Study Notes in Machine Learning

Contents:

• 1. Preliminaries
  • 1.1. Overview of Probability Measure Theory
    • 1.1.1. Measure, Probability Space, Random Variable, Radon-Nikodym Derivative and Stochastic Process
    • 1.1.2. Marginalization, Conditional Expectation, Conditional Probablity and Bayes’ Rules
  • 1.2. Covariance Matrix
    • 1.2.1. Property 1-4. Classic representation of covariance by expectation (or mean).
    • 1.2.2. Property 1-5. Invariance to centralization.
    • 1.2.3. Theorem 1-5. Matrix arithmetics of covariance matrix.
    • 1.2.4. Theorem 1-6. Positive definiteness of covariance matrix.
    • 1.2.5. Property 1-6. Sample covariance represneted by rank-1 sum.
    • 1.2.6. Theorem 1-7. Block decomposition of covariance matrix.
  • 1.3. Multivariate Gaussian Distribution
    • 1.3.1. Theorem 1-8. Gaussian maximum likelihood estimators.
    • 1.3.2. Theorem 1-9. Bias of Gaussian MLE.
    • 1.3.3. Property 1-7. Shape of contours of Gaussian density.
    • 1.3.4. Theorem 1-10. Conditional density of multivariate Guassian.
• 2. Basic Neural Networks
  • 2.1. Recurrent Networks
    • 2.1.1. Model 3-1. LSTM with Single Forget Gate.
    • 2.1.2. Model 3-2. LSTM with Multiple Forget Gate.
    • 2.1.3. PyTorch implementation of basic LSTM classifier
  • 2.2. Autoencoder Networks

Indices and tables

• Index

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