Course

Machine Learning

Stanford University

This course provides a comprehensive introduction to machine learning and statistical pattern recognition. Students will explore:

  • Supervised Learning:
    • Generative/Discriminative Learning
    • Parametric/Non-parametric Learning
    • Neural Networks
    • Support Vector Machines
  • Unsupervised Learning:
    • Clustering
    • Dimensionality Reduction
    • Kernel Methods
  • Learning Theory:
    • Bias/Variance Tradeoffs
    • VC Theory
    • Large Margins
  • Reinforcement Learning and Adaptive Control

The course will also cover recent applications of machine learning, including:

  • Robotic Control
  • Data Mining
  • Autonomous Navigation
  • Bioinformatics
  • Speech Recognition
  • Text and Web Data Processing

Prerequisites include a foundational knowledge of computer science, basic probability theory, and linear algebra.

Course Lectures
  • This module introduces the motivation behind machine learning and its various applications across industries. Students will learn about the class logistics and the fundamental definitions of machine learning.

    It provides an overview of:

    • Supervised Learning
    • Learning Theory
    • Unsupervised Learning
    • Reinforcement Learning
  • This module focuses on the application of supervised learning in the context of autonomous driving. Key topics include:

    • ALVINN
    • Linear Regression
    • Gradient Descent Techniques
    • Matrix Derivative Notation
    • Derivation of Normal Equations

    Students will gain hands-on experience with these concepts, applying them to real-world scenarios.

  • This module delves into the concepts of underfitting and overfitting, critical aspects of model performance in machine learning. Topics include:

    • Parametric and Non-parametric Algorithms
    • Locally Weighted Regression
    • Probabilistic Interpretation of Linear Regression
    • Logistic Regression and Perceptron

    Students will learn to identify and address these issues to improve model accuracy.

  • Newton's Method
    Andrew Ng

    This module introduces Newton's Method, a powerful optimization algorithm used in machine learning. Students will explore:

    • Exponential Family Distributions
    • Bernoulli and Gaussian Examples
    • General Linear Models (GLMs)
    • Softmax Regression

    Practical examples will illustrate how these concepts are applied in various machine learning scenarios.

  • This module covers discriminative algorithms, contrasting them with generative algorithms. Key topics include:

    • Gaussian Discriminant Analysis (GDA)
    • Relationship between GDA and Logistic Regression
    • Naive Bayes Classifiers
    • Laplace Smoothing Technique

    Students will understand how to implement these algorithms in various contexts.

  • This module explores the Multinomial Event Model, focusing on non-linear classifiers and neural networks. Topics covered include:

    • Intuitive Understanding of Support Vector Machines (SVM)
    • Notation for SVM
    • Functional and Geometric Margins

    Students will learn how these concepts apply to real-world data problems.

  • This module focuses on the Optimal Margin Classifier, introducing students to advanced concepts such as:

    • Lagrange Duality
    • Karush-Kuhn-Tucker (KKT) Conditions
    • SVM Dual
    • The Concept of Kernels

    Practical exercises will help students understand these advanced theoretical concepts.

  • Kernels
    Andrew Ng

    In this module, students will gain insights into Kernels and their role in creating non-linear decision boundaries. Key topics include:

    • Mercer's Theorem
    • Soft Margin SVM
    • Coordinate Ascent Algorithm
    • Sequential Minimization Optimization (SMO) Algorithm
    • Applications of SVM

    This module combines theory with practical applications to show how kernels enhance SVMs.

  • This module addresses the Bias/Variance Tradeoff, which is essential for understanding model performance. Key topics include:

    • Empirical Risk Minimization (ERM)
    • The Union Bound
    • Hoeffding Inequality
    • Uniform Convergence - Finite Hypothesis Class
    • Sample Complexity Bound and Error Bound

    In-depth discussions will help students grasp the implications of bias and variance in model development.

  • This module extends the discussion of Uniform Convergence to cases with infinite hypothesis classes. Topics covered include:

    • The Concept of "Shatter" and VC Dimension
    • SVM Examples
    • Model Selection
    • Cross Validation and Feature Selection

    Students will learn how these concepts relate to creating robust machine learning models.

  • This module discusses Bayesian Statistics and Regularization techniques in the context of machine learning. Key topics include:

    • Online Learning Techniques
    • Advice for Applying Machine Learning Algorithms
    • Debugging and Fixing Learning Algorithms
    • Diagnostics for Bias & Variance
    • Error Analysis and Getting Started on Learning Problems

    Students will gain practical insights into how to apply Bayesian methods effectively.

  • This module introduces the concept of Unsupervised Learning, covering key techniques like:

    • K-means Clustering Algorithm
    • Mixtures of Gaussians and the EM Algorithm
    • Jensen's Inequality
    • The EM Algorithm

    Students will engage in practical exercises to understand how these techniques are applied in real-world data analysis.

  • This module focuses on the Mixture of Gaussian models and their applications, including:

    • Mixture of Naive Bayes for Text Clustering
    • Factor Analysis
    • Restrictions on a Covariance Matrix
    • EM for Factor Analysis

    Students will learn how to implement and interpret these models in various contexts.

  • This module discusses the Factor Analysis Model and techniques for dimensionality reduction. Key topics include:

    • EM for Factor Analysis
    • Principal Component Analysis (PCA)
    • PCA as a Dimensionality Reduction Algorithm
    • Applications of PCA, including Face Recognition

    Engagement in practical applications will illustrate the importance of PCA in data analysis.

  • This module covers Latent Semantic Indexing (LSI) and its mathematical foundations. Topics include:

    • Singular Value Decomposition (SVD) Implementation
    • Independent Component Analysis (ICA)
    • The Application of ICA
    • Cumulative Distribution Function (CDF) and the ICA Algorithm

    Students will learn about LSI's role in information retrieval and text analysis.

  • This module explores the Applications of Reinforcement Learning, focusing on key concepts such as:

    • Markov Decision Process (MDP)
    • Defining Value & Policy Functions
    • Optimal Value Function
    • Value Iteration and Policy Iteration

    Students will learn how reinforcement learning can be applied to complex decision-making scenarios.

  • This module addresses the Generalization to Continuous States, crucial for developing robust reinforcement learning algorithms. Topics include:

    • Discretization and the Curse of Dimensionality
    • Models and Simulators
    • Fitted Value Iteration
    • Finding Optimal Policy

    Students will engage in exercises to apply these concepts in developing effective models.

  • This module covers State-action Rewards in reinforcement learning and introduces concepts such as:

    • Finite Horizon MDPs
    • Dynamical Systems
    • Examples of Dynamical Models
    • Linear Quadratic Regulation (LQR)
    • Computing Rewards and Riccati Equation

    Students will learn how to apply these concepts to real-world decision-making scenarios.

  • This module offers practical advice for applying machine learning effectively, focusing on:

    • Debugging Reinforcement Learning Algorithms
    • Linear Quadratic Regularization (LQR)
    • Differential Dynamic Programming (DDP)
    • Kalman Filter & Linear Quadratic Gaussian (LQG)
    • Predict/Update Steps of Kalman Filter

    Students will engage in practical exercises to reinforce learning and application.

  • This module introduces Partially Observable MDPs (POMDPs) and discusses their significance, covering:

    • Policy Search Techniques
    • Reinforce Algorithm
    • Pegasus Algorithm
    • Applications of Reinforcement Learning

    Students will learn about the challenges and strategies associated with POMDPs in complex environments.