Note
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Machine learning algorithm selection example#
In this example we use the MLAlgoSelection class to perform a grid
search over different algorithms and hyperparameter values.
from __future__ import annotations
import matplotlib.pyplot as plt
from numpy import linspace
from numpy import sort
from numpy.random import default_rng
from gemseo.algos.design_space import DesignSpace
from gemseo.datasets.io_dataset import IODataset
from gemseo.mlearning.core.selection import MLAlgoSelection
from gemseo.mlearning.regression.quality.mse_measure import MSEMeasure
rng = default_rng(54321)
Build dataset#
The data are generated from the function \(f(x)=x^2\). The input data \(\{x_i\}_{i=1,\cdots,20}\) are chosen at random over the interval \([0,1]\). The output value \(y_i = f(x_i) + \varepsilon_i\) corresponds to the evaluation of \(f\) at \(x_i\) corrupted by a Gaussian noise \(\varepsilon_i\) with zero mean and standard deviation \(\sigma=0.05\).
n = 20
x = sort(rng.random(n))
y = x**2 + rng.normal(0, 0.05, n)
dataset = IODataset()
dataset.add_variable("x", x[:, None], dataset.INPUT_GROUP)
dataset.add_variable("y", y[:, None], dataset.OUTPUT_GROUP)
Build selector#
We consider three regression models, with different possible hyperparameters. A mean squared error quality measure is used with a k-folds cross validation scheme (5 folds).
selector = MLAlgoSelection(
dataset, MSEMeasure, measure_evaluation_method_name="KFOLDS", n_folds=5
)
selector.add_candidate(
"LinearRegressor",
penalty_level=[0, 0.1, 1, 10, 20],
l2_penalty_ratio=[0, 0.5, 1],
fit_intercept=[True],
)
selector.add_candidate(
"PolynomialRegressor",
degree=[2, 3, 4, 10],
penalty_level=[0, 0.1, 1, 10],
l2_penalty_ratio=[1],
fit_intercept=[True, False],
)
rbf_space = DesignSpace()
rbf_space.add_variable("epsilon", 1, "float", 0.01, 0.1, 0.05)
selector.add_candidate(
"RBFRegressor",
calib_space=rbf_space,
calib_algo={"algo_name": "PYDOE_FULLFACT", "n_samples": 16},
smooth=[0, 0.01, 0.1, 1, 10, 100],
)
INFO - 16:21:59: *** Start DOEScenario execution ***
INFO - 16:21:59: DOEScenario
INFO - 16:21:59: Disciplines: MLAlgoAssessor
INFO - 16:21:59: MDO formulation: DisciplinaryOpt
INFO - 16:21:59: Optimization problem:
INFO - 16:21:59: minimize criterion(epsilon)
INFO - 16:21:59: with respect to epsilon
INFO - 16:21:59: over the design space:
INFO - 16:21:59: +---------+-------------+-------+-------------+-------+
INFO - 16:21:59: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:59: +---------+-------------+-------+-------------+-------+
INFO - 16:21:59: | epsilon | 0.01 | 0.05 | 0.1 | float |
INFO - 16:21:59: +---------+-------------+-------+-------------+-------+
INFO - 16:21:59: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 16:21:59: 6%|▋ | 1/16 [00:00<00:00, 66.73 it/sec, feas=True, obj=0.00433]
INFO - 16:21:59: 12%|█▎ | 2/16 [00:00<00:00, 71.89 it/sec, feas=True, obj=0.00767]
INFO - 16:21:59: 19%|█▉ | 3/16 [00:00<00:00, 73.38 it/sec, feas=True, obj=0.0154]
INFO - 16:21:59: 25%|██▌ | 4/16 [00:00<00:00, 74.74 it/sec, feas=True, obj=0.032]
INFO - 16:22:00: 31%|███▏ | 5/16 [00:00<00:00, 75.47 it/sec, feas=True, obj=0.0645]
INFO - 16:22:00: 38%|███▊ | 6/16 [00:00<00:00, 75.56 it/sec, feas=True, obj=0.123]
INFO - 16:22:00: 44%|████▍ | 7/16 [00:00<00:00, 75.69 it/sec, feas=True, obj=0.223]
INFO - 16:22:00: 50%|█████ | 8/16 [00:00<00:00, 75.97 it/sec, feas=True, obj=0.382]
INFO - 16:22:00: 56%|█████▋ | 9/16 [00:00<00:00, 76.08 it/sec, feas=True, obj=0.62]
INFO - 16:22:00: 62%|██████▎ | 10/16 [00:00<00:00, 76.14 it/sec, feas=True, obj=0.962]
INFO - 16:22:00: 69%|██████▉ | 11/16 [00:00<00:00, 76.19 it/sec, feas=True, obj=1.43]
INFO - 16:22:00: 75%|███████▌ | 12/16 [00:00<00:00, 76.31 it/sec, feas=True, obj=2.05]
INFO - 16:22:00: 81%|████████▏ | 13/16 [00:00<00:00, 76.34 it/sec, feas=True, obj=2.85]
INFO - 16:22:00: 88%|████████▊ | 14/16 [00:00<00:00, 76.40 it/sec, feas=True, obj=3.84]
INFO - 16:22:00: 94%|█████████▍| 15/16 [00:00<00:00, 76.38 it/sec, feas=True, obj=5.05]
INFO - 16:22:00: 100%|██████████| 16/16 [00:00<00:00, 76.38 it/sec, feas=True, obj=6.51]
INFO - 16:22:00: Optimization result:
INFO - 16:22:00: Optimizer info:
INFO - 16:22:00: Status: None
INFO - 16:22:00: Message: None
INFO - 16:22:00: Solution:
INFO - 16:22:00: Objective: 0.004329869274089288
INFO - 16:22:00: Design space:
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | epsilon | 0.01 | 0.01 | 0.1 | float |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: *** End DOEScenario execution ***
INFO - 16:22:00: *** Start DOEScenario execution ***
INFO - 16:22:00: DOEScenario
INFO - 16:22:00: Disciplines: MLAlgoAssessor
INFO - 16:22:00: MDO formulation: DisciplinaryOpt
INFO - 16:22:00: Optimization problem:
INFO - 16:22:00: minimize criterion(epsilon)
INFO - 16:22:00: with respect to epsilon
INFO - 16:22:00: over the design space:
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | epsilon | 0.01 | 0.01 | 0.1 | float |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 16:22:00: 6%|▋ | 1/16 [00:00<00:00, 65.36 it/sec, feas=True, obj=0.00392]
INFO - 16:22:00: 12%|█▎ | 2/16 [00:00<00:00, 70.40 it/sec, feas=True, obj=0.00489]
INFO - 16:22:00: 19%|█▉ | 3/16 [00:00<00:00, 73.10 it/sec, feas=True, obj=0.0056]
INFO - 16:22:00: 25%|██▌ | 4/16 [00:00<00:00, 74.62 it/sec, feas=True, obj=0.00582]
INFO - 16:22:00: 31%|███▏ | 5/16 [00:00<00:00, 75.38 it/sec, feas=True, obj=0.00558]
INFO - 16:22:00: 38%|███▊ | 6/16 [00:00<00:00, 75.67 it/sec, feas=True, obj=0.00512]
INFO - 16:22:00: 44%|████▍ | 7/16 [00:00<00:00, 76.17 it/sec, feas=True, obj=0.00454]
INFO - 16:22:00: 50%|█████ | 8/16 [00:00<00:00, 76.40 it/sec, feas=True, obj=0.00395]
INFO - 16:22:00: 56%|█████▋ | 9/16 [00:00<00:00, 76.74 it/sec, feas=True, obj=0.00343]
INFO - 16:22:00: 62%|██████▎ | 10/16 [00:00<00:00, 77.01 it/sec, feas=True, obj=0.00304]
INFO - 16:22:00: 69%|██████▉ | 11/16 [00:00<00:00, 77.14 it/sec, feas=True, obj=0.00277]
INFO - 16:22:00: 75%|███████▌ | 12/16 [00:00<00:00, 77.33 it/sec, feas=True, obj=0.00258]
INFO - 16:22:00: 81%|████████▏ | 13/16 [00:00<00:00, 77.52 it/sec, feas=True, obj=0.00246]
INFO - 16:22:00: 88%|████████▊ | 14/16 [00:00<00:00, 77.61 it/sec, feas=True, obj=0.00237]
INFO - 16:22:00: 94%|█████████▍| 15/16 [00:00<00:00, 77.76 it/sec, feas=True, obj=0.00231]
INFO - 16:22:00: 100%|██████████| 16/16 [00:00<00:00, 77.80 it/sec, feas=True, obj=0.00226]
INFO - 16:22:00: Optimization result:
INFO - 16:22:00: Optimizer info:
INFO - 16:22:00: Status: None
INFO - 16:22:00: Message: None
INFO - 16:22:00: Solution:
INFO - 16:22:00: Objective: 0.0022624675787187524
INFO - 16:22:00: Design space:
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | epsilon | 0.01 | 0.1 | 0.1 | float |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: *** End DOEScenario execution ***
INFO - 16:22:00: *** Start DOEScenario execution ***
INFO - 16:22:00: DOEScenario
INFO - 16:22:00: Disciplines: MLAlgoAssessor
INFO - 16:22:00: MDO formulation: DisciplinaryOpt
INFO - 16:22:00: Optimization problem:
INFO - 16:22:00: minimize criterion(epsilon)
INFO - 16:22:00: with respect to epsilon
INFO - 16:22:00: over the design space:
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | epsilon | 0.01 | 0.1 | 0.1 | float |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 16:22:00: 6%|▋ | 1/16 [00:00<00:00, 69.56 it/sec, feas=True, obj=0.00305]
INFO - 16:22:00: 12%|█▎ | 2/16 [00:00<00:00, 74.26 it/sec, feas=True, obj=0.00307]
INFO - 16:22:00: 19%|█▉ | 3/16 [00:00<00:00, 75.25 it/sec, feas=True, obj=0.00297]
INFO - 16:22:00: 25%|██▌ | 4/16 [00:00<00:00, 76.19 it/sec, feas=True, obj=0.0028]
INFO - 16:22:00: 31%|███▏ | 5/16 [00:00<00:00, 76.96 it/sec, feas=True, obj=0.00263]
INFO - 16:22:00: 38%|███▊ | 6/16 [00:00<00:00, 77.18 it/sec, feas=True, obj=0.00251]
INFO - 16:22:00: 44%|████▍ | 7/16 [00:00<00:00, 77.57 it/sec, feas=True, obj=0.00242]
INFO - 16:22:00: 50%|█████ | 8/16 [00:00<00:00, 77.84 it/sec, feas=True, obj=0.00237]
INFO - 16:22:00: 56%|█████▋ | 9/16 [00:00<00:00, 77.85 it/sec, feas=True, obj=0.00233]
INFO - 16:22:00: 62%|██████▎ | 10/16 [00:00<00:00, 77.97 it/sec, feas=True, obj=0.0023]
INFO - 16:22:00: 69%|██████▉ | 11/16 [00:00<00:00, 78.04 it/sec, feas=True, obj=0.00228]
INFO - 16:22:00: 75%|███████▌ | 12/16 [00:00<00:00, 78.10 it/sec, feas=True, obj=0.00226]
INFO - 16:22:00: 81%|████████▏ | 13/16 [00:00<00:00, 78.25 it/sec, feas=True, obj=0.00224]
INFO - 16:22:00: 88%|████████▊ | 14/16 [00:00<00:00, 77.78 it/sec, feas=True, obj=0.00223]
INFO - 16:22:00: 94%|█████████▍| 15/16 [00:00<00:00, 77.78 it/sec, feas=True, obj=0.00222]
INFO - 16:22:00: 100%|██████████| 16/16 [00:00<00:00, 77.84 it/sec, feas=True, obj=0.00221]
INFO - 16:22:00: Optimization result:
INFO - 16:22:00: Optimizer info:
INFO - 16:22:00: Status: None
INFO - 16:22:00: Message: None
INFO - 16:22:00: Solution:
INFO - 16:22:00: Objective: 0.002207251533907032
INFO - 16:22:00: Design space:
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | epsilon | 0.01 | 0.1 | 0.1 | float |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: *** End DOEScenario execution ***
INFO - 16:22:00: *** Start DOEScenario execution ***
INFO - 16:22:00: DOEScenario
INFO - 16:22:00: Disciplines: MLAlgoAssessor
INFO - 16:22:00: MDO formulation: DisciplinaryOpt
INFO - 16:22:00: Optimization problem:
INFO - 16:22:00: minimize criterion(epsilon)
INFO - 16:22:00: with respect to epsilon
INFO - 16:22:00: over the design space:
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | epsilon | 0.01 | 0.1 | 0.1 | float |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 16:22:00: 6%|▋ | 1/16 [00:00<00:00, 66.68 it/sec, feas=True, obj=0.00254]
INFO - 16:22:00: 12%|█▎ | 2/16 [00:00<00:00, 66.97 it/sec, feas=True, obj=0.0025]
INFO - 16:22:00: 19%|█▉ | 3/16 [00:00<00:00, 70.49 it/sec, feas=True, obj=0.00248]
INFO - 16:22:00: 25%|██▌ | 4/16 [00:00<00:00, 72.58 it/sec, feas=True, obj=0.00248]
INFO - 16:22:00: 31%|███▏ | 5/16 [00:00<00:00, 73.85 it/sec, feas=True, obj=0.00248]
INFO - 16:22:00: 38%|███▊ | 6/16 [00:00<00:00, 74.67 it/sec, feas=True, obj=0.0025]
INFO - 16:22:00: 44%|████▍ | 7/16 [00:00<00:00, 75.31 it/sec, feas=True, obj=0.00253]
INFO - 16:22:00: 50%|█████ | 8/16 [00:00<00:00, 75.55 it/sec, feas=True, obj=0.00256]
INFO - 16:22:00: 56%|█████▋ | 9/16 [00:00<00:00, 75.87 it/sec, feas=True, obj=0.00259]
INFO - 16:22:00: 62%|██████▎ | 10/16 [00:00<00:00, 76.09 it/sec, feas=True, obj=0.00263]
INFO - 16:22:00: 69%|██████▉ | 11/16 [00:00<00:00, 76.24 it/sec, feas=True, obj=0.00267]
INFO - 16:22:00: 75%|███████▌ | 12/16 [00:00<00:00, 76.45 it/sec, feas=True, obj=0.00272]
INFO - 16:22:00: 81%|████████▏ | 13/16 [00:00<00:00, 76.69 it/sec, feas=True, obj=0.00276]
INFO - 16:22:00: 88%|████████▊ | 14/16 [00:00<00:00, 76.79 it/sec, feas=True, obj=0.00281]
INFO - 16:22:00: 94%|█████████▍| 15/16 [00:00<00:00, 76.17 it/sec, feas=True, obj=0.00286]
INFO - 16:22:00: 100%|██████████| 16/16 [00:00<00:00, 76.36 it/sec, feas=True, obj=0.00291]
INFO - 16:22:00: Optimization result:
INFO - 16:22:00: Optimizer info:
INFO - 16:22:00: Status: None
INFO - 16:22:00: Message: None
INFO - 16:22:00: Solution:
INFO - 16:22:00: Objective: 0.002476990894836162
INFO - 16:22:00: Design space:
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | epsilon | 0.01 | 0.028 | 0.1 | float |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: *** End DOEScenario execution ***
INFO - 16:22:00: *** Start DOEScenario execution ***
INFO - 16:22:00: DOEScenario
INFO - 16:22:00: Disciplines: MLAlgoAssessor
INFO - 16:22:00: MDO formulation: DisciplinaryOpt
INFO - 16:22:00: Optimization problem:
INFO - 16:22:00: minimize criterion(epsilon)
INFO - 16:22:00: with respect to epsilon
INFO - 16:22:00: over the design space:
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: | epsilon | 0.01 | 0.028 | 0.1 | float |
INFO - 16:22:00: +---------+-------------+-------+-------------+-------+
INFO - 16:22:00: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 16:22:00: 6%|▋ | 1/16 [00:00<00:00, 66.37 it/sec, feas=True, obj=0.00292]
INFO - 16:22:00: 12%|█▎ | 2/16 [00:00<00:00, 71.90 it/sec, feas=True, obj=0.00326]
INFO - 16:22:00: 19%|█▉ | 3/16 [00:00<00:00, 73.66 it/sec, feas=True, obj=0.00361]
INFO - 16:22:00: 25%|██▌ | 4/16 [00:00<00:00, 74.98 it/sec, feas=True, obj=0.00398]
INFO - 16:22:00: 31%|███▏ | 5/16 [00:00<00:00, 75.95 it/sec, feas=True, obj=0.00435]
INFO - 16:22:00: 38%|███▊ | 6/16 [00:00<00:00, 76.46 it/sec, feas=True, obj=0.00474]
INFO - 16:22:00: 44%|████▍ | 7/16 [00:00<00:00, 76.86 it/sec, feas=True, obj=0.00513]
INFO - 16:22:00: 50%|█████ | 8/16 [00:00<00:00, 77.23 it/sec, feas=True, obj=0.00553]
INFO - 16:22:00: 56%|█████▋ | 9/16 [00:00<00:00, 77.41 it/sec, feas=True, obj=0.00594]
INFO - 16:22:00: 62%|██████▎ | 10/16 [00:00<00:00, 77.69 it/sec, feas=True, obj=0.00636]
INFO - 16:22:00: 69%|██████▉ | 11/16 [00:00<00:00, 77.87 it/sec, feas=True, obj=0.00679]
INFO - 16:22:00: 75%|███████▌ | 12/16 [00:00<00:00, 78.00 it/sec, feas=True, obj=0.00723]
INFO - 16:22:00: 81%|████████▏ | 13/16 [00:00<00:00, 78.14 it/sec, feas=True, obj=0.00767]
INFO - 16:22:00: 88%|████████▊ | 14/16 [00:00<00:00, 78.26 it/sec, feas=True, obj=0.00813]
INFO - 16:22:00: 94%|█████████▍| 15/16 [00:00<00:00, 78.27 it/sec, feas=True, obj=0.00859]
INFO - 16:22:01: 100%|██████████| 16/16 [00:00<00:00, 78.29 it/sec, feas=True, obj=0.00906]
INFO - 16:22:01: Optimization result:
INFO - 16:22:01: Optimizer info:
INFO - 16:22:01: Status: None
INFO - 16:22:01: Message: None
INFO - 16:22:01: Solution:
INFO - 16:22:01: Objective: 0.002919064447634629
INFO - 16:22:01: Design space:
INFO - 16:22:01: +---------+-------------+-------+-------------+-------+
INFO - 16:22:01: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:01: +---------+-------------+-------+-------------+-------+
INFO - 16:22:01: | epsilon | 0.01 | 0.01 | 0.1 | float |
INFO - 16:22:01: +---------+-------------+-------+-------------+-------+
INFO - 16:22:01: *** End DOEScenario execution ***
INFO - 16:22:01: *** Start DOEScenario execution ***
INFO - 16:22:01: DOEScenario
INFO - 16:22:01: Disciplines: MLAlgoAssessor
INFO - 16:22:01: MDO formulation: DisciplinaryOpt
INFO - 16:22:01: Optimization problem:
INFO - 16:22:01: minimize criterion(epsilon)
INFO - 16:22:01: with respect to epsilon
INFO - 16:22:01: over the design space:
INFO - 16:22:01: +---------+-------------+-------+-------------+-------+
INFO - 16:22:01: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:01: +---------+-------------+-------+-------------+-------+
INFO - 16:22:01: | epsilon | 0.01 | 0.01 | 0.1 | float |
INFO - 16:22:01: +---------+-------------+-------+-------------+-------+
INFO - 16:22:01: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 16:22:01: 6%|▋ | 1/16 [00:00<00:00, 69.61 it/sec, feas=True, obj=0.00846]
INFO - 16:22:01: 12%|█▎ | 2/16 [00:00<00:00, 73.90 it/sec, feas=True, obj=0.0119]
INFO - 16:22:01: 19%|█▉ | 3/16 [00:00<00:00, 75.89 it/sec, feas=True, obj=0.0148]
INFO - 16:22:01: 25%|██▌ | 4/16 [00:00<00:00, 76.72 it/sec, feas=True, obj=0.0172]
INFO - 16:22:01: 31%|███▏ | 5/16 [00:00<00:00, 77.44 it/sec, feas=True, obj=0.019]
INFO - 16:22:01: 38%|███▊ | 6/16 [00:00<00:00, 77.91 it/sec, feas=True, obj=0.0213]
INFO - 16:22:01: 44%|████▍ | 7/16 [00:00<00:00, 78.07 it/sec, feas=True, obj=0.0921]
INFO - 16:22:01: 50%|█████ | 8/16 [00:00<00:00, 78.28 it/sec, feas=True, obj=11.9]
INFO - 16:22:01: 56%|█████▋ | 9/16 [00:00<00:00, 78.43 it/sec, feas=True, obj=0.0761]
INFO - 16:22:01: 62%|██████▎ | 10/16 [00:00<00:00, 77.91 it/sec, feas=True, obj=0.0533]
INFO - 16:22:01: 69%|██████▉ | 11/16 [00:00<00:00, 78.01 it/sec, feas=True, obj=0.0483]
INFO - 16:22:01: 75%|███████▌ | 12/16 [00:00<00:00, 78.10 it/sec, feas=True, obj=0.0466]
INFO - 16:22:01: 81%|████████▏ | 13/16 [00:00<00:00, 78.18 it/sec, feas=True, obj=0.0461]
INFO - 16:22:01: 88%|████████▊ | 14/16 [00:00<00:00, 78.25 it/sec, feas=True, obj=0.0461]
INFO - 16:22:01: 94%|█████████▍| 15/16 [00:00<00:00, 78.32 it/sec, feas=True, obj=0.0464]
INFO - 16:22:01: 100%|██████████| 16/16 [00:00<00:00, 78.23 it/sec, feas=True, obj=0.0468]
INFO - 16:22:01: Optimization result:
INFO - 16:22:01: Optimizer info:
INFO - 16:22:01: Status: None
INFO - 16:22:01: Message: None
INFO - 16:22:01: Solution:
INFO - 16:22:01: Objective: 0.00846290490101175
INFO - 16:22:01: Design space:
INFO - 16:22:01: +---------+-------------+-------+-------------+-------+
INFO - 16:22:01: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:22:01: +---------+-------------+-------+-------------+-------+
INFO - 16:22:01: | epsilon | 0.01 | 0.01 | 0.1 | float |
INFO - 16:22:01: +---------+-------------+-------+-------------+-------+
INFO - 16:22:01: *** End DOEScenario execution ***
Select best candidate#
best_algo = selector.select()
best_algo
Plot results#
Plot the best models from each candidate algorithm
finex = linspace(0, 1, 1000)
for candidate in selector.candidates:
algo = candidate[0]
print(algo)
predy = algo.predict(finex[:, None])[:, 0]
plt.plot(finex, predy, label=algo.SHORT_ALGO_NAME)
plt.scatter(x, y, label="Training points")
plt.legend()
plt.show()
LinearRegressor(fit_intercept=True, input_names=(), l2_penalty_ratio=0.0, output_names=(), parameters={}, penalty_level=0.0, random_state=0, transformer={})
based on the scikit-learn library
built from 20 learning samples
PolynomialRegressor(degree=4, fit_intercept=True, input_names=(), l2_penalty_ratio=1.0, output_names=(), parameters={}, penalty_level=0.0, random_state=0, transformer={})
based on the scikit-learn library
built from 20 learning samples
RBFRegressor(der_function=None, epsilon=0.1, function=multiquadric, input_names=(), norm=euclidean, output_names=(), parameters={}, smooth=0.1, transformer={})
based on the SciPy library
built from 20 learning samples
Total running time of the script: (0 minutes 2.029 seconds)