Exploring the GPy packageΒΆ
In [1]:
import time
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
In [2]:
n = 10
np.random.seed(int(time.time()))
t = np.random.rand(n)
x = np.random.rand(n)
y_u = np.multiply(np.exp(-t), np.sin(2*np.pi*x))
y_f = (4*np.pi**2 - 1) * np.multiply(np.exp(-t), np.sin(2*np.pi*x))
In [3]:
import GPy
In [4]:
kernel = GPy.kern.RBF(input_dim=2)
kernel
Out[4]:
| rbf. | value | constraints | priors |
|---|---|---|---|
| variance | 1.0 | +ve | |
| lengthscale | 1.0 | +ve |
In [5]:
m = GPy.models.GPRegression(np.matrix([t, x]).T, y_u.reshape(y_u.size,1),kernel)
In [6]:
from IPython.display import display
display(m)
Model: GP regression
Objective: 11.39911599767793
Number of Parameters: 3
Number of Optimization Parameters: 3
Updates: True
| GP_regression. | value | constraints | priors |
|---|---|---|---|
| rbf.variance | 1.0 | +ve | |
| rbf.lengthscale | 1.0 | +ve | |
| Gaussian_noise.variance | 1.0 | +ve |
In [7]:
fig = m.plot()
display(GPy.plotting.show(fig, filename='basic_gp_regression_notebook_2d'))
/usr/local/lib/python3.6/site-packages/matplotlib/figure.py:1743: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.
In [8]:
m.optimize(messages=True)
Running L-BFGS-B (Scipy implementation) Code:
runtime i f |g|
00s00 0003 1.797920e+01 3.159042e+02
00s03 0012 3.656938e+00 9.295373e+00
00s06 0023 6.417812e-01 7.386639e-03
00s09 0035 6.255299e-01 4.347322e-06
00s10 0040 6.255208e-01 1.657704e-08
00s12 0045 6.255205e-01 6.876193e-11
00s12 0046 6.255205e-01 6.876193e-11
Runtime: 00s12
Optimization status: Converged
Out[8]:
<paramz.optimization.optimization.opt_lbfgsb at 0x1067d2ba8>
In [9]:
m.optimize_restarts(num_restarts = 10)
Optimization restart 1/10, f = 0.6255204911801915
Optimization restart 2/10, f = 0.6255204901419562
Optimization restart 3/10, f = 0.6255214894302625
Optimization restart 4/10, f = 0.6255204755438637
Optimization restart 5/10, f = 0.625520537160762
Optimization restart 6/10, f = 0.6255204592848189
Optimization restart 7/10, f = 0.6255204754204922
Optimization restart 8/10, f = 0.6255213104151442
Optimization restart 9/10, f = 0.6255213338652572
Optimization restart 10/10, f = 0.6255205894920346
Out[9]:
[<paramz.optimization.optimization.opt_lbfgsb at 0x1067d2ba8>,
<paramz.optimization.optimization.opt_lbfgsb at 0x10317ffd0>,
<paramz.optimization.optimization.opt_lbfgsb at 0x1067d2908>,
<paramz.optimization.optimization.opt_lbfgsb at 0x103fce0f0>,
<paramz.optimization.optimization.opt_lbfgsb at 0x10667c668>,
<paramz.optimization.optimization.opt_lbfgsb at 0x10780b080>,
<paramz.optimization.optimization.opt_lbfgsb at 0x10781fdd8>,
<paramz.optimization.optimization.opt_lbfgsb at 0x10781f3c8>,
<paramz.optimization.optimization.opt_lbfgsb at 0x10667c400>,
<paramz.optimization.optimization.opt_lbfgsb at 0x10781fda0>,
<paramz.optimization.optimization.opt_lbfgsb at 0x1067d2a58>]
In [10]:
display(m)
Model: GP regression
Objective: 0.6255204592848189
Number of Parameters: 3
Number of Optimization Parameters: 3
Updates: True
| GP_regression. | value | constraints | priors |
|---|---|---|---|
| rbf.variance | 0.15041095424439307 | +ve | |
| rbf.lengthscale | 0.23136896502224594 | +ve | |
| Gaussian_noise.variance | 3.0641250798197575e-11 | +ve |
In [11]:
fig = m.plot()
GPy.plotting.show(fig, filename='basic_gp_regression_notebook_optimized')
/usr/local/lib/python3.6/site-packages/matplotlib/figure.py:1743: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.
Out[11]:
