このコースについて
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初級レベル

約21時間で修了

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

英語

字幕:英語, ギリシャ語, スペイン語

習得するスキル

Linear RegressionVector CalculusMultivariable CalculusGradient Descent

100%オンライン

自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

初級レベル

約21時間で修了

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

英語

字幕:英語, ギリシャ語, スペイン語

シラバス - 本コースの学習内容

1
4時間で修了

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件のビデオ (合計46分), 4 readings, 6 quizzes
10件のビデオ
Rise Over Run4 分
Definition of a derivative10 分
Differentiation examples & special cases7 分
Product rule4 分
Chain rule5 分
Taming a beast5 分
See you next module!39
4件の学習用教材
About Imperial College & the team5 分
How to be successful in this course5 分
Grading Policy5 分
Additional Readings & Helpful References5 分
6の練習問題
Matching functions visually20 分
Matching the graph of a function to the graph of its derivative20 分
Let's differentiate some functions20 分
Practicing the product rule20 分
Practicing the chain rule20 分
Unleashing the toolbox20 分
2
3時間で修了

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件のビデオ (合計41分), 5 quizzes
9件のビデオ
The Jacobian5 分
Jacobian applied6 分
The Sandpit4 分
The Hessian5 分
Reality is hard4 分
See you next module!23
5の練習問題
Practicing partial differentiation20 分
Calculating the Jacobian20 分
Bigger Jacobians!20 分
Calculating Hessians20 分
Assessment: Jacobians and Hessians20 分
3
3時間で修了

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.

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6件のビデオ (合計19分), 4 quizzes
6件のビデオ
Simple neural networks5 分
More simple neural networks4 分
See you next module!34
3の練習問題
Multivariate chain rule exercise20 分
Simple Artificial Neural Networks20 分
Training Neural Networks25 分
4
2時間で修了

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件のビデオ (合計41分), 5 quizzes
9件のビデオ
Power series derivation9 分
Power series details6 分
Examples5 分
Linearisation5 分
Multivariate Taylor6 分
See you next module!28
5の練習問題
Matching functions and approximations20 分
Applying the Taylor series15 分
Taylor series - Special cases10 分
2D Taylor series15 分
Taylor Series Assessment20 分
4.7
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Mathematics for Machine Learning: Multivariate Calculus からの人気レビュー

by 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.

by 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.

講師

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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

インペリアル・カレッジ・ロンドン(Imperial College London)について

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....

Mathematics for Machine Learningの専門講座について

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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