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Mathematics for Machine Learning: Multivariate Calculus

Approx. 18 hours to complete

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Course Summary

This course teaches Multivariate Calculus and its applications in Machine Learning. Students will learn the necessary mathematical tools to understand and implement machine learning algorithms.

Key Learning Points

Understand multivariable calculus and its applications in machine learning
Implement machine learning algorithms using multivariate calculus
Develop a deeper understanding of the mathematical concepts behind machine learning

Job Positions & Salaries of people who have taken this course might have

Machine Learning Engineer
- USA: $112,000
- India: ₹1,200,000
- Spain: €40,000
Data Scientist
- USA: $117,000
- India: ₹1,000,000
- Spain: €35,000
Artificial Intelligence Researcher
- USA: $120,000
- India: ₹1,500,000
- Spain: €45,000

Learning Outcomes

Ability to apply multivariable calculus concepts to machine learning algorithms
Understanding of mathematical modeling and optimization in machine learning
Proficiency in linear algebra

Prerequisites or good to have knowledge before taking this course

Calculus 1 and 2
Linear Algebra

Course Difficulty Level

Intermediate

Course Format

Self-paced
Online
Video lectures
Assignments and quizzes

Similar Courses

Applied Machine Learning
Deep Learning

Related Education Paths

Notable People in This Field

Ian Goodfellow
Yann LeCun

Related Books

Description

This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. We start at the very beginning with a refresher on the “rise over run” formulation of a slope, before converting this to the formal definition of the gradient of a function. We then start to build up a set of tools for making calculus easier and faster. Next, we learn how to calculate vectors that point up hill on multidimensional surfaces and even put this into action using an interactive game. We take a look at how we can use calculus to build approximations to functions, as well as helping us to quantify how accurate we should expect those approximations to be. We also spend some time talking about where calculus comes up in the training of neural networks, before finally showing you how it is applied in linear regression models. This course is intended to offer an intuitive understanding of calculus, as well as the language necessary to look concepts up yourselves when you get stuck. Hopefully, without going into too much detail, you’ll still come away with the confidence to dive into some more focused machine learning courses in future.

Outline

What is calculus?
Welcome to Multivariate Calculus
Welcome to Module 1!
Functions
Rise Over Run
Definition of a derivative
Differentiation examples & special cases
Product rule
Chain rule
Taming a beast
See you next module!
About Imperial College & the team
How to be successful in this course
Grading Policy
Additional Readings & Helpful References
Matching functions visually
Matching the graph of a function to the graph of its derivative
Let's differentiate some functions
Practicing the product rule
Practicing the chain rule
Unleashing the toolbox

Multivariate calculus
Welcome to Module 2!
Variables, constants & context
Differentiate with respect to anything
The Jacobian
Jacobian applied
The Sandpit
The Hessian
Reality is hard
See you next module!
Practicing partial differentiation
Calculating the Jacobian
Bigger Jacobians!
Calculating Hessians
Assessment: Jacobians and Hessians

Multivariate chain rule and its applications
Welcome to Module 3!
Multivariate chain rule
More multivariate chain rule
Simple neural networks
More simple neural networks
See you next module!
Multivariate chain rule exercise
Simple Artificial Neural Networks
Training Neural Networks

Taylor series and linearisation
Welcome to Module 4!
Building approximate functions
Power series
Power series derivation
Power series details
Examples
Linearisation
Multivariate Taylor
See you next module!
Matching functions and approximations
Applying the Taylor series
Taylor series - Special cases
2D Taylor series
Taylor Series Assessment

Intro to optimisation
Welcome to Module 5!
Gradient Descent
Constrained optimisation
See you next module!
Newton-Raphson in one dimension
Checking Newton-Raphson
Lagrange multipliers
Optimisation scenarios

Regression
Simple linear regression
General non linear least squares
Doing least squares regression analysis in practice
Wrap up of this course
Did you like the course? Let us know!
Linear regression
Fitting a non-linear function

Summary of User Reviews

Key Aspect Users Liked About This Course

Thorough and clear explanations of complex concepts

Pros from User Reviews

In-depth coverage of topics
Well-structured course materials
Challenging and engaging assignments
Experienced and knowledgeable instructor
Applicable to real-world problems

Cons from User Reviews

Requires strong math background
Some technical issues with the platform
Lack of interaction with other students
Limited practical examples
Not suitable for beginners

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