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Linear Algebra Basics & Probability Fundamentals for Machine Learning

This background text explores linear algebra concepts such as vectors in Euclidean space and probability fundamentals including Bayes' theorem, independence, mean, variance, and various distributions like Bernoulli, Binomial, and Normal (Gaussian).

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Linear Algebra Basics & Probability Fundamentals for Machine Learning

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  1. Background for Machine Learning (I) UsmanRoshan

  2. Linear algebra • Vector: • ordered collection of numbers • point in some Euclidean space • Examples: • x : (1, 2) • y : (3, 5) • z : (4, 1)

  3. Linear algebra • x : (1, 2), y : (3, 5),z : (4, 1) • y – x = (3-1,5-2)=(2,3) • x – z = (1-4,2-1)=(-3,1)

  4. Linear algebra • x : (1, 2), y : (3, 5),z : (4, 1) • Length of vector in Euclidean space • Length of x =

  5. Linear algebra

  6. Linear algebra θ

  7. Linear algebra θ

  8. Linear algebra

  9. Probability • Read Appendix of textbook Introduction to Machine by EthemAlpaydin • Bayes theorem • Independence • Mean • Variance • Distributions • Bernoulli • Binomial • Normal (Gaussian)

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