deep_learning_from_scratch_exercise_3.py

deep_learning_from_scratch_exercise_3.py

import pandas as pd
import torch

"""
Complete the code below to perform stochastic gradient descent
on a linear regression.

Try to find a sufficient learning rate and number of iterations. 
"""

# Input data
url = r"https://raw.githubusercontent.com/thomasnield/machine-learning-demo-data/master/regression/linear_normal.csv"
data = pd.read_csv(url, header=0)

# Convert data to PyTorch Tensors
X = torch.tensor(data.iloc[:, 0].values, dtype=torch.float32)
Y = torch.tensor(data.iloc[:, 1].values, dtype=torch.float32)

n = data.shape[0]  # rows

# Building the model from scratch
# No requires_grad=True needed here because we are doing the math ourselves!
m = torch.tensor(0.0)
b = torch.tensor(0.0)

sample_size = 1  # sample size
L = ?  # The learning Rate
epochs = ?  # The number of iterations to perform gradient descent

# Performing Stochastic Gradient Descent
for i in range(epochs):
    # PyTorch equivalent of np.random.choice
    idx = torch.randint(0, n, (sample_size,))
    x_sample = X[idx]
    y_sample = Y[idx]

    # The current predicted value of Y
    Y_pred = m * x_sample + b

    # d/dm derivative of loss function (Calculated manually)
    # We use torch.sum() instead of Python's sum() for tensor speed
    D_m = (-2 / sample_size) * torch.sum(x_sample * (y_sample - Y_pred))

    # d/db derivative of loss function (Calculated manually)
    D_b = (-2 / sample_size) * torch.sum(y_sample - Y_pred)

    # Update m and b using basic arithmetic
    m = m - L * D_m
    b = b - L * D_b

    # print progress
    if i % 10000 == 0:
        print(f"Iteration {i}: m = {m.item():.4f}, b = {b.item():.4f}")

print(f"\nFinal Equation: y = {m.item():.4f}x + {b.item():.4f}")





# --- MATPLOTLIB VISUALIZATION ---
import matplotlib.pyplot as plt

# 1. Convert tensors back to numpy arrays for matplotlib compatibility
x_data = X.numpy()
y_data = Y.numpy()

# 2. Calculate the predicted Y values across the whole dataset to draw the line
y_line = m.item() * x_data + b.item()

# 3. Create the plot

plt.figure(figsize=(8, 6))

# Plot the original dataset as a scatter plot
plt.scatter(x_data, y_data, color='blue', alpha=0.6, label='Original Data')

# Plot the regression line
plt.plot(x_data, y_line, color='red', linewidth=2, label=f'Regression Line\ny = {m.item():.4f}x + {b.item():.4f}')

# 4. Add styling and labels
plt.title('Linear Regression using Manual PyTorch SGD', fontsize=14)
plt.xlabel('X', fontsize=12)
plt.ylabel('Y', fontsize=12)
plt.legend(loc='upper left')
plt.grid(True, linestyle='--', alpha=0.7)

# 5. Display the chart
plt.show()