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Machine Learning Math Foundations (1) — Calculus

Preface: I never thought I'd use college calculus, linear algebra, and probability again—if I had another chance I'd study them to death.

Preface: I never thought I’d use college calculus, linear algebra, and probability again in this life. If heaven gave me another chance, I’d study those three courses to death.

Viewpoint

The core calculus problem for machine learning is extrema. Core skills are partial derivatives and gradients.

Functions

Definition: For set A, apply mapping f, written f(A) → set B; B = f(A). Common functions from school:

image

From Limits to Derivatives

  • Sequence limits Given a sequence (x1 to xn), n → ∞, constant a; for arbitrarily small b, however large n, always xn - a < b, then…

  • Higher-order partial derivatives image

From Directional Derivatives to Gradients

  • Directional derivative image p is distance between two points in 3D. It can be shown: image

  • Gradient image image Postscript: Organized carefully; more to add. You might also like: my pandas, matplotlib, and numpy ML notes.