Locally_weighted_regression.py

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

plt.style.use("seaborn")
# Loading CSV files from local storage 
dfx = pd.read_csv('weightedX_LOWES.csv') 
dfy = pd.read_csv('weightedY_LOWES.csv') 
# Getting data from DataFrame Object and storing in numpy n-dim arrays 
X = dfx.values 
Y = dfy.values
# function to calculate W weight diagnal Matric used in calculation of predictions 
def get_WeightMatrix_for_LOWES(query_point, Training_examples, Bandwidth): 
# M is the No of training examples 
M = Training_examples.shape[0] 
# Initialising W with identity matrix 
W = np.mat(np.eye(M)) 
# calculating weights for query points 
for i in range(M): 
	xi = Training_examples[i] 
	denominator = (-2 * Bandwidth * Bandwidth) 
	W[i, i] = np.exp(np.dot((xi-query_point), (xi-query_point).T)/denominator) 
	return W 
# function to make predictions 
def predict(training_examples, Y, query_x, Bandwidth): 
M = Training_examples.shape[0] 
all_ones = np.ones((M, 1)) 
X_ = np.hstack((training_examples, all_ones)) 
qx = np.mat([query_x, 1]) 
W = get_WeightMatrix_for_LOWES(qx, X_, Bandwidth) 
# calculating parameter theta 
theta = np.linalg.pinv(X_.T*(W * X_))*(X_.T*(W * Y)) 
# calculating predictions 
pred = np.dot(qx, theta) 
return theta, pred
# visualise predicted values with respect 
# to original target values 

Bandwidth = 0.1
X_test = np.linspace(-2, 2, 20) 
Y_test = [] 
for query in X_test: 
theta, pred = predict(X, Y, query, Bandwidth) 
Y_test.append(pred[0][0]) 
horizontal_axis = np.array(X) 
vertical_axis = np.array(Y) 
plt.title("Tau / Bandwidth Param %.2f"% Bandwidth) 
plt.scatter(horizontal_axis, vertical_axis) 
Y_test = np.array(Y_test) 
plt.scatter(X_test, Y_test, color ='red') 
plt.show()