Foundations for Machine Learning

Currently Playing: Integral calculus for Machine Learning | Mathematical foundations for ML [Lecture 19]

Why should machine learning practitioners care about integrals? When people think of machine learning, they often focus on algorithms and data, but the mathematical backbone is often overlooked. Integral calculus, in particular, plays a vital role in understanding key concepts like optimization and accumulation of change. In the latest lecture of the Foundations for Machine Learning series, I discuss: 1) The Basics of Integration: Definite and indefinite integrals, with clear explanations and examples. 3) The Fundamental Theorem of Calculus: How integration and differentiation are reverse processes—and why this matters for optimization in ML. 3) Visual Intuition: Integration as the accumulation of change—think of it as summing infinitesimal areas under a curve. Applications in Machine Learning: -Optimization: Techniques like gradient descent use integrals to minimize loss functions. -Probability Distributions: Calculating areas under probability density functions (PDFs) is nothing but integration. -Continuous Change: In generative AI, integral concepts are often used to approximate functions and model continuous variations in data. I also simplify Riemann sums to show how they approximate integrals by summing areas of rectangles. Shrink the rectangles infinitely, and you get the exact area under the curve—just like how differentiation finds the instantaneous rate of change. Whether you are learning ML for the first time or brushing up on concepts, having a solid grasp of integrals is essential. It allows you to visualize how changes accumulate over a range—exactly what happens in most ML models. This lecture is designed to build intuition, not complexity. Link to the lecture: https://youtu.be/fsNSz0c_BMM