Free online courseMatrix Calculus For Machine Learning

Conteúdo do Curso

• Video class: Lecture 1 Part 1: Introduction and Motivation

  0h57m

• Exercise: In the context of matrix calculus, if A and B are matrices and you define a function F(X) = XAX, what is the correct form of the derivative dF with respect to X, assuming X is also a matrix?

• Video class: Lecture 1 Part 2: Derivatives as Linear Operators

  0h48m

• Exercise: What is the primary purpose of using derivatives in the context of linearization for machine learning?

• Video class: Lecture 2 Part 1: Derivatives in Higher Dimensions: Jacobians and Matrix Functions

  1h13m

• Exercise: In the context of transformations using matrix calculus, what does a linear map from R2 to R2 effectively accomplish?

• Video class: Lecture 2 Part 2: Vectorization of Matrix Functions

  0h30m

• Exercise: In the context of matrix calculus, when dealing with a function f(A) = A^3 where A is a square matrix, what does the derivative df represent in terms of dA?

• Video class: Lecture 3 Part 1: Kronecker Products and Jacobians

  0h53m

• Exercise: What is the Jacobian matrix for the transformation function of a 2x2 matrix to its LU decomposition?

• Video class: Lecture 3 Part 2: Finite-Difference Approximations

  0h51m

• Exercise: What is one reason why error increases when delta x becomes too small in finite difference calculations?

• Video class: Lecture 4 Part 1: Gradients and Inner Products in Other Vector Spaces

  1h03m

• Exercise: In the context of finite difference approximations for derivatives, what advantage does the central difference method have over the forward difference method?

• Video class: Lecture 4 Part 2: Nonlinear Root Finding, Optimization, and Adjoint Gradient Methods

  0h44m

• Exercise: What function does Newton's Method approximate to find the roots of an equation?

• Video class: Lecture 5 Part 1: Derivative of Matrix Determinant and Inverse

  0h28m

• Exercise: In the context of matrix calculus for computing the derivatives, what is required to define a derivative in a vector space?

• Video class: Lecture 5 Part 2: Forward Automatic Differentiation via Dual Numbers

  0h36m

• Exercise: What is one of the key benefits of automatic differentiation as highlighted in the text?

• Video class: Lecture 5 Part 3: Differentiation on Computational Graphs

  0h32m

• Exercise: In the context of forward mode and reverse mode automatic differentiation, what is the main reason one might choose to calculate derivatives using reverse mode over forward mode?

• Video class: Lecture 6 Part 1: Adjoint Differentiation of ODE Solutions

  0h58m

• Exercise: In numerical solution of ordinary differential equations (ODEs), which method is commonly used for discretizing the derivative in order to approximate the solution at discrete time steps?

• Video class: Lecture 6 Part 2: Calculus of Variations and Gradients of Functionals

  0h42m

• Exercise: What is the primary goal when taking the derivative of a functional in the context of calculus of variations?

• Video class: Lecture 7 Part 1: Derivatives of Random Functions

  1h06m

• Exercise: In the context of differentiating random functions, which of the following statements best describes the 'reparameterization trick'?

• Video class: Lecture 7 Part 2: Second Derivatives, Bilinear Forms, and Hessian Matrices

  0h46m

• Exercise: What is the primary purpose of calculating the second derivative in matrix calculus, especially in the context of machine learning?

• Video class: Lecture 8 Part 1: Derivatives of Eigenproblems

  0h36m

• Exercise: What is one way to generate a random vector uniformly on the surface of a sphere in n-dimensional space?

• Video class: Lecture 8 Part 2: Automatic Differentiation on Computational Graphs

  1h05m

• Exercise: In the context of matrix calculus for machine learning, consider a computation graph formed by sequences of operations. If a computation graph is described as a Directed Acyclic Graph (DAG), which of the following statements is TRUE about the graph?