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Machine Learning Fundamentals and Advanced Topics

This course provides a comprehensive introduction to machine learning for graduate students, covering foundational theory, algorithms, additional learning models, and advanced theoretical topics over 14 weeks.

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Syllabus

39 chapters, 129 modules, 308 lessons and quizzes.

  1. 01Getting Started1 modules · 2 lessons

    Getting Started

  2. 02Graduate Course Overview and Notation2 modules · 5 lessons

    Course Structure for Graduate Students

    Notation Conventions

  3. 03Introduction to Machine Learning Theory1 modules · 1 lessons

    Foundations of Machine Learning

  4. 04Statistical Learning Framework Fundamentals3 modules · 6 lessons

    Components of the Statistical Learning Framework

    Prediction Rule and Error of a Classifier

    Data Generation Model

  5. 05Empirical Risk Minimization and Overfitting2 modules · 4 lessons

    Empirical Risk Minimization

    Overfitting in Empirical Risk Minimization

  6. 06Empirical Risk Minimization with Inductive Bias2 modules · 5 lessons

    Introduction to Empirical Risk Minimization with Inductive Bias

    Finite Hypothesis Classes

  7. 07Understanding Halfspaces in Binary Classification4 modules · 6 lessons

    Introduction to Halfspaces

    Implementing ERM for Halfspaces

    Perceptron Algorithm for Halfspaces

    VC Dimension of Halfspaces

  8. 08Advanced Topics in Machine Learning1 modules · 1 lessons

    Introduction to Advanced Machine Learning Topics

  9. 09Advanced Topics in Machine Learning1 modules · 1 lessons

    Introduction to Advanced Machine Learning Topics

  10. 10Foundations of Machine Learning1 modules · 1 lessons

    Introduction to Part II

  11. 11Linear Regression for Modeling Relationships3 modules · 7 lessons

    Introduction to Linear Regression

    Least Squares Algorithm

    Linear Regression for Polynomial Regression Tasks

  12. 12Mastering Feature Representation for Machine Learning3 modules · 10 lessons

    Feature Manipulation and Normalization

    Feature Learning

    Feature Selection Techniques

  13. 13Computational Complexity of Learning Algorithms3 modules · 8 lessons

    Formal Definition of Computational Complexity

    Implementing the ERM Rule

    Efficient Learnability and Hardness of Learning

  14. 14Covering and Rademacher Complexity4 modules · 6 lessons

    Covering Numbers and Properties

    Rademacher Complexity via Chaining

    Agnostic PAC Learnability

    Realizable PAC Learnability and ϵ-Nets

  15. 15Understanding VC-Dimension in Machine Learning4 modules · 9 lessons

    Introduction to VC-Dimension

    Examples of VC-Dimension

    The Fundamental Theorem of PAC Learning

    Proof of the Fundamental Theorem

  16. 16Multiclass Learnability and the Natarajan Dimension5 modules · 10 lessons

    Introduction to Multiclass Learnability

    The Natarajan Dimension

    The Multiclass Fundamental Theorem

    Calculating the Natarajan Dimension

    On Good and Bad ERMs

  17. 17Understanding Compression Bounds in Machine Learning3 modules · 10 lessons

    Introduction to Compression Bounds

    Examples of Compression Schemes

    Theoretical Implications

  18. 18Nonuniform Learnability: Sample Size Flexibility2 modules · 5 lessons

    Introduction to Nonuniform Learnability

    Relation to Agnostic PAC Learnability

  19. 19Clustering Techniques and Dimensionality Reduction5 modules · 15 lessons

    Introduction to Clustering

    Clustering Algorithms

    Dimensionality Reduction

    Theoretical Foundations

    Advanced Topics

  20. 20Nonuniform Learnability and Structural Risk Minimization5 modules · 11 lessons

    Characterizing Nonuniform Learnability

    Structural Risk Minimization (SRM)

    Minimum Description Length and Occam's Razor

    Other Notions of Learnability

    Discussing Different Notions of Learnability

  21. 21Generalizing the Learning Model4 modules · 11 lessons

    Relaxing the Realizability Assumption

    Generalizing to Various Learning Tasks

    Uniform Convergence and Learnability

    Finite Classes Are Agnostic PAC Learnable

  22. 22Model Selection and Validation4 modules · 15 lessons

    Model Selection Using SRM

    Validation Techniques

    Remedies for Bad Performance

    Convex Learning Problems

  23. 23Convex Learning Problems and Regularization5 modules · 12 lessons

    Convex Learning Problems

    Learnability of Convex Learning Problems

    Surrogate Loss Functions

    Regularized Loss Minimization

    Stability and Learnability

  24. 24Model Selection and Validation Techniques3 modules · 6 lessons

    Introduction to Model Selection

    Approaches to Model Selection

    Model Selection and Error Types

  25. 25Gradient Descent and Stochastic Gradient Descent6 modules · 13 lessons

    Gradient Descent Algorithm

    Analysis of Gradient Descent

    Subgradients and Subgradient Descent

    Stochastic Gradient Descent

    Variants of Stochastic Gradient Descent

    SGD for Learning Tasks

  26. 26k Nearest Neighbors Algorithm3 modules · 7 lessons

    Introduction to k-NN Rule

    Analysis of 1-NN Rule

    Efficient Implementation of NN Rule

  27. 27Understanding the Bias-Complexity Tradeoff in Machine Learning3 modules · 6 lessons

    The No-Free-Lunch Theorem and Prior Knowledge

    Error Decomposition and the Bias-Complexity Tradeoff

    Learnability of Infinite-size Hypothesis Classes

  28. 28Clustering and Dimensionality Reduction Techniques8 modules · 10 lessons

    Introduction to Clustering

    Linkage-Based Clustering Algorithms

    k-Means and Other Cost Minimization Clusterings

    Spectral Clustering

    Information Bottleneck Method

    Principal Component Analysis (PCA)

    Random Projections and Johnson-Lindenstrauss Lemma

    Compressed Sensing

  29. 29Introduction to Feedforward Neural Networks4 modules · 8 lessons

    Structure of Feedforward Neural Networks

    Learning with Neural Networks

    Expressive Power of Neural Networks

    Sample Complexity of Neural Networks

  30. 30Multiclass Classification and Ranking5 modules · 15 lessons

    Multiclass Classification

    Linear Multiclass Predictors

    Structured Output Prediction and Ranking

    Bipartite Ranking and Multivariate Performance Measures

    Decision Trees

  31. 31Probably Approximately Correct Learning2 modules · 5 lessons

    Introduction to PAC Learning

    Sample Complexity in PAC Learning

  32. 32Support Vector Machines for Large Margin Classification3 modules · 8 lessons

    Margin and Hard-SVM

    Soft-SVM and Regularization

    Kernels for SVM

  33. 33Rademacher Complexity and Generalization Bounds4 modules · 10 lessons

    Introduction to Rademacher Complexity

    Rademacher Complexity of Linear Classes

    Generalization Bounds for Linear Predictors

    Generalization Bounds for Predictors with Low ℓ1 Norm

  34. 34Runtime and Optimization of Neural Networks2 modules · 6 lessons

    Computational Complexity of Training Neural Networks

    SGD and Backpropagation for Neural Networks

  35. 35Logistic Regression for Classification2 modules · 5 lessons

    Introduction to Logistic Regression

    Logistic Loss Function and ERM Problem

  36. 36Boosting: Improving Weak Learners6 modules · 11 lessons

    Introduction to Boosting

    Weak Learnability

    Efficient Implementation of ERM for Decision Stumps

    AdaBoost Algorithm

    Linear Combinations of Base Hypotheses

    AdaBoost for Face Recognition

  37. 37Online Learning Fundamentals6 modules · 19 lessons

    Introduction to Online Learning

    Online Classification in the Realizable Case

    Online Classification in the Unrealizable Case

    Online Convex Optimization

    Additional Topics

    The Online Perceptron Algorithm

  38. 38PAC-Bayes Bounds and Measure Concentration3 modules · 14 lessons

    PAC-Bayes Bounds

    Measure Concentration Inequalities

    Linear Algebra Review

  39. 39Bibliography and References in Machine Learning1 modules · 4 lessons

    Key References in Machine Learning

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Machine Learning Fundamentals and Advanced Topics