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Table of Contents
Contents ii
1 Introduction
2 Overview of Probability
I Statistical Learning Theory
3 Binary Classification
4 Finite Hypothesis Sets
5 Probably Approximately Correct
6 Learning Shapes
7 Rademacher Complexity
8 VC Theory
9 The VC Inequality
10 General Loss Functions
11 Covering Numbers
12 Model Selection
II Optimization
13 Optimization
14 Convexity
15 Lagrangian Duality
16 KKT Conditions
17 Support Vector Machines I
18 Support Vector Machines II
19 Iterative Algorithms
20 Convergence
21 Gradient Descent
22 Extensions of Gradient Descent
23 Stochastic Gradient Descent
III Deep Learning
24 Neural Networks
25 Universal Approximation
26 Convolutional Neural Networks
27 Robustness
28 Generative Adversarial Nets
Bibliography
Summary
Learning is the process of transforming information and experience into knowledge and understanding. Machine Learning is the study of algorithms and models for computer systems to carry out certain tasks independently, based on the results of a learning process. Machine learning lies at the intersection of approximation theory, probability theory, statistics, and optimization theory. The goal of machine learning is to come up with a function h:X!Y, where X is a space of inputs or features, and Y consists of outputs or responses. The course mainly deals with supervised learning, where we have a collection of input-output data pairs and the goal is to learn a function from this data. Approximation theory, optimization, and statistics play crucial roles in machine learning tasks. Neural networks, optimization algorithms like gradient descent, and the importance of generalization in learning are discussed in detail.