Lesson 3.8: Comparing Models
You have built a powerful toolkit of linear and non-linear classifiers. This final lesson of Module 3 is a practical guide to model selection. We will compare Logistic Regression, Decision Trees, and SVMs across several key dimensions, creating a mental 'cheat sheet' to help you choose the right tool for the job.
Part 1: The Core Tradeoffs
There is no single "best" model for all problems. The choice of algorithm is always a series of tradeoffs. The three most important tradeoffs for a practitioner are:
- Performance vs. Interpretability: A simple, understandable model vs. a complex, "black box" model that may be more accurate.
- Bias vs. Variance: A model with strong assumptions (high bias) vs. a highly flexible model that might overfit (high variance).
- Speed vs. Scalability: How quickly can the model be trained, and how well does it handle very large datasets?
Part 2: The Model 'Cheat Sheet'
| Criterion | Logistic Regression | Decision Tree | SVM (with Kernel) |
|---|---|---|---|
| Interpretability | Excellent | Very Good | Poor |
| Performance (Non-Linear) | Poor | Good | Excellent |
| Bias-Variance | High Bias, Low Variance | Low Bias, High Variance | Flexible (via `C`) |
| Feature Scaling | Required | Not Required | Required |
| Training Speed | Fast | Fast | Slow (on large N) |
Part 3: Deep Dive into the Tradeoffs
Logistic Regression is King: In regulated industries like banking (credit scoring) or insurance, you must be able to explain *why* your model made a decision. The coefficients of a logistic regression provide this directly (e.g., "the odds of default increase by 1.2x for every $10k in loan amount").
Decision Trees are a close second: The flowchart of rules is highly transparent and easy to explain to a non-technical audience.
SVMs are Black Boxes: The decision boundary created by a kernel SVM in a high-dimensional feature space is virtually impossible for a human to interpret. You know *what* it decided, but not *why*.
SVMs excel: The RBF kernel allows SVMs to create incredibly complex and smooth decision boundaries, often leading to the best raw performance on complex classification tasks.
Decision Trees are good, but "blocky": They can approximate any shape, but their axis-aligned splits create a "staircase" boundary which can be inefficient.
Logistic Regression fails: Without manual feature engineering (like polynomial features), it can only produce a straight line.
SVMs suffer on large N: The core SVM algorithm involves calculations on pairs of data points, making its complexity somewhere between and . This becomes prohibitively slow for datasets with hundreds of thousands of samples.
Trees and Linear models are fast: They scale much more favorably, closer to , making them suitable for very large datasets.
- Is interpretability a MUST? (e.g., for regulatory reasons)
- Yes: Start with **Logistic Regression**. It's your best-in-class, interpretable baseline.
- Is the relationship likely to be highly non-linear and complex?
- Yes: Try a **Kernel SVM** or a **Decision Tree**.
- Is your dataset very large (N > 100,000)?
- Yes: An SVM might be too slow. A **Decision Tree** (or better yet, a Random Forest) is a better choice.
- Your Default Starting Point: Always start with the simplest model first. **Logistic Regression** is a fantastic baseline. Any more complex model must prove that it provides a significant performance uplift to justify its loss of interpretability and increased complexity.
What's Next? The Power of the Crowd
Congratulations! You have completed Module 3. You have mastered not just linear models, but a whole suite of powerful non-linear classifiers.
However, we noted that the Decision Tree's greatest weakness is its high variance and tendency to overfit. This makes it a poor predictive model on its own.
In **Module 4: The Power of the Crowd: Ensemble Methods**, we will learn how to turn this weakness into a strength. We will see that by combining hundreds of these "weak," unstable decision trees, we can create an incredibly powerful, stable, and accurate predictive machine. This is the principle behind **Random Forest** and **Gradient Boosting**, the two most dominant algorithms in all of modern machine learning for tabular data.