3. Kernel & Non-Parametric Methods - Advance Machine Learning
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3. Kernel & Non-Parametric Methods

3. Kernel & Non-Parametric Methods

Advanced machine learning methods enable the modeling of complex and non-linear relationships in data. Kernel methods, such as support vector machines, utilize high-dimensional feature spaces through the kernel trick, enhancing flexibility and accuracy. Non-parametric models such as k-Nearest Neighbors, Parzen Windows, and Decision Trees provide adaptability without assuming a fixed form, although they require careful parameter tuning and are sensitive to noise and high-dimensionality.

31 sections

Sections

Navigate through the learning materials and practice exercises.

  1. 3
    Kernel & Non-Parametric Methods

    This section discusses advanced machine learning methods that allow for...

  2. 3.1
    Kernel Methods: Motivation And Basics

    Kernel methods extend linear models to capture non-linear relationships in...

  3. 3.1.1
    Limitations Of Linear Models

    Linear models struggle to capture non-linear relationships in data,...

  4. 3.1.2
    Kernel Trick

    The kernel trick allows for efficient computation of dot products in...

  5. 3.1.3
    Common Kernels

    The section outlines common kernel functions used in machine learning models...

  6. 3.2
    Support Vector Machines (Svm) With Kernels

    This section discusses Support Vector Machines (SVM), focusing on their...

  7. 3.2.1

    This section reviews Support Vector Machines (SVM) and their application of...

  8. 3.2.2
    Svm With Kernels

    Support Vector Machines (SVM) leverage kernel tricks to effectively handle...

  9. 3.2.3
    Soft Margin And C Parameter

    This section discusses the soft margin concept in support vector machines...

  10. 3.2.4
    Advantages And Challenges

    Kernel methods and non-parametric models offer powerful advantages in...

  11. 3.3
    Non-Parametric Methods: Overview

    This section introduces non-parametric methods in machine learning, defining...

  12. 3.3.1
    Parametric Vs Non-Parametric

    This section outlines the fundamental differences between parametric and...

  13. 3.4
    K-Nearest Neighbors (K-Nn)

    k-Nearest Neighbors (k-NN) is a non-parametric method used for...

  14. 3.4.1

    The section introduces the k-Nearest Neighbors (k-NN) algorithm, focusing on...

  15. 3.4.2
    Distance Metrics

    Distance metrics are key mathematical techniques used to quantify the...

  16. 3.4.3
    Pros And Cons

    This section discusses the advantages and disadvantages of the k-Nearest...

  17. 3.5
    Parzen Windows And Kernel Density Estimation (Kde)

    This section discusses Parzen Windows and Kernel Density Estimation (KDE),...

  18. 3.5.1
    Probability Density Estimation

    Probability Density Estimation involves estimating the underlying...

  19. 3.5.2
    Parzen Window Method

    The Parzen Window Method is a non-parametric technique used to estimate the...

  20. 3.5.3
    Choice Of Kernel

    This section discusses the importance of selecting an appropriate kernel in...

  21. 3.5.4
    Curse Of Dimensionality

    The Curse of Dimensionality refers to the challenges faced in...

  22. 3.6
    Decision Trees

    Decision Trees are a powerful non-parametric method for classification and...

  23. 3.6.1
    Structure And Splitting

    This section discusses the tree-like structure of decision trees and the...

  24. 3.6.2
    Impurity Measures

    This section introduces the concepts of Gini Index and Entropy as measures...

  25. 3.6.3
    Pruning And Overfitting

    Pruning is an essential technique used in decision tree models to prevent...

  26. 3.6.4

    This section highlights the key advantages of decision trees as a machine...

  27. 3.7
    Model Selection And Hyperparameter Tuning

    This section covers the essential techniques for model selection and...

  28. 3.7.1
    Cross-Validation

    Cross-validation is a technique to assess the effectiveness of a model by...

  29. 3.7.2
    Grid Search & Random Search

    Grid Search and Random Search are techniques for hyperparameter tuning in...

  30. 3.7.3
    Bias-Variance Trade-Off

    The Bias-Variance Trade-Off discusses the balance necessary between bias and...

  31. 3.8
    Real-World Applications

    This section outlines the practical applications of kernel methods and...

What we have learnt

  • Not all patterns can be captured using simple linear models, necessitating advanced methods.
  • Kernel methods allow for efficient computation in high-dimensional spaces while maintaining flexibility.
  • Non-parametric methods grow with data and avoid fixed parameter assumptions, making them powerful for various applications.

Key Concepts

-- Kernel Trick
A technique that allows for implicit mapping of input features to high-dimensional spaces to facilitate linear separation.
-- Support Vector Machine (SVM)
A supervised learning algorithm that finds the hyperplane that maximizes the margin between classes.
-- kNearest Neighbors (kNN)
A non-parametric method that classifies a data point based on the majority label of its k nearest neighbors.
-- Decision Trees
A model that makes decisions based on feature-based splits to reduce impurity and improve classification.

Additional Learning Materials

Supplementary resources to enhance your learning experience.