Probabilistic Machine Learning Notes
These notes are based on "Probabilistic Machine Learning" by Kevin Murphy — a comprehensive modern treatment of machine learning from a probabilistic perspective. This guide makes these concepts accessible to undergraduates while maintaining the depth needed for practical understanding.
What is Probabilistic Machine Learning?
Probabilistic ML treats machine learning as a problem of inference under uncertainty. Instead of just making predictions, we quantify how confident we are in those predictions. This is crucial for real-world applications where decisions have consequences.
Key idea: Everything is uncertain — our data is noisy, our models are approximations, and we never have enough data. Probability theory gives us a principled framework to reason about this uncertainty.
Why the Probabilistic Perspective?
- Quantified Uncertainty: Know when to trust your model's predictions
- Principled Learning: Derive optimal learning algorithms from first principles
- Regularization: Prevent overfitting through priors and Bayesian inference
- Model Comparison: Compare different models in a principled way
- Decision Making: Make optimal decisions under uncertainty
Topics Covered
| Topic | What You'll Learn |
|---|---|
| Probability | Foundation of uncertainty quantification |
| Statistics | Inference, estimation, and hypothesis testing |
| Decision Theory | Making optimal choices under uncertainty |
| Information Theory | Measuring information and uncertainty |
| Optimization | Finding the best model parameters |
| Discriminant Analysis | Generative vs. discriminative models |
| Linear & Logistic Regression | Foundational supervised learning |
| Neural Networks | Deep learning architectures (FFN, CNN, RNN) |
| Trees & Ensembles | Decision trees, random forests, boosting |
| Exemplar Methods | KNN, metric learning |
| Self-Supervised Learning | Learning from unlabeled data |
| Recommendation Systems | Collaborative filtering and matrix factorization |
Prerequisites
To get the most from these notes:
- Calculus: Derivatives, gradients, chain rule
- Linear Algebra: Matrices, eigenvalues, matrix decompositions
- Basic Probability: Random variables, expectations, common distributions
- Programming: Python with NumPy, familiarity with ML libraries helpful
How to Use These Notes
- Start with foundations: Probability and statistics chapters build the foundation
- Understand the "why": Focus on intuition before equations
- Connect concepts: Many ideas recur across chapters (e.g., MLE, regularization)
- Practice: Implement algorithms to solidify understanding
Let's dive in!