 it/sec, feas=True, obj=5.43e+4]
    INFO - 16:21:24:     38%|███▊      | 38/100 [00:00<00:00, 125.23 it/sec, feas=True, obj=5.74e+4]
    INFO - 16:21:24:     39%|███▉      | 39/100 [00:00<00:00, 125.19 it/sec, feas=True, obj=6.05e+4]
    INFO - 16:21:24:     40%|████      | 40/100 [00:00<00:00, 124.40 it/sec, feas=True, obj=6.35e+4]
    INFO - 16:21:24:     41%|████      | 41/100 [00:00<00:00, 125.06 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     42%|████▏     | 42/100 [00:00<00:00, 124.94 it/sec, feas=True, obj=2.75e+4]
    INFO - 16:21:24:     43%|████▎     | 43/100 [00:00<00:00, 124.85 it/sec, feas=True, obj=3.82e+4]
    INFO - 16:21:24:     44%|████▍     | 44/100 [00:00<00:00, 124.75 it/sec, feas=True, obj=4.42e+4]
    INFO - 16:21:24:     45%|████▌     | 45/100 [00:00<00:00, 124.71 it/sec, feas=True, obj=4.9e+4]
    INFO - 16:21:24:     46%|████▌     | 46/100 [00:00<00:00, 124.64 it/sec, feas=True, obj=5.28e+4]
    INFO - 16:21:24:     47%|████▋     | 47/100 [00:00<00:00, 124.59 it/sec, feas=True, obj=5.61e+4]
    INFO - 16:21:24:     48%|████▊     | 48/100 [00:00<00:00, 124.55 it/sec, feas=True, obj=5.93e+4]
    INFO - 16:21:24:     49%|████▉     | 49/100 [00:00<00:00, 124.53 it/sec, feas=True, obj=6.24e+4]
    INFO - 16:21:24:     50%|█████     | 50/100 [00:00<00:00, 124.50 it/sec, feas=True, obj=6.54e+4]
    INFO - 16:21:24:     51%|█████     | 51/100 [00:00<00:00, 124.99 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     52%|█████▏    | 52/100 [00:00<00:00, 124.90 it/sec, feas=True, obj=2.99e+4]
    INFO - 16:21:24:     53%|█████▎    | 53/100 [00:00<00:00, 124.79 it/sec, feas=True, obj=3.96e+4]
    INFO - 16:21:24:     54%|█████▍    | 54/100 [00:00<00:00, 124.73 it/sec, feas=True, obj=4.51e+4]
    INFO - 16:21:24:     55%|█████▌    | 55/100 [00:00<00:00, 124.66 it/sec, feas=True, obj=5e+4]
    INFO - 16:21:24:     56%|█████▌    | 56/100 [00:00<00:00, 124.58 it/sec, feas=True, obj=5.43e+4]
    INFO - 16:21:24:     57%|█████▋    | 57/100 [00:00<00:00, 124.54 it/sec, feas=True, obj=5.78e+4]
    INFO - 16:21:24:     58%|█████▊    | 58/100 [00:00<00:00, 124.53 it/sec, feas=True, obj=6.11e+4]
    INFO - 16:21:24:     59%|█████▉    | 59/100 [00:00<00:00, 124.50 it/sec, feas=True, obj=6.41e+4]
    INFO - 16:21:24:     60%|██████    | 60/100 [00:00<00:00, 124.49 it/sec, feas=True, obj=6.66e+4]
    INFO - 16:21:24:     61%|██████    | 61/100 [00:00<00:00, 124.92 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     62%|██████▏   | 62/100 [00:00<00:00, 124.84 it/sec, feas=True, obj=3.18e+4]
    INFO - 16:21:24:     63%|██████▎   | 63/100 [00:00<00:00, 124.76 it/sec, feas=True, obj=4.07e+4]
    INFO - 16:21:24:     64%|██████▍   | 64/100 [00:00<00:00, 124.69 it/sec, feas=True, obj=4.6e+4]
    INFO - 16:21:24:     65%|██████▌   | 65/100 [00:00<00:00, 124.61 it/sec, feas=True, obj=5.09e+4]
    INFO - 16:21:24:     66%|██████▌   | 66/100 [00:00<00:00, 124.54 it/sec, feas=True, obj=5.53e+4]
    INFO - 16:21:24:     67%|██████▋   | 67/100 [00:00<00:00, 124.50 it/sec, feas=True, obj=5.92e+4]
    INFO - 16:21:24:     68%|██████▊   | 68/100 [00:00<00:00, 124.48 it/sec, feas=True, obj=6.25e+4]
    INFO - 16:21:24:     69%|██████▉   | 69/100 [00:00<00:00, 124.47 it/sec, feas=True, obj=6.52e+4]
    INFO - 16:21:24:     70%|███████   | 70/100 [00:00<00:00, 124.42 it/sec, feas=True, obj=6.71e+4]
    INFO - 16:21:24:     71%|███████   | 71/100 [00:00<00:00, 124.81 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     72%|███████▏  | 72/100 [00:00<00:00, 124.75 it/sec, feas=True, obj=3.32e+4]
    INFO - 16:21:24:     73%|███████▎  | 73/100 [00:00<00:00, 124.69 it/sec, feas=True, obj=4.15e+4]
    INFO - 16:21:24:     74%|███████▍  | 74/100 [00:00<00:00, 124.64 it/sec, feas=True, obj=4.69e+4]
    INFO - 16:21:24:     75%|███████▌  | 75/100 [00:00<00:00, 124.56 it/sec, feas=True, obj=5.19e+4]
    INFO - 16:21:24:     76%|███████▌  | 76/100 [00:00<00:00, 124.51 it/sec, feas=True, obj=5.63e+4]
    INFO - 16:21:24:     77%|███████▋  | 77/100 [00:00<00:00, 124.46 it/sec, feas=True, obj=6.01e+4]
    INFO - 16:21:24:     78%|███████▊  | 78/100 [00:00<00:00, 124.42 it/sec, feas=True, obj=6.32e+4]
    INFO - 16:21:24:     79%|███████▉  | 79/100 [00:00<00:00, 124.36 it/sec, feas=True, obj=6.55e+4]
    INFO - 16:21:24:     80%|████████  | 80/100 [00:00<00:00, 124.34 it/sec, feas=True, obj=6.72e+4]
    INFO - 16:21:24:     81%|████████  | 81/100 [00:00<00:00, 124.69 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:24:     82%|████████▏ | 82/100 [00:00<00:00, 124.63 it/sec, feas=True, obj=3.44e+4]
    INFO - 16:21:24:     83%|████████▎ | 83/100 [00:00<00:00, 124.58 it/sec, feas=True, obj=4.23e+4]
    INFO - 16:21:24:     84%|████████▍ | 84/100 [00:00<00:00, 124.50 it/sec, feas=True, obj=4.78e+4]
    INFO - 16:21:25:     85%|████████▌ | 85/100 [00:00<00:00, 124.46 it/sec, feas=True, obj=5.3e+4]
    INFO - 16:21:25:     86%|████████▌ | 86/100 [00:00<00:00, 124.40 it/sec, feas=True, obj=5.74e+4]
    INFO - 16:21:25:     87%|████████▋ | 87/100 [00:00<00:00, 124.35 it/sec, feas=True, obj=6.09e+4]
    INFO - 16:21:25:     88%|████████▊ | 88/100 [00:00<00:00, 124.29 it/sec, feas=True, obj=6.35e+4]
    INFO - 16:21:25:     89%|████████▉ | 89/100 [00:00<00:00, 124.25 it/sec, feas=True, obj=6.53e+4]
    INFO - 16:21:25:     90%|█████████ | 90/100 [00:00<00:00, 124.20 it/sec, feas=True, obj=6.67e+4]
    INFO - 16:21:25:     91%|█████████ | 91/100 [00:00<00:00, 124.49 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:25:     92%|█████████▏| 92/100 [00:00<00:00, 124.79 it/sec, feas=True, obj=6.89e+4]
    INFO - 16:21:25:     93%|█████████▎| 93/100 [00:00<00:00, 125.09 it/sec, feas=True, obj=4.03e+4]
    INFO - 16:21:25:     94%|█████████▍| 94/100 [00:00<00:00, 125.37 it/sec, feas=True, obj=2.71e+4]
    INFO - 16:21:25:     95%|█████████▌| 95/100 [00:00<00:00, 125.67 it/sec, feas=True, obj=2.07e+4]
    INFO - 16:21:25:     96%|█████████▌| 96/100 [00:00<00:00, 125.96 it/sec, feas=True, obj=1.78e+4]
    INFO - 16:21:25:     97%|█████████▋| 97/100 [00:00<00:00, 126.22 it/sec, feas=True, obj=1.68e+4]
    INFO - 16:21:25:     98%|█████████▊| 98/100 [00:00<00:00, 126.50 it/sec, feas=True, obj=1.69e+4]
    INFO - 16:21:25:     99%|█████████▉| 99/100 [00:00<00:00, 126.77 it/sec, feas=True, obj=1.76e+4]
    INFO - 16:21:25:    100%|██████████| 100/100 [00:00<00:00, 127.00 it/sec, feas=True, obj=1.87e+4]
    INFO - 16:21:25: Optimization result:
    INFO - 16:21:25:    Optimizer info:
    INFO - 16:21:25:       Status: None
    INFO - 16:21:25:       Message: None
    INFO - 16:21:25:    Solution:
    INFO - 16:21:25:       Objective: 4136.820826715568
    INFO - 16:21:25:       Design space:
    INFO - 16:21:25:          +------------------+-------------+-------------------+-------------+-------+
    INFO - 16:21:25:          | Name             | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:25:          +------------------+-------------+-------------------+-------------+-------+
    INFO - 16:21:25:          | penalty_level    |      0      | 4.444444444444445 |      40     | float |
    INFO - 16:21:25:          | l2_penalty_ratio |      0      |         0         |      1      | float |
    INFO - 16:21:25:          +------------------+-------------+-------------------+-------------+-------+
    INFO - 16:21:25: *** End DOEScenario execution ***

(np.float64(4.444444444444445), np.float64(0.0), np.float64(4136.820826715568))

Get the history#

calibration.dataset
GROUP inputs outputs
VARIABLE penalty_level l2_penalty_ratio criterion learning
COMPONENT 0 0 0 0
0 0.000000 0.0 162525.860760 8.767875e-23
1 4.444444 0.0 4136.820827 4.546714e+02
2 8.888889 0.0 13371.034446 1.375915e+03
3 13.333333 0.0 17860.819693 2.176736e+03
4 17.777778 0.0 23914.366014 3.005032e+03
... ... ... ... ...
95 22.222222 1.0 17820.599507 1.982580e+03
96 26.666667 1.0 16816.595592 2.285780e+03
97 31.111111 1.0 16894.821607 2.561538e+03
98 35.555556 1.0 17602.178769 2.812662e+03
99 40.000000 1.0 18674.751406 3.041823e+03

100 rows × 4 columns



Visualize the results#

penalty_level = calibration.get_history("penalty_level").flatten()
l2_penalty_ratio = calibration.get_history("l2_penalty_ratio").flatten()
criterion = calibration.get_history("criterion").flatten()
learning = calibration.get_history("learning").flatten()

triang = Triangulation(penalty_level, l2_penalty_ratio)

fig = plt.figure()
ax = fig.add_subplot(1, 2, 1)
ax.tricontourf(triang, criterion, cmap="Purples")
ax.scatter(x_opt["penalty_level"][0], x_opt["l2_penalty_ratio"][0])
ax.set_xlabel("penalty level")
ax.set_ylabel("l2 penalty ratio")
ax.set_title("Test measure")
ax = fig.add_subplot(1, 2, 2)
ax.tricontourf(triang, learning, cmap="Purples")
ax.scatter(x_opt["penalty_level"][0], x_opt["l2_penalty_ratio"][0])
ax.set_xlabel("penalty level")
ax.set_ylabel("l2 penalty ratio")
ax.set_title("Learning measure")

plt.show()
Test measure, Learning measure

Add an optimization stage#

calibration_space = DesignSpace()
calibration_space.add_variable("penalty_level", 1, "float", 0.0, 40.0, 0.0)
calibration_space.add_variable("l2_penalty_ratio", 1, "float", 0.0, 1.0, 0.5)
calibration = MLAlgoCalibration(
    "PolynomialRegressor",
    dataset,
    ["penalty_level", "l2_penalty_ratio"],
    calibration_space,
    MSEMeasure,
    measure_evaluation_method_name=measure_evaluation_method_name,
    measure_options=measure_options,
    degree=10,
)
calibration.execute("NLOPT_COBYLA", max_iter=100)
x_opt2 = calibration.optimal_parameters
f_opt2 = calibration.optimal_criterion

fig = plt.figure()
ax = fig.add_subplot(1, 2, 1)
ax.tricontourf(triang, criterion, cmap="Purples")
ax.scatter(x_opt["penalty_level"][0], x_opt["l2_penalty_ratio"][0])
ax.scatter(x_opt2["penalty_level"][0], x_opt2["l2_penalty_ratio"][0], color="red")
ax.set_xlabel("penalty level")
ax.set_ylabel("l2 penalty ratio")
ax.set_title("Test measure")
ax = fig.add_subplot(1, 2, 2)
ax.tricontourf(triang, learning, cmap="Purples")
ax.scatter(x_opt["penalty_level"][0], x_opt["l2_penalty_ratio"][0])
ax.scatter(x_opt2["penalty_level"][0], x_opt2["l2_penalty_ratio"][0], color="red")
ax.set_xlabel("penalty level")
ax.set_ylabel("l2 penalty ratio")
ax.set_title("Learning measure")
plt.show()

n_iterations = len(calibration.scenario.disciplines[0].cache)
print(f"MSE with DOE: {f_opt} (100 evaluations)")
print(f"MSE with OPT: {f_opt2} ({n_iterations} evaluations)")
print(f"MSE reduction:{round((f_opt2 - f_opt) / f_opt * 100)}%")
Test measure, Learning measure
    INFO - 16:21:25: *** Start MDOScenario execution ***
    INFO - 16:21:25: MDOScenario
    INFO - 16:21:25:    Disciplines: MLAlgoAssessor
    INFO - 16:21:25:    MDO formulation: DisciplinaryOpt
    INFO - 16:21:25: Optimization problem:
    INFO - 16:21:25:    minimize criterion(penalty_level, l2_penalty_ratio)
    INFO - 16:21:25:    with respect to l2_penalty_ratio, penalty_level
    INFO - 16:21:25:    over the design space:
    INFO - 16:21:25:       +------------------+-------------+-------+-------------+-------+
    INFO - 16:21:25:       | Name             | Lower bound | Value | Upper bound | Type  |
    INFO - 16:21:25:       +------------------+-------------+-------+-------------+-------+
    INFO - 16:21:25:       | penalty_level    |      0      |   0   |      40     | float |
    INFO - 16:21:25:       | l2_penalty_ratio |      0      |  0.5  |      1      | float |
    INFO - 16:21:25:       +------------------+-------------+-------+-------------+-------+
    INFO - 16:21:25: Solving optimization problem with algorithm NLOPT_COBYLA:
    INFO - 16:21:25:      1%|          | 1/100 [00:00<00:00, 109.06 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:25:      2%|▏         | 2/100 [00:00<00:00, 111.56 it/sec, feas=True, obj=4.06e+4]
    INFO - 16:21:25:      3%|▎         | 3/100 [00:00<00:00, 113.30 it/sec, feas=True, obj=4.28e+4]
    INFO - 16:21:25:      4%|▍         | 4/100 [00:00<00:00, 114.27 it/sec, feas=True, obj=5.16e+4]
    INFO - 16:21:25:      5%|▌         | 5/100 [00:00<00:00, 114.58 it/sec, feas=True, obj=4.66e+4]
    INFO - 16:21:25:      6%|▌         | 6/100 [00:00<00:00, 114.70 it/sec, feas=True, obj=3.63e+4]
    INFO - 16:21:25:      7%|▋         | 7/100 [00:00<00:00, 114.64 it/sec, feas=True, obj=3.03e+4]
    INFO - 16:21:25:      8%|▊         | 8/100 [00:00<00:00, 114.75 it/sec, feas=True, obj=2.03e+4]
    INFO - 16:21:25:      9%|▉         | 9/100 [00:00<00:00, 114.67 it/sec, feas=True, obj=2.75e+3]
    INFO - 16:21:25:     10%|█         | 10/100 [00:00<00:00, 115.82 it/sec, feas=True, obj=493]
    INFO - 16:21:25:     11%|█         | 11/100 [00:00<00:00, 118.18 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:25:     12%|█▏        | 12/100 [00:00<00:00, 120.40 it/sec, feas=True, obj=1.63e+5]
    INFO - 16:21:25:     13%|█▎        | 13/100 [00:00<00:00, 119.90 it/sec, feas=True, obj=5.23e+3]
    INFO - 16:21:25:     14%|█▍        | 14/100 [00:00<00:00, 120.48 it/sec, feas=True, obj=493]
    INFO - 16:21:25:     15%|█▌        | 15/100 [00:00<00:00, 120.93 it/sec, feas=True, obj=493]
    INFO - 16:21:25:     16%|█▌        | 16/100 [00:00<00:00, 121.31 it/sec, feas=True, obj=493]
    INFO - 16:21:25: Optimization result:
    INFO - 16:21:25:    Optimizer info:
    INFO - 16:21:25:       Status: None
    INFO - 16:21:25:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:25:    Solution:
    INFO - 16:21:25:       Objective: 493.1818200496802
    INFO - 16:21:25:       Design space:
    INFO - 16:21:25:          +------------------+-------------+-----------------------+-------------+-------+
    INFO - 16:21:25:          | Name             | Lower bound |         Value         | Upper bound | Type  |
    INFO - 16:21:25:          +------------------+-------------+-----------------------+-------------+-------+
    INFO - 16:21:25:          | penalty_level    |      0      | 2.289834988289385e-15 |      40     | float |
    INFO - 16:21:25:          | l2_penalty_ratio |      0      |   0.5765298371174132  |      1      | float |
    INFO - 16:21:25:          +------------------+-------------+-----------------------+-------------+-------+
    INFO - 16:21:25: *** End MDOScenario execution ***
MSE with DOE: 4136.820826715568 (100 evaluations)
MSE with OPT: 493.1818200496802 (1 evaluations)
MSE reduction:-88%

Total running time of the script: (0 minutes 1.517 seconds)

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