LocallyWeightedRegression.py

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt


def kernel(data, point, xmat, k):
    m, n = np.shape(xmat)
    ws = np.mat(np.eye((m)))
    for j in range(m):
        diff = point - data[j]
        ws[j, j] = np.exp(diff * diff.T / (-2.0 * k**2))
    return ws


def local_weight(data, point, xmat, ymat, k):
    wei = kernel(data, point, xmat, k)
    return (data.T * (wei * data)).I * (data.T * (wei * ymat.T))
 

def local_weight_regression(xmat, ymat, k):
    m, _ = np.shape(xmat)
    ypred = np.zeros(m)
    for i in range(m):
        ypred[i] = xmat[i] * local_weight(xmat, xmat[i], xmat, ymat, k)
    return ypred


df = pd.read_csv('tips.csv')
features = np.array(df.total_bill)
labels = np.array(df.tip) 

m = features.shape[0]
mtip = np.mat(labels)

data = np.hstack((np.ones((m, 1)), np.mat(features).T))

ypred = local_weight_regression(data, mtip, 0.5)

indices = data[:, 1].argsort(0)
xsort = data[indices][:, 0]

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.scatter(features, labels, color='blue')
ax.plot(xsort[:, 1], ypred[indices], color = 'red', linewidth=3)
plt.xlabel('Total bill')
plt.ylabel('Tip')
plt.show()