Transformations and Automatic Differentiation in Computational Thinking - Lecture 3

This lecture introduces linear and nonlinear transformations and automatic differentiation for univariate, scalar-valued multivariate, and vector-valued functions. It also demonstrates minimizing a machine-learning loss function and discusses transformations in Julia.

Syllabus

Introduction by MIT's Prof. Alan Edelman.
Agenda of Lecture0-1:30 Transformations and Automatic Differentiations.
General Linear Transformation.
Shear Transformation.
Non-Linear Transformation(Warp).
Rotation.
Compose Transformation(Rotate followed by Warp).
More Transformations(xy, rθ).
Linear and Non-Linear Transformations.
Linear combinations of Images.
Functions in Maths and in Julia(Short form, anonymous and long form).
Automatic Differentiation of Univariates.
Scalar Valued Multivariate Functions.
Automatic Differentiation: Scalar valued and Multivariate Functions.
Minimizing "loss function" in Machine Learning.
Transformations: Vector Valued Multivariate Functions.
Automatic Differentiation of Transformations.
But what is a transformation, really?.
Significance of Determinants in Scaling.
Resource for Automatic Differentiation in 10 minutes with Julia.