Lecture Notes

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Lessons on Mathematics for Machine Learning

  1. Introduction: Course Details and Topics
  2. Differential Calculus: Differentiation, product and chain rules, vectors and matrices
  3. Taylor's Expansion: Converge, residue, high-dimensions, Hessian
  4. Vector Spaces:
  5. Inner Product Spaces: Inner products, operators
  6. Understand Mappings: Mappings, Linear Maps, Solving Linear Systems
  7. Eigensystems:
  8. Principal Component Analysis (PCA): Covariance matrices, dimensionality reduction, PCA, Duality
  9. Singular Value Decomposition (SVD): Singular Valued Decomposition, SVD, general linear maps
  10. Optimisation: Gradient descent, quadratic minima, differing length scales
  11. Stochastic Gradient Descent: SGD, momentum, step size, ADAM
  12. Constrained Optimisation:
  13. Convexity: Convex sets, convex functions, Jensen's inequality
  14. Support Vector Machines: Support Vector Machines, maximum margins
  15. Kernel Trick: The Kernel Trick, SVMs, Regression
  16. Wasserstein GANs: GANs, Wasserstein distance, Duality, WGANs
  17. Under Construction: Stuff
  18. Under Construction: Stuff
  19. Probability: Probability, Random Variables, Expectations
  20. On Becoming a Scientist: interpeting data, standard errors, confidence tests
  21. Bayesian Inference: Bayes, Conjugate Priors, Uninformative Priors
  22. Integral Calculus: Riemann Integration, integration by parts, gaussian integrals
  23. Gaussian Processes: Gaussian Processes, regression
  24. Probabilistic Inference: Hierarchical Models, Mixture of Gaussians, Expectation Maximisation
  25. MCMC: Monte Carlo methods, MCMC, Variational Methods
  26. Entropy: Entropy, Coding, Maximum Entropy
  27. Information Theory: Information, KL-divergence, Minimum Description Length
  28. When Machine Learning Works: When ML Works, Bias Variance
  29. Over-Fitting: Overfitting, regularisation, feature selection
  30. Symmetry: Inductive Bias, Symmetry, Invariance, Group theory