Advance Machine Learning | 1. Learning Theory & Generalization by Abraham | Learn Smarter
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1. Learning Theory & Generalization

The principles of learning theory and generalization form the foundation for machine learning, exploring essential questions about model performance on unseen data. Key elements like statistical learning theory, the bias-variance trade-off, and PAC learning are central to understanding how models can effectively learn from limited data while maintaining generalization. The balance between model complexity and performance is emphasized, with various techniques—such as regularization and cross-validation—serving as practical tools for achieving optimal model evaluation and design.

Sections

  • 1

    Learning Theory & Generalization

    This section discusses core principles of learning theory and generalization in machine learning, emphasizing their importance for model performance.

    Learning Practice

  • 1.1

    What Is Learning Theory?

    Learning theory provides a mathematical framework for understanding machine learning algorithms, answering fundamental questions about model learning and performance.

    Learning Practice

  • 1.2

    Key Components Of A Learning Problem

    This section outlines the formal elements that compose every learning problem in machine learning.

    Learning Practice

  • 1.3

    Generalization And Overfitting

    This section discusses the concepts of generalization and overfitting in machine learning.

    Learning Practice

  • 1.3.1

    Generalization

    Generalization refers to a model's ability to perform well on unseen data, while overfitting occurs when a model is too complex and learns noise from the training data.

    Learning Practice

  • 1.3.2

    Overfitting

    Overfitting occurs when a model learns too much noise and specific patterns from the training data, leading to poor generalization on unseen data.

    Learning Practice

  • 1.3.3

    Underfitting

    Underfitting occurs when a machine learning model is too simplistic to capture the underlying trend of the data, resulting in high training and test error.

    Learning Practice

  • 1.4

    Bias-Variance Trade-Off

    The bias-variance trade-off is a fundamental concept in machine learning that balances the errors caused by bias and variance in a model.

    Learning Practice

  • 1.5

    Probably Approximately Correct (Pac) Learning

    PAC learning provides a formal framework for understanding the learnability of concepts within a model under specific conditions.

    Learning Practice

  • 1.6

    Vc Dimension (Vapnik–chervonenkis Dimension)

    The VC dimension quantifies the capacity of a hypothesis class in terms of its ability to classify different sets of points.

    Learning Practice

  • 1.7

    Rademacher Complexity

    Rademacher complexity measures the richness of a function class based on its ability to fit random noise, impacting model generalization.

    Learning Practice

  • 1.8

    Uniform Convergence And Generalization Bounds

    Uniform convergence ensures that the empirical risk converges uniformly to true risk across a hypothesis class, providing a framework for establishing generalization bounds.

    Learning Practice

  • 1.9

    Structural Risk Minimization (Srm)

    Structural Risk Minimization (SRM) balances model complexity with empirical error to improve generalization in machine learning.

    Learning Practice

  • 1.10

    Regularization And Generalization

    Regularization is a technique that adds a penalty term to the loss function, allowing models to achieve better generalization by controlling their complexity.

    Learning Practice

  • 1.11

    Cross-Validation And Model Selection

    Cross-validation is a resampling method that estimates model performance and prevents overfitting in machine learning.

    Learning Practice

  • 1.12

    Generalization In Deep Learning

    This section discusses how deep learning models exhibit surprising generalization capabilities despite being over-parameterized.

    Learning Practice

References

AML ch1.pdf

Class Notes

Memorization

What we have learnt

  • Learning theory provides a ...
  • Generalization is crucial f...
  • The bias-variance trade-off...

Final Test

Revision Tests