Lecture

The Motivation & Applications of Machine Learning

This module introduces the motivation behind machine learning and its applications across diverse fields. It outlines the logistics of the course while defining machine learning concepts.

Key topics include:

  • Motivation & Applications of Machine Learning
  • Logistics of the Class
  • Overview of Supervised Learning
  • Overview of Learning Theory
  • Overview of Unsupervised Learning
  • Overview of Reinforcement Learning

Course Lectures
  • This module introduces the motivation behind machine learning and its applications across diverse fields. It outlines the logistics of the course while defining machine learning concepts.

    Key topics include:

    • Motivation & Applications of Machine Learning
    • Logistics of the Class
    • Overview of Supervised Learning
    • Overview of Learning Theory
    • Overview of Unsupervised Learning
    • Overview of Reinforcement Learning
  • This module focuses on an application of supervised learning, specifically autonomous driving. It discusses ALVINN and various regression techniques, including:

    • Linear Regression
    • Gradient Descent
    • Batch and Stochastic Gradient Descent

    The module also covers matrix derivative notation for deriving normal equations and the derivation of those equations.

  • This module examines underfitting and overfitting concepts, crucial for understanding model performance. It introduces:

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

    These concepts help in selecting and tuning models effectively.

  • Newton's Method
    Andrew Ng

    This module introduces Newton's Method, a powerful optimization technique. It covers:

    • Exponential Family
    • Bernoulli and Gaussian examples
    • General Linear Models (GLMs)
    • Multinomial Example
    • Softmax Regression

    Students learn how these concepts apply to various machine learning problems.

  • This module explores discriminative algorithms in contrast to generative algorithms. It includes:

    • Gaussian Discriminant Analysis (GDA)
    • The relationship between GDA and Logistic Regression
    • Naive Bayes and Laplace Smoothing

    These algorithms are fundamental in classification tasks.

  • This module discusses the Multinomial Event Model, focusing on non-linear classifiers and neural networks. Key points include:

    • Applications of Neural Networks
    • Intuition about Support Vector Machines (SVM)
    • Notation for SVM
    • Functional and Geometric Margins

    The insights gained here form the basis for understanding complex classifiers.

  • This module covers the Optimal Margin Classifier through the lens of SVM. It includes:

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

    Understanding these principles is crucial for developing effective classification models.

  • Kernels
    Andrew Ng

    This module discusses Kernels and their application in machine learning. It includes:

    • Mercer's Theorem
    • Non-linear Decision Boundaries and Soft Margin SVM
    • Coordinate Ascent Algorithm
    • Sequential Minimization Optimization (SMO) Algorithm
    • Applications of SVM

    These concepts enhance understanding of complex decision boundaries in classification.

  • This module focuses on the Bias/Variance Tradeoff, a critical concept in model evaluation. Topics include:

    • Empirical Risk Minimization (ERM)
    • The Union Bound
    • Hoeffding Inequality
    • Uniform Convergence - The Case of Finite Hypothesis Space (H)
    • Sample Complexity Bound
    • Error Bound and Uniform Convergence Theorem

    These concepts are essential for understanding model performance and generalization.

  • This module explores Uniform Convergence in the case of infinite hypothesis spaces. Topics include:

    • The Concept of 'Shatter' and VC Dimension
    • SVM Example
    • Model Selection
    • Cross Validation
    • Feature Selection

    Understanding these concepts aids in effective model selection and evaluation strategies.

  • This module introduces Bayesian Statistics and Regularization. It covers:

    • Online Learning
    • Advice for Applying Machine Learning Algorithms
    • Debugging Learning Algorithms
    • Diagnostics for Bias & Variance
    • Optimization Algorithm Diagnostics
    • Error Analysis
    • Getting Started on a Learning Problem

    These insights help in effectively applying machine learning techniques in practice.

  • This module delves into the concept of Unsupervised Learning. It covers key algorithms such as:

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

    Understanding these algorithms is essential for exploratory data analysis and pattern recognition.

  • This module focuses on Mixtures of Gaussian and their applications. Key topics include:

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

    These concepts are vital for understanding probabilistic models and their applications in different domains.

  • This module introduces the Factor Analysis Model and its applications in dimensionality reduction. Topics include:

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

    These techniques are essential for feature extraction and reducing data complexity.

  • This module covers Latent Semantic Indexing (LSI) and its applications in information retrieval. Key topics include:

    • Singular Value Decomposition (SVD) Implementation
    • Independent Component Analysis (ICA)
    • Applications of ICA
    • Cumulative Distribution Function (CDF)
    • ICA Algorithm

    Understanding LSI and ICA is crucial for advanced data analysis and natural language processing tasks.

  • This module explores various applications of Reinforcement Learning. It includes:

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

    These concepts are essential for understanding decision-making processes in uncertain environments.

  • This module addresses the generalization of reinforcement learning to continuous states. It covers:

    • Discretization & Curse of Dimensionality
    • Models/Simulators
    • Fitted Value Iteration
    • Finding Optimal Policy

    Understanding these concepts is critical for applying reinforcement learning in real-world scenarios.

  • This module discusses the concept of State-action Rewards in reinforcement learning. Key topics include:

    • Finite Horizon MDPs
    • The Concept of Dynamical Systems
    • Examples of Dynamical Models
    • Linear Quadratic Regulation (LQR)
    • Linearizing a Non-Linear Model
    • Computing Rewards and the Riccati Equation

    These concepts are fundamental to modeling and solving dynamic decision-making problems.

  • This module provides practical advice for applying machine learning techniques. It includes:

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

    These insights help practitioners effectively apply RL algorithms in various applications.

  • This module introduces Partially Observable Markov Decision Processes (POMDPs) and their applications. Key topics include:

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

    Understanding POMDPs is essential for decision-making in environments with incomplete information.