[Math] Mathematical Background Required for Advanced Machine Learning Concepts

data analysismachine learning

What are the must-know concepts and best resources for preparing the mathematical background for advanced machine learning studies?

Currently, looking into the book What is Mathematics? by Richard Courant to strengthen my fundamentals. Are there any better references that can help? And would it be worth spending time on such basic concepts like number system, congruences etc?

Also, looking for more study material that can help me take a step towards a deeper understanding of the subject towards the discipline of data science and machine learning.

Best Answer

It definitely depends on what you want to do, since ML is a relatively large and diverse field now. A quick summary might be something like this:

Basics (i.e. needed for the more advanced ones below)

  • Linear algebra (e.g. matrix operations and decompositions, vector spaces)
  • Multivariate calculus (e.g. gradients and jacobians for optimization)
  • Basic probability and statistics (e.g. basic distributions & estimators)
  • Algorithmic analysis
  • Basic signal processing (e.g. convolutions, Fourier series)

Mathematical Theory (e.g. PAC theory)

  • Analysis & measure theory (e.g. advanced probability)
  • Functional analysis

Probabilistic Modelling (e.g. Bayesian deep learning, generative modelling)

  • Stochastic processes & information theory (e.g. MCMC, variational inference)
  • Advanced statistics (e.g. properties of estimators, convergence of distributions)

Implementation-Oriented ML

  • Optimization (e.g. convex optimization)
  • Numerical analysis (e.g. discretizations)
  • Computational numerics (e.g. error accumulation, matrix algorithms)

(Just to link some relevant questions on how to study basic ML mathematically to this one: [1], [2], [3], [4], [5], [6], [7], [8], [9], [10] )

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