Об этом курсе
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Прибл. 21 часа на выполнение

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


Субтитры: Английский, Греческий, Испанский

Приобретаемые навыки

Linear RegressionVector CalculusMultivariable CalculusGradient Descent

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Прибл. 21 часа на выполнение

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


Субтитры: Английский, Греческий, Испанский

Программа курса: что вы изучите

4 ч. на завершение

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 видео ((всего 46 мин.)), 4 материалов для самостоятельного изучения, 6 тестов
10 видео
Rise Over Run4мин
Definition of a derivative10мин
Differentiation examples & special cases7мин
Product rule4мин
Chain rule5мин
Taming a beast5мин
See you next module!39
4 материала для самостоятельного изучения
About Imperial College & the team5мин
How to be successful in this course5мин
Grading Policy5мин
Additional Readings & Helpful References5мин
6 практического упражнения
Matching functions visually20мин
Matching the graph of a function to the graph of its derivative20мин
Let's differentiate some functions20мин
Practicing the product rule20мин
Practicing the chain rule20мин
Unleashing the toolbox20мин
3 ч. на завершение

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.

9 видео ((всего 41 мин.)), 5 тестов
9 видео
The Jacobian5мин
Jacobian applied6мин
The Sandpit4мин
The Hessian5мин
Reality is hard4мин
See you next module!23
5 практического упражнения
Practicing partial differentiation20мин
Calculating the Jacobian20мин
Bigger Jacobians!20мин
Calculating Hessians20мин
Assessment: Jacobians and Hessians20мин
3 ч. на завершение

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 видео ((всего 19 мин.)), 4 тестов
6 видео
Simple neural networks5мин
More simple neural networks4мин
See you next module!34
3 практического упражнения
Multivariate chain rule exercise20мин
Simple Artificial Neural Networks20мин
Training Neural Networks25мин
2 ч. на завершение

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 видео ((всего 41 мин.)), 5 тестов
9 видео
Power series derivation9мин
Power series details6мин
Multivariate Taylor6мин
See you next module!28
5 практического упражнения
Matching functions and approximations20мин
Applying the Taylor series15мин
Taylor series - Special cases10мин
2D Taylor series15мин
Taylor Series Assessment20мин
Рецензии: 243Chevron Right


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Лучшие отзывы о курсе Mathematics for Machine Learning: Multivariate Calculus

автор: 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.

автор: 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.



Samuel J. Cooper

Dyson School of Design Engineering

David Dye

Professor of Metallurgy
Department of Materials

A. Freddie Page

Strategic Teaching Fellow
Dyson School of Design Engineering

О Имперский колледж Лондона

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....

О специализации ''Mathematics for Machine Learning'

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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