Least-squares approximation¶
The following description is taken from scikit-learn version 0.18.2 [1].
The Least Squares method fits a linear model with coefficients \({\bf \beta} = \left(\beta_0, \beta_1,\dotsc,\beta_{nx}\right)\) to minimize the residual sum of squares between the observed responses in the dataset, and the responses predicted by the linear approximation. Mathematically it solves a problem of the form:
where \({\bf X} = \left(1,{{\bf x}^{(1)}}^T,\dots,{{\bf x}^{(nt)}}^T\right)^T\) with dimensions (\(nt\times nx+1\)).
Usage¶
import matplotlib.pyplot as plt
import numpy as np
from smt.surrogate_models import LS
xt = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
yt = np.array([0.0, 1.0, 1.5, 0.9, 1.0])
sm = LS()
sm.set_training_values(xt, yt)
sm.train()
num = 100
x = np.linspace(0.0, 4.0, num)
y = sm.predict_values(x)
plt.plot(xt, yt, "o")
plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.legend(["Training data", "Prediction"])
plt.show()
___________________________________________________________________________
LS
___________________________________________________________________________
Problem size
# training points. : 5
___________________________________________________________________________
Training
Training ...
Training - done. Time (sec): 0.0000000
___________________________________________________________________________
Evaluation
# eval points. : 100
Predicting ...
Predicting - done. Time (sec): 0.0000000
Prediction time/pt. (sec) : 0.0000000
Options¶
Option |
Default |
Acceptable values |
Acceptable types |
Description |
---|---|---|---|---|
print_global |
True |
None |
[‘bool’] |
Global print toggle. If False, all printing is suppressed |
print_training |
True |
None |
[‘bool’] |
Whether to print training information |
print_prediction |
True |
None |
[‘bool’] |
Whether to print prediction information |
print_problem |
True |
None |
[‘bool’] |
Whether to print problem information |
print_solver |
True |
None |
[‘bool’] |
Whether to print solver information |
data_dir |
None |
None |
[‘str’] |
Directory for loading / saving cached data; None means do not save or load |