Hướng dẫn local polynomial regression python

FDApy

Note

Click here to download the full example code

This notebook shows how to perform a local polynomial regression on one and two-dimensional data.

# Author: Steven Golovkine 
# License: MIT

# shinx_gallery_thumbnail_number = 2

import matplotlib.pyplot as plt
import numpy as np

from FDApy.preprocessing.smoothing.local_polynomial import LocalPolynomial

We generate some one-dimensional data to perform local polynomial smoothing.

X = np.random.normal[0, 1, 100]
Y = 2 * np.sin[X] + np.random.normal[0, 0.25, 100]
Y_true = 2 * np.sin[np.linspace[-2, 2, 200]]

Fit local polynomials

# Fit local polynomials
lp = LocalPolynomial[kernel_name="epanechnikov", bandwidth=2, degree=2]
lp.fit[X, Y]

# Plot the results
plt.scatter[X, Y, alpha=0.5, color='blue', label='Noisy']
plt.scatter[np.sort[X], lp.X_fit_, color='red', label='Estimated']
plt.plot[np.linspace[-2, 2, 200], Y_true, 'green', label='True']
plt.legend[]

Out:

Estimate the curve on a regular grid.

# Estimation on a grid
y_pred = lp.predict[np.linspace[-2, 2, 500]]

# Plot the results
plt.scatter[X, Y, alpha=0.5, color='blue', label='noisy']
plt.scatter[np.linspace[-2, 2, 500], y_pred, color='red', label='Prediction']
plt.plot[np.linspace[-2, 2, 200], Y_true, color='green', label='True']
plt.legend[]

Out:

We will now do the same using two-dimensional data.

X = np.random.randn[2, 100]
Y = -1 * np.sin[X[0]] + 0.5 * np.cos[X[1]] + 0.2 * np.random.randn[100]
X0 = np.mgrid[-10:10:1, -10:10:1] / 10
X0 = np.vstack[[X0[0].ravel[], X0[1].ravel[]]]

Fit local polynomials

# Fit local polynomials
lp = LocalPolynomial[kernel_name="epanechnikov", bandwidth=2, degree=1]
lp.fit[X, Y]

# Plot the results
fig = plt.figure[]
ax = fig.add_subplot[111, projection='3d']
_ = ax.scatter[X[0], X[1], Y]
_ = ax.scatter[X[0], X[1], lp.X_fit_, color='red']

Estimate the curve on a regular surface.

# Estimation on a grid
y_pred = lp.predict[X0]

# Plot the results
fig = plt.figure[]
ax = fig.add_subplot[111, projection='3d']
_ = ax.scatter[X[0], X[1], Y]
_ = ax.scatter[X0[0], X0[1], y_pred, color='red']