Lecture

Mixture of Gaussian

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.


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.