Polynomial

class skfda.misc.covariances.Polynomial(*, variance=1, intercept=0, slope=1, degree=2)

Polynomial covariance function.

The covariance function is

\[K(x, x') = \sigma^2 (\alpha x^T x' + c)^d\]

where \(\sigma^2\) is the scale of the variance, \(\alpha\) is the slope, \(d\) the degree of the polynomial and \(c\) is the intercept.

Heatmap plot of the covariance function:

from skfda.misc.covariances import Polynomial
import matplotlib.pyplot as plt

Polynomial().heatmap(limits=(0, 1))
plt.show()

Example of Gaussian process trajectories using this covariance:

from skfda.misc.covariances import Polynomial
from skfda.datasets import make_gaussian_process
import matplotlib.pyplot as plt

gp = make_gaussian_process(
        n_samples=10, cov=Polynomial(), random_state=0)
gp.plot()
plt.show()

Default representation in a Jupyter notebook:

from skfda.misc.covariances import Polynomial

Polynomial()

\[K(x, x') = \sigma^2 (\alpha x^T x' + c)^d \\\text{where:}\begin{aligned}\qquad\sigma^2 &= 1 \\c &= 0 \\\alpha &= 1 \\d &= 2 \\\end{aligned}\]

Methods

heatmap([limits])	Return a heatmap plot of the covariance function.
to_sklearn()	Convert it to a sklearn kernel, if there is one.

Parameters:

• variance (float) –

• intercept (float) –

• slope (float) –

• degree (float) –

heatmap(limits=(-1, 1))

Return a heatmap plot of the covariance function.

Parameters:

limits (Tuple[float, float]) –

Return type:

Figure

to_sklearn()

Convert it to a sklearn kernel, if there is one.

Return type:

Kernel