pages/Logistic Regression.py

import streamlit as st

st.set_page_config(page_title="Logistic Regression", page_icon="🔐", layout="wide")

# Title
st.markdown("<h1 style='text-align: center;'>🔐 Logistic Regression - Made Simple</h1>", unsafe_allow_html=True)

# What is Logistic Regression?
st.header("📚 What is Logistic Regression?")
st.markdown("""
Logistic Regression is a **classification algorithm** used to predict **discrete outcomes** (like Yes/No, 0/1, Spam/Not Spam).

Think of it like:
> “Based on your features (like age, income, health), should you get insurance? Yes or No?”

### Key Facts:
- It's a **supervised learning** algorithm.
- Despite the name, it’s used for **classification**, not regression.
- It outputs a **probability** between 0 and 1 using the **sigmoid function**.
""")

# Use Cases
st.header("🎯 Real-World Use Cases")
st.markdown("""
- 📧 **Spam Detection**: Is this email spam or not?
- 🏥 **Medical Diagnosis**: Does a patient have diabetes or not?
- 👥 **Customer Churn**: Will a customer leave the company?
- 💳 **Fraud Detection**: Is this transaction fraudulent?
""")

# How it works
st.header("⚙️ How Does Logistic Regression Work?")
st.markdown("Let's break it down step-by-step:")

with st.expander("🔢 Step 1: Make a Linear Equation (just like Linear Regression)"):
    st.latex(r"z = w_0 + w_1x_1 + w_2x_2 + \ldots + w_nx_n")
    st.markdown("""
    - We calculate a **weighted sum** of the input features.
    - It's just a straight line equation where weights decide how important each feature is.
    """)

with st.expander("🧪 Step 2: Pass it into a Sigmoid Function"):
    st.latex(r"\sigma(z) = \frac{1}{1 + e^{-z}}")
    st.markdown("""
    - The sigmoid turns the output into a **probability** between 0 and 1.
    - If the output is close to 1 → Class 1  
      If close to 0 → Class 0
    """)

    st.image("https://upload.wikimedia.org/wikipedia/commons/8/88/Logistic-curve.svg",
             caption="S-Shaped Sigmoid Curve", use_column_width=True)

with st.expander("🧠 Step 3: Make the Final Prediction"):
    st.markdown("""
    - If \\( \sigma(z) > 0.5 \\), we predict **Class 1**  
    - Else, we predict **Class 0**
    """)

# Visualize the Flow
st.header("🔄 Visualization of the Process")
st.markdown("Feature inputs → Weighted sum → Sigmoid function → Probability → Class label")

# Loss Function
st.header("❌ Loss Function - Binary Cross Entropy")
st.markdown("To improve the model, we need to know **how wrong it is**. That’s where the loss function comes in.")
st.latex(r"Loss = - [y \cdot \log(\hat{y}) + (1 - y) \cdot \log(1 - \hat{y})]")
st.markdown("""
- If predicted probability (\\( \hat{y} \\)) is far from actual label (\\( y \\)), the loss is high.
- This helps adjust weights to improve predictions.
""")

# Evaluation Metrics
st.header("📏 Evaluation Metrics Explained Simply")

with st.expander("1️⃣ Accuracy"):
    st.latex(r"Accuracy = \frac{TP + TN}{TP + TN + FP + FN}")
    st.markdown("**How often** did we get it right?")

with st.expander("2️⃣ Precision (When you care about False Positives)"):
    st.latex(r"Precision = \frac{TP}{TP + FP}")
    st.markdown("Out of all predicted **Positives**, how many were **correct**?")

with st.expander("3️⃣ Recall (When you care about False Negatives)"):
    st.latex(r"Recall = \frac{TP}{TP + FN}")
    st.markdown("Out of all actual **Positives**, how many did we catch?")

with st.expander("4️⃣ F1 Score (Balance between Precision and Recall)"):
    st.latex(r"F1 = 2 \cdot \frac{Precision \cdot Recall}{Precision + Recall}")
    st.markdown("It balances both **precision** and **recall**.")

with st.expander("5️⃣ ROC-AUC"):
    st.markdown("""
    - 📈 ROC: Curve that plots **True Positive Rate** vs **False Positive Rate**  
    - 🧠 AUC: Area Under Curve — closer to 1 = better performance
    """)

# Summary
st.header("✅ Quick Summary")
st.markdown("""
- Logistic Regression is great for **binary and multi-class classification**
- Uses **sigmoid function** to map outputs to probability
- Optimizes using **log loss**
- Simple, fast, and interpretable model — best for **linearly separable** data
- Evaluate using metrics like Accuracy, Precision, Recall, F1, and ROC-AUC
""")

st.success("🎉 Great job! You've just mastered the basics of Logistic Regression.")