Simple Gradient Descent on predicting Boston Housing

SImple Gradient Descent implementations Examples

Here we are using Boston Housing Dataset which is provided by sklearn package.

If you don’t have sklearn installed, you may install via pip

pip install -U scikit-learn

Load Boston Housing Dataset

import numpy as np
from sklearn.datasets import load_boston

boston = load_boston()
print(X.shape)
# (506, 13)

Load Feature Data

boston['feature_names']
# array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',
# 'TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='<U7')

Load Target Data

actual = boston["target"]
print(y.shape)
# (506, )

Wrap Data with Pandas

import pandas as pd

data = pd.DataFrame(X, columns=boston["feature_names"])
data["RealData"] = actual  # for comparison of predictions

Apply Gradient Descent

num_epoch = 100000
num_data = X.shape[0]
learning_rate = 0.000003

w = np.random.uniform(low=-1.0, high=1.0, size=13)
b = np.random.uniform(low=-1.0, high=1.0)


for epoch in range(num_epoch):
    predict = X.dot(w) + b
    error = np.abs(predict - actual).mean()
    
    # Assume that error < 5 will be enough
    if error < 5:
        break
        
    if epoch % 10000 == 0:    
        print("{0} epoch, error={1}".format(epoch, error))
        
    w = w - learning_rate * (predict-actual).dot(X) / num_data
    b = b - learning_rate * (predict-actual).mean()
    
print("{0} epoch, error={1}".format(epoch, error))

Results

0 epoch, error=44.21782491690112
10000 epoch, error=5.465574626842506
20000 epoch, error=5.080520144919618
25569 epoch, error=4.999989852544409