The SVM Dual and the Kernel Trick: The Math Explained Step by Step

How can a machine learning model work in infinite dimensions without ever computing a single coordinate? The answer is the SVM dual and the kernel trick. 📖 Read this lesson as an article, chapter by chapter: https://easy-explain-app.vercel.app/lesson... 📱 Free Android app: https://easy-explain-app.vercel.app/downlo... In this lesson we start from the hard-margin primal, build the Lagrangian, derive w as a sum of alpha times y times x, and obtain the dual that depends only on inner products. We solve a tiny example by hand, explain support vectors through complementary slackness, add the soft margin with the box constraint on alpha, and show it equals hinge loss. Then we prove a polynomial kernel equals an explicit feature map, see why the RBF kernel is infinite dimensional, touch on Mercer's condition, cover support vector regression, and check everything against scikit-learn's SVC. This is lesson 43 of Machine Learning from Zero to Advanced. It builds on lesson 37 (Lagrange multipliers and KKT) and lesson 21 (SVM geometry). Next up: Expectation-Maximization for Gaussian mixtures. 0:00 Intro 0:42 Primal and Lagrangian 2:41 The Dual 3:53 Worked Example 6:39 Soft Margin and Hinge 8:57 Kernel Trick 11:07 RBF and Mercer 13:02 Regression and Python 14:46 Recap #MachineLearning #SVM #KernelTrick #Optimization #DataScience