Calculus for Machine Learning and Data Science - Week 2

Gradients

Introduction to Tangent planes

Partial derivatives - Part 1

• di f over di x

Partial derivatives - Part 2

Gradients

• Knowing partial derivatives is know about pretty much what a gradient is

• nabla f collection of all the partial derivatives

Gradients and maxima/minima

• the tangent plane actually pararell to the floor in every local minimum and maximum

• we deal with partial derivatives

• both of the slopes of the tangent lines given by the partial derivatives are 0

• set all the partial derivatives 0

Optimization with gradients: An example

• find where di T over di x is 0 and di T over di y is 0

• check the candidates

Optimization using gradients - Analytical method

Gradient Descent

Optimization using Gradient Descent in one variable - Part 1

• 오메가 상수(Omega constant)

• repeat

Optimization using Gradient Descent in one variable - Part 2

Optimization using Gradient Descent in one variable - Part 3

Optimization using Gradient Descent in two variables

Optimization using Gradient Descent - Least squares

Optimization using Gradient Descent - Least squares with multiple observations