课程信息
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第 1 门课程(共 1 门)

100% 在线

立即开始,按照自己的计划学习。

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初级

完成时间大约为21 小时

建议:6 weeks of study, 2-5 hours/week...

英语(English)

字幕:英语(English), 希腊语, 西班牙语(Spanish)

您将获得的技能

Linear RegressionVector CalculusMultivariable CalculusGradient Descent

第 1 门课程(共 1 门)

100% 在线

立即开始,按照自己的计划学习。

可灵活调整截止日期

根据您的日程表重置截止日期。

初级

完成时间大约为21 小时

建议:6 weeks of study, 2-5 hours/week...

英语(English)

字幕:英语(English), 希腊语, 西班牙语(Spanish)

教学大纲 - 您将从这门课程中学到什么

1
完成时间为 4 小时

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. Often, 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 of 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.

...
10 个视频 (总计 46 分钟), 4 个阅读材料, 6 个测验
10 个视频
Welcome to Module 1!1分钟
Functions4分钟
Rise Over Run4分钟
Definition of a derivative10分钟
Differentiation examples & special cases7分钟
Product rule4分钟
Chain rule5分钟
Taming a beast5分钟
See you next module!39
4 个阅读材料
About Imperial College & the team5分钟
How to be successful in this course5分钟
Grading Policy5分钟
Additional Readings & Helpful References5分钟
6 个练习
Matching functions visually20分钟
Matching the graph of a function to the graph of its derivative20分钟
Let's differentiate some functions20分钟
Practicing the product rule20分钟
Practicing the chain rule20分钟
Unleashing the toolbox20分钟
2
完成时间为 3 小时

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.

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9 个视频 (总计 41 分钟), 5 个测验
9 个视频
Variables, constants & context7分钟
Differentiate with respect to anything4分钟
The Jacobian5分钟
Jacobian applied6分钟
The Sandpit4分钟
The Hessian5分钟
Reality is hard4分钟
See you next module!23
5 个练习
Practicing partial differentiation20分钟
Calculating the Jacobian20分钟
Bigger Jacobians!20分钟
Calculating Hessians20分钟
Assessment: Jacobians and Hessians20分钟
3
完成时间为 3 小时

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.

...
6 个视频 (总计 19 分钟), 4 个测验
6 个视频
Multivariate chain rule2分钟
More multivariate chain rule5分钟
Simple neural networks5分钟
More simple neural networks4分钟
See you next module!34
3 个练习
Multivariate chain rule exercise20分钟
Simple Artificial Neural Networks20分钟
Training Neural Networks25分钟
4
完成时间为 2 小时

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.

...
9 个视频 (总计 41 分钟), 5 个测验
9 个视频
Building approximate functions3分钟
Power series3分钟
Power series derivation9分钟
Power series details6分钟
Examples5分钟
Linearisation5分钟
Multivariate Taylor6分钟
See you next module!28
5 个练习
Matching functions and approximations20分钟
Applying the Taylor series15分钟
Taylor series - Special cases10分钟
2D Taylor series15分钟
Taylor Series Assessment20分钟
4.7
243 个审阅Chevron Right

29%

完成这些课程后已开始新的职业生涯

23%

通过此课程获得实实在在的工作福利

来自Mathematics for Machine Learning: Multivariate Calculus的热门评论

创建者 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.

创建者 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.

讲师

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Samuel J. Cooper

Lecturer
Dyson School of Design Engineering
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David Dye

Professor of Metallurgy
Department of Materials
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A. Freddie Page

Strategic Teaching Fellow
Dyson School of Design Engineering

关于 伦敦帝国学院

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....

关于 Mathematics for Machine Learning 专项课程

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

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