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Topics

Foundations

• Probability Space, Random Variables, Expectation, Variance

Distributions

• Gaussian Distribution, Bernoulli, Binomial, Poisson, Exponential Family

Estimation

• MLE (Maximum Likelihood Estimation), MAP, Bayes’ Rule

Distance and Inference

• Mahalanobis Distance, Confidence Interval, Bias-Variance Tradeoff

Study Resources & Scope used to study

[1] Mathematics for Machine Learning - Deisenroth, Faisal, and Ong

• Probability and Distribution
  • 6.1 Construction of Probability Space
  • 6.2 Discrete/Continuous Probabilities
  • 6.6 Conjugacy and the Exponential Family

[2] Deep Learning - Goodfellow, Bengio, and Courville

• Probability and Information Theory
  • 3.9 Common Probability Distributions
  • 3.10 Useful Properties of Common Functions
  • 3.11 Bayes’ Rule
  • 3.12 Technical Details of Continuous Variables

[3] Pattern Recognition and Machine Learning - Bishop

• Probability and Estimation
  • Chapters 1–2: Probability Distributions, Bayesian Inference, MLE, MAP
  • Chapter 8: Mahalanobis Distance, Confidence Intervals

[4] Python Code

• Implementations for Gaussian sampling, MLE, and bias-variance tradeoff analysis.