Machine Learning

Course Description

This course provides a broad introduction to machine learning and statistical pattern recognition.

Topics include: 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 discuss recent applications of machine learning, such as robotic control, data mining, autonomous navigation, bioinformatics, speech recognition, and text and web data processing.

Prerequisites: Knowledge of basic computer science principles and skills, at a level sufficient to write a reasonably non-trivial computer program; familiarity with basic probability theory; familiarity with basic linear algebra.

Lectures

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   Lecture 1 - The Motivation & Applications of Machine Learning

   The Motivation & Applications of Machine Learning, The Logistics of the Class, The Definition of Machine Learning, The Overview of Supervised Learning, The Overview of Learning Theory, The Overview of Unsupervised Learning, The Overview of Reinforcement Learning
   

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   Lecture 2 - An Application of Supervised Learning - Autonomous Deriving

   An Application of Supervised Learning - Autonomous Deriving, ALVINN, Linear Regression, Gradient Descent, Batch Gradient Descent, Stochastic Gradient Descent (Incremental Descent), Matrix Derivative Notation for Deriving Normal Equations, Derivation of Normal Equations
   

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   Lecture 3 - The Concept of Underfitting and Overfitting

   The Concept of Underfitting and Overfitting, The Concept of Parametric Algorithms and Non-parametric Algorithms, Locally Weighted Regression, The Probabilistic Interpretation of Linear Regression, The motivation of Logistic Regression, Logistic Regression, Perceptron
   

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   Lecture 4 - Newton's Method

   Newton's Method, Exponential Family, Bernoulli Example, Gaussian Example, General Linear Models (GLMs), Multinomial Example, Softmax Regression
   

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   Lecture 5 - Discriminative Algorithms

   Discriminative Algorithms, Generative Algorithms, Gaussian Discriminant Analysis (GDA), GDA and Logistic Regression, Naive Bayes, Laplace Smoothing

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   Lecture 6 - Multinomial Event Model

   Multinomial Event Model, Non-linear Classifiers, Neural Network, Applications of Neural Network, Intuitions about Support Vector Machine (SVM), Notation for SVM, Functional and Geometric Margins
   

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   Lecture 7 - Optimal Margin Classifier

   Optimal Margin Classifier, Lagrange Duality, Karush-Kuhn-Tucker (KKT) Conditions, SVM Dual, The Concept of Kernels
   

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   Lecture 8 - Kernels

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

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   Lecture 9 - Bias/variance Tradeoff

   Bias/variance Tradeoff, Empirical Risk Minimization (ERM), The Union Bound, Hoeffding Inequality, Uniform Convergence - The Case of Finite H, Sample Complexity Bound, Error Bound, Uniform Convergence Theorem & Corollary
   

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    Lecture 10 - Uniform Convergence - The Case of Infinite H

    Uniform Convergence - The Case of Infinite H, The Concept of 'Shatter' and VC Dimension, SVM Example, Model Selection, Cross Validation, Feature Selection
    

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    Lecture 11 - Bayesian Statistics and Regularization

    Bayesian Statistics and Regularization, Online Learning, Advice for Applying Machine Learning Algorithms, Debugging/fixing Learning Algorithms, Diagnostics for Bias & Variance, Optimization Algorithm Diagnostics, Diagnostic Example - Autonomous Helicopter, Error Analysis, Getting Started on a Learning Problem
    

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    Lecture 12 - The Concept of Unsupervised Learning

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

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    Lecture 13 - Mixture of Gaussian

    Mixture of Gaussian, Mixture of Naive Bayes - Text clustering (EM Application), Factor Analysis, Restrictions on a Covariance Matrix, The Factor Analysis Model, EM for Factor Analysis
    

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    Lecture 14 - The Factor Analysis Model

    The Factor Analysis Model,0 EM for Factor Analysis, Principal Component Analysis (PCA), PCA as a Dimensionality Reduction Algorithm, Applications of PCA, Face Recognition by Using PCA
    

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    Lecture 15 - Latent Semantic Indexing (LSI)

    Latent Semantic Indexing (LSI), Singular Value Decomposition (SVD) Implementation, Independent Component Analysis (ICA), The Application of ICA, Cumulative Distribution Function (CDF), ICA Algorithm, The Applications of ICA
    

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    Lecture 16 - Applications of Reinforcement Learning

    Applications of Reinforcement Learning, Markov Decision Process (MDP), Defining Value & Policy Functions, Value Function, Optimal Value Function, Value Iteration, Policy Iteration
    

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    Lecture 17 - Generalization to Continuous States

    Generalization to Continuous States, Discretization & Curse of Dimensionality, Models/Simulators, Fitted Value Iteration, Finding Optimal Policy
    

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    Lecture 18 - State-action Rewards

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

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    Lecture 19 - Advice for Applying Machine Learning

    Advice for Applying Machine Learning, Debugging Reinforcement Learning (RL) Algorithm, Linear Quadratic Regularization (LQR), Differential Dynamic Programming (DDP), Kalman Filter & Linear Quadratic Gaussian (LQG), Predict/update Steps of Kalman Filter, Linear Quadratic Gaussian (LQG)
    

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    Lecture 20 - Partially Observable MDPs (POMDPs)

    Partially Observable MDPs (POMDPs), Policy Search, Reinforce Algorithm, Pegasus Algorithm, Pegasus Policy Search, Applications of Reinforcement Learning