Understanding Logistic Regression from Scratch

 Logistic regression is one of the most popular methods at the intersection of statistics and machine learning.

Despite its name including “regression”, it’s actually a classification model that predicts “0 or 1”. 

With its intuitive probabilistic interpretation and simple implementation, it's widely used in a variety of fields, from business to healthcare and web analytics.

1. What is Logistic Regression?

While general linear regression predicts continuous values, logistic regression outputs the probability of an event occurring.

By classifying instances as class 1 if the resulting probability exceeds a threshold, and class 0 if it falls below, it solves binary classification problems.

Estimation is performed by maximising the log-likelihood function to best explain the correct labels.

Mathematically, it involves finding the gradient and iteratively updating, meaning you can complete learning with just a few lines of code using Python’s `scikit-learn` or `statsmodels`.

2. Where is it Used?

Due to its high interpretability and low implementation cost, logistic regression is often the first choice in many industries and applications.

- Medical Diagnosis: Predicting whether a patient has a disease based on test results and medical history.

- Credit Scoring: Determining creditworthiness based on an applicant’s attributes and credit history.

- Customer Churn Prediction: Estimating the risk of cancellation based on purchase history and usage frequency.

- Marketing: Binary classification of email open rates and advertising click-through rates.

- HR & Recruitment: Evaluating candidate suitability and the risk of early departure based on applicant information.

- Anomaly Detection in Manufacturing: Determining the presence of equipment failure based on sensor data.

By looking at the weights and odds ratios, you can intuitively understand how much each explanatory variable influences the result.

3. Benefits of Learning It?

- It’s easy to explain the impact of variables on the result to business stakeholders using odds ratios and the signs of coefficients.

- It’s a good first step to learning evaluation metrics (ROC curve, AUC, Precision-Recall).

- Compared to decision trees or SVMs, it can provide numerical justification for “why” a prediction was made.

- It provides a foundation for developing to multi-class classification (Softmax regression).

- It can serve as foundational knowledge for hierarchical Bayesian models and generalised linear models.

- You can incorporate probabilistic predictions directly into subsequent decision-making, such as credit ratings and patient risk scoring.

- Understanding maximum likelihood estimation, gradient methods, and regularisation can be applied to deep learning.

- Overfitting can be suppressed by combining regularisation and variable selection.

- It can be implemented with just a few lines of code using standard Python/R libraries, and can handle large datasets using mini-batch learning.

Summary

Logistic regression is not only directly applicable to your work but also an essential stepping stone to more advanced algorithms. 

Let’s start by implementing logistic regression with your own hands and experiencing the fun of probabilistic prediction.

If you want to learn logistic regression, we recommend this book (access here).