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Matrix Calculus for Machine Learning and Beyond

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023

Lecture 1 Part 2: Derivatives as Linear Operators

Lecture 8 Part 1: Derivatives of Eigenproblems

Lecture 1 Part 1: Introduction and Motivation

Lecture 2 Part 2: Vectorization of Matrix Functions

Lecture 3 Part 1: Kronecker Products and Jacobians

Lecture 3 Part 2: Finite-Difference Approximations

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

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

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

Lecture 6 Part 1: Adjoint Differentiation of ODE Solutions

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

Lecture 5 Part 1: Derivative of Matrix Determinant and Inverse

Lecture 7 Part 1: Derivatives of Random Functions

Lecture 5 Part 2: Forward Automatic Differentiation via Dual Numbers

Lecture 8 Part 2: Automatic Differentiation on Computational Graphs

Lecture 6 Part 2: Calculus of Variations and Gradients of Functionals

Lecture 5 Part 3: Differentiation on Computational Graphs

Machine Learning, Modeling, and Simulation Principles