課程信息
4.7
874 個評分
134 個審閱
專項課程
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
初級

初級

完成時間(小時)

完成時間大約為22 小時

建議:6 weeks of study, 2-5 hours/week...
可選語言

英語(English)

字幕:英語(English)

您將獲得的技能

Linear RegressionVector CalculusMultivariable CalculusGradient Descent
專項課程
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
初級

初級

完成時間(小時)

完成時間大約為22 小時

建議:6 weeks of study, 2-5 hours/week...
可選語言

英語(English)

字幕:英語(English)

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 4 小時

What is calculus?

Understanding calculus is central to understanding machine learning! You can think of calculus as simply a set of tools for analysing the relationship between functions and their inputs. Typically, in machine learning, we are trying to find the inputs which enable a function to best match the data. We start this module from the basics, by recalling what a function is and where we might encounter one. Following this, we talk about the how, when sketching a function on a graph, the slope describes the rate of change off the output with respect to an input. Using this visual intuition we next derive a robust mathematical definition of a derivative, which we then use to differentiate some interesting functions. Finally, by studying a few examples, we develop four handy time saving rules that enable us to speed up differentiation for many common scenarios. ...
Reading
10 個視頻 (總計 46 分鐘), 4 個閱讀材料, 6 個測驗
Video10 個視頻
Welcome to Module 1!1分鐘
Functions4分鐘
Rise Over Run4分鐘
Definition of a derivative10分鐘
Differentiation examples & special cases7分鐘
Product rule4分鐘
Chain rule5分鐘
Taming a beast5分鐘
See you next module!分鐘
Reading4 個閱讀材料
About Imperial College & the team5分鐘
How to be successful in this course5分鐘
Grading Policy5分鐘
Additional Readings & Helpful References5分鐘
Quiz6 個練習
Matching functions visually20分鐘
Matching the graph of a function to the graph of its derivative20分鐘
Let's differentiate some functions20分鐘
Practicing the product rule20分鐘
Practicing the chain rule20分鐘
Unleashing the toolbox20分鐘
2
完成時間(小時)
完成時間為 3 小時

Multivariate calculus

Building on the foundations of the previous module, we now generalise our calculus tools to handle multivariable systems. This means we can take a function with multiple inputs and determine the influence of each of them separately. It would not be unusual for a machine learning method to require the analysis of a function with thousands of inputs, so we will also introduce the linear algebra structures necessary for storing the results of our multivariate calculus analysis in an orderly fashion. ...
Reading
9 個視頻 (總計 41 分鐘), 5 個測驗
Video9 個視頻
Variables, constants & context7分鐘
Differentiate with respect to anything4分鐘
The Jacobian5分鐘
Jacobian applied6分鐘
The Sandpit4分鐘
The Hessian5分鐘
Reality is hard4分鐘
See you next module!分鐘
Quiz5 個練習
Practicing partial differentiation20分鐘
Calculating the Jacobian20分鐘
Bigger Jacobians!20分鐘
Calculating Hessians20分鐘
Assessment: Jacobians and Hessians20分鐘
3
完成時間(小時)
完成時間為 3 小時

Multivariate chain rule and its applications

Having seen that multivariate calculus is really no more complicated than the univariate case, we now focus on applications of the chain rule. Neural networks are one of the most popular and successful conceptual structures in machine learning. They are build up from a connected web of neurons and inspired by the structure of biological brains. The behaviour of each neuron is influenced by a set of control parameters, each of which needs to be optimised to best fit the data. The multivariate chain rule can be used to calculate the influence of each parameter of the networks, allow them to be updated during training. ...
Reading
6 個視頻 (總計 19 分鐘), 4 個測驗
Video6 個視頻
Multivariate chain rule2分鐘
More multivariate chain rule5分鐘
Simple neural networks5分鐘
More simple neural networks4分鐘
See you next module!分鐘
Quiz3 個練習
Multivariate chain rule exercise20分鐘
Simple Artificial Neural Networks20分鐘
Training Neural Networks25分鐘
4
完成時間(小時)
完成時間為 2 小時

Taylor series and linearisation

The Taylor series is a method for re-expressing functions as polynomial series. This approach is the rational behind the use of simple linear approximations to complicated functions. In this module, we will derive the formal expression for the univariate Taylor series and discuss some important consequences of this result relevant to machine learning. Finally, we will discuss the multivariate case and see how the Jacobian and the Hessian come in to play. ...
Reading
9 個視頻 (總計 41 分鐘), 5 個測驗
Video9 個視頻
Building approximate functions3分鐘
Power series3分鐘
Power series derivation9分鐘
Power series details6分鐘
Examples5分鐘
Linearisation5分鐘
Multivariate Taylor6分鐘
See you next module!分鐘
Quiz5 個練習
Matching functions and approximations20分鐘
Applying the Taylor series15分鐘
Taylor series - Special cases10分鐘
2D Taylor series15分鐘
Taylor Series Assessment20分鐘
4.7
134 個審閱Chevron Right

熱門審閱

創建者 DPNov 26th 2018

Great course to develop some understanding and intuition about the basic concepts used in optimization. Last 2 weeks were a bit on a lower level of quality then the rest in my opinion but still great.

創建者 JTNov 13th 2018

Excellent course. I completed this course with no prior knowledge of multivariate calculus and was successful nonetheless. It was challenging and extremely interesting, informative, and well designed.

講師

Avatar

Samuel J. Cooper

Lecturer
Dyson School of Design Engineering
Avatar

David Dye

Professor of Metallurgy
Department of Materials
Avatar

A. Freddie Page

Strategic Teaching Fellow
Dyson School of Design Engineering

關於 Imperial College London

Imperial College London is a world top ten university with an international reputation for excellence in science, engineering, medicine and business. located in the heart of London. Imperial is a multidisciplinary space for education, research, translation and commercialisation, harnessing science and innovation to tackle global challenges. Imperial students benefit from a world-leading, inclusive educational experience, rooted in the College’s world-leading research. Our online courses are designed to promote interactivity, learning and the development of core skills, through the use of cutting-edge digital technology....

關於 Mathematics for Machine Learning 專項課程

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science. In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require basic Python and numpy knowledge. At the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning....
Mathematics for Machine Learning

常見問題

  • 注册以便获得证书后,您将有权访问所有视频、测验和编程作业(如果适用)。只有在您的班次开课之后,才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程,可能无法访问某些作业。

  • 您注册课程后,将有权访问专项课程中的所有课程,并且会在完成课程后获得证书。您的电子课程证书将添加到您的成就页中,您可以通过该页打印您的课程证书或将其添加到您的领英档案中。如果您只想阅读和查看课程内容,可以免费旁听课程。

還有其他問題嗎?請訪問 學生幫助中心