18 409 Algorithmic Aspects Of Machine Learning Spring 2015

Modern machine learning models often feel like black boxes, leaving developers to wonder why certain algorithms succeed while others fail. To build truly robust systems, you must understand the mathematical and algorithmic guarantees that underpin these powerful tools. This text-only course guides you through the theoretical foundations of machine learning, transitioning from empirical trial-and-error to rigorous algorithmic analysis. You will discover how to design, evaluate, and prove the correctness of core machine learning algorithms, giving you a deeper appreciation of the mathematics that drive modern AI. What you'll learn: 1. Understand the foundational mathematical concepts, including high-dimensional probability and linear algebra basics. 2. Analyze the theoretical guarantees of classic algorithms for clustering, dimensionality reduction, and regression. 3. Explore modern optimization techniques, including gradient descent variants and their convergence rates. 4. Evaluate learning models through the lens of computational complexity and sample complexity. 5. Practice formulating algorithmic guarantees for fundamental machine learning problems. 6. Examine contemporary topics like algorithmic fairness and robustness in modern model design. The course begins with essential mathematical terminology and foundational definitions before moving into the step-by-step analysis of key algorithms. You will progress from basic optimization principles to advanced theoretical guarantees, learning to think like an algorithmic researcher. This course is designed for aspiring data scientists, programmers, and mathematically curious beginners who want to move beyond library APIs and understand the theoretical 'why' behind machine learning. No advanced background in machine learning theory is required. Start reading today to unlock the mathematical principles that make machine learning algorithms work.