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Mathematics for Machine Learning: Multivariate Calculus
  • Level Foundation
  • المدة 18 ساعات hours
  • الطبع بواسطة Imperial College London
  • Offered by

عن

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.

الوحدات

Welcome to this course

    • 1 Videos
    • 4 Readings
    • 1 Discussion
    • 1 Plugin
Show info about module content

1 Discussions

  • Nice to meet you!

1 Videos

  • Welcome to Multivariate Calculus

4 Readings

  • About Imperial College & the team
  • How to be successful in this course
  • Grading Policy
  • Additional Readings & Helpful References

Back to basics: functions

    • 2 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Matching functions visually

2 Videos

  • Welcome to Module 1!
  • Functions

Gradients and derivatives

    • 3 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Matching the graph of a function to the graph of its derivative
  • Let's differentiate some functions

3 Videos

  • Rise Over Run
  • Definition of a derivative
  • Differentiation examples & special cases

Time saving rules

    • 3 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Practicing the product rule
  • Practicing the chain rule

3 Videos

  • Product rule
  • Chain rule
  • Taming a beast

Assessment

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Unleashing the toolbox

1 Videos

  • See you next module!

Moving to multivariate

    • 3 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Practicing partial differentiation

3 Videos

  • Welcome to Module 2!
  • Variables, constants & context
  • Differentiate with respect to anything

Jacobians - vectors of derivatives

    • 2 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Calculating the Jacobian
  • Bigger Jacobians!

2 Videos

  • The Jacobian
  • Jacobian applied

The sandpit game

    • 4 Videos
    • 2 Lab
    • 2 Assignment
Show info about module content

2 Assignment

  • Calculating Hessians
  • Assessment: Jacobians and Hessians

2 Labs

  • The Sandpit
  • The Sandpit - Part 2

4 Videos

  • The Sandpit
  • The Hessian
  • Reality is hard
  • See you next module!

Chain rule intro.

    • 3 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Multivariate chain rule exercise

3 Videos

  • Welcome to Module 3!
  • Multivariate chain rule
  • More multivariate chain rule

Neural Networks

    • 3 Videos
    • 1 Discussion
    • 1 Lab
    • 1 Programming
    • 2 Assignment
Show info about module content

1 Programming

  • Backpropagation

2 Assignment

  • Simple Artificial Neural Networks
  • Training Neural Networks

1 Discussions

  • I ❤️ backpropagation

1 Labs

  • Backpropagation

3 Videos

  • Simple neural networks
  • More simple neural networks
  • See you next module!

Taylor series for approximations

    • 6 Videos
    • 1 Plugin
    • 2 Assignment
Show info about module content

2 Assignment

  • Matching functions and approximations
  • Applying the Taylor series

6 Videos

  • Welcome to Module 4!
  • Building approximate functions
  • Power series
  • Power series derivation
  • Power series details
  • Examples

Multivariable Taylor Series

    • 3 Videos
    • 3 Assignment
Show info about module content

3 Assignment

  • Taylor series - Special cases
  • 2D Taylor series
  • Taylor Series Assessment

3 Videos

  • Linearisation
  • Multivariate Taylor
  • See you next module!

Fitting as minimisation problem

    • 2 Videos
    • 1 Discussion
    • 1 Lab
    • 2 Assignment
Show info about module content

2 Assignment

  • Newton-Raphson in one dimension
  • Checking Newton-Raphson

1 Discussions

  • Steepest strategies

1 Labs

  • Gradient descent in a sandpit

2 Videos

  • Welcome to Module 5!
  • Gradient Descent

Lagrange multipliers

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Lagrange multipliers

1 Videos

  • Constrained optimisation

Assessment

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Optimisation scenarios

1 Videos

  • See you next module!

Into to linear regression

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Linear regression

1 Videos

  • Simple linear regression

Non-linear regression

    • 3 Videos
    • 1 Readings
    • 1 Plugin
    • 1 Lab
    • 1 Programming
    • 1 Assignment
Show info about module content

1 Programming

  • Fitting the distribution of height data

1 Assignment

  • Fitting a non-linear function

1 Labs

  • Fitting the distribution of heights data

3 Videos

  • General non linear least squares
  • Doing least squares regression analysis in practice
  • Wrap up of this course

1 Readings

  • Did you like the course? Let us know!

Auto Summary

Enhance your machine learning skills with "Mathematics for Machine Learning: Multivariate Calculus" by Coursera. This foundational course delves into multivariate calculus, essential for developing machine learning techniques. With a focus on intuitive understanding, you'll explore gradients, vectors, and applications in neural networks and linear regression. The 1080-minute course offers flexible subscription options: Starter, Professional, and Paid. Ideal for aspiring data scientists and AI enthusiasts, this course equips you with the confidence to tackle advanced machine learning topics.

Samuel J. Cooper
Instructors

Samuel J. Cooper

David Dye
Instructors

David Dye

A. Freddie Page
Instructors

A. Freddie Page