Math 0-1: Matrix Calculus In Data Science & Machine Learning

Math 0-1: Matrix Calculus In Data Science & Machine Learning
Published 11/2023
MP4 | Video: h264, 1920×1080 | Audio: AAC, 44.1 KHz

What you’ll learn

Derive matrix and vector derivatives for linear and quadratic forms

Solve common optimization problems (least squares, Gaussian, financial portfolio)

Understand and implement Gradient Descent and Newton’s method

Learn to use the Matrix Cookbook

Requirements

Competence with Calculus and Linear Algebra

Optional: Familiarity with Python, Numpy, and Matplotlib to implement optimization techniques

Description

Overview

Section 1: Introduction

Lecture 1 Introduction and Outline

Lecture 2 How to succeed in this course

Lecture 3 Where to get the code

Section 2: Matrix and Vector Derivatives

Lecture 4 Derivatives – Section Introduction

Lecture 5 Linear Form

Lecture 6 Quadratic Form (pt 1)

Lecture 7 Quadratic Form (pt 2)

Lecture 8 Exercise: Quadratic

Lecture 9 Exercise: Least Squares

Lecture 10 Exercise: Gaussian

Lecture 11 Chain Rule

Lecture 12 Chain Rule in Matrix Form

Lecture 13 Chain Rule Generalized

Lecture 14 Exercise: Quadratic with Constraints

Lecture 15 Left and Right Inverse as Optimization Problems

Lecture 16 Derivative of Determinant

Lecture 17 Derivatives – Section Summary

Lecture 18 Suggestion Box

Section 3: Optimization Techniques

Lecture 19 Optimization – Section Introduction

Lecture 20 Second Derivative Test in Multiple Dimensions

Lecture 21 Gradient Descent (One Dimension)

Lecture 22 Gradient Descent (Multiple Dimensions)

Lecture 23 Newton’s Method (One Dimension)

Lecture 24 Newton’s Method (Multiple Dimensions)

Lecture 25 Exercise: Newton’s Method for Least Squares

Lecture 26 Exercise: Code Preparation

Lecture 27 Gradient Descent and Newton’s Method in Python

Lecture 28 Optimization – Section Summary

Section 4: Appendix / FAQ Finale

Lecture 29 BONUS

Students and professionals interested in the math behind AI, data science and machine learning