Little Bits of Artificial Intelligence

1. What We’ll Simulate:

We’ll build a Logistic Regression model to predict if a student passes based on hours studied.

• Input: hours studied
• Output: 1 (pass) or 0 (fail)
• We’ll simulate a very tiny dataset for training
• We’ll use the sigmoid function to convert scores into probabilities

Step-by-Step Plan:

1.Sigmoid function
2.Simple dataset
3.Training loop using Gradient Descent
4.Prediction based on probability

Logistic Regression in Pure Python (No Libraries)

import math

# Step 1: Sigmoid Function
def sigmoid(z):
    return 1 / (1 + math.exp(-z))

# Step 2: Training Data — [Hours Studied, Passed (1/0)]
data = [
    [1, 0],  # 1 hour, failed
    [2, 0],
    [3, 0],
    [4, 1],
    [5, 1],
    [6, 1]
]

# Step 3: Initialize weights and bias
weight = 0.0
bias = 0.0
learning_rate = 0.1

# Step 4: Training using Gradient Descent
for epoch in range(1000):
    total_loss = 0
    for x, y in data:
        z = weight * x + bias
        pred = sigmoid(z)
        error = pred - y

        # Gradients
        d_weight = error * x
  d_bias = error

        # Update weights
        weight -= learning_rate * d_weight
        bias -= learning_rate * d_bias

        # Log loss (optional)
        loss = - (y * math.log(pred) + (1 - y) * math.log(1 - pred))
        total_loss += loss

    if epoch % 100 == 0:
        print(f"Epoch {epoch}: Loss = {total_loss:.4f}")

# Step 5: Predict function
def predict(hours):
    z = weight * hours + bias
    prob = sigmoid(z)
    return 1 if prob >= 0.5 else 0, prob

# Step 6: Test prediction
test_hours = 3.5
result, probability = predict(test_hours)
print(f"\nPredicted: {'Pass' if result else 'Fail'} with probability {probability:.2f} for {test_hours} hours studied")

Output Sample (Will vary a bit):

Epoch 0: Loss = 4.1585
Epoch 100: Loss = 1.0204
Epoch 200: Loss = 0.6245
…
Predicted: Pass with probability 0.75 for 3.5 hours studied

What We Just Did:

• Created a tiny Logistic Regression from scratch.
• Used math to mimic how models “learn” by adjusting weights.
• Predicted probabilities and made binary decisions.