À propos de ce cours
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Approx. 21 heures pour terminer

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


Sous-titres : Anglais, Grec, Espagnol

Compétences que vous acquerrez

Linear RegressionVector CalculusMultivariable CalculusGradient Descent

100 % en ligne

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.

Niveau débutant

Approx. 21 heures pour terminer

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


Sous-titres : Anglais, Grec, Espagnol

Programme du cours : ce que vous apprendrez dans ce cours

4 heures pour terminer

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 vidéos (Total 46 min), 4 lectures, 6 quiz
10 vidéos
Rise Over Run4 min
Definition of a derivative10 min
Differentiation examples & special cases7 min
Product rule4 min
Chain rule5 min
Taming a beast5 min
See you next module!39s
4 lectures
About Imperial College & the team5 min
How to be successful in this course5 min
Grading Policy5 min
Additional Readings & Helpful References5 min
6 exercices pour s'entraîner
Matching functions visually20 min
Matching the graph of a function to the graph of its derivative20 min
Let's differentiate some functions20 min
Practicing the product rule20 min
Practicing the chain rule20 min
Unleashing the toolbox20 min
3 heures pour terminer

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 vidéos (Total 41 min), 5 quiz
9 vidéos
The Jacobian5 min
Jacobian applied6 min
The Sandpit4 min
The Hessian5 min
Reality is hard4 min
See you next module!23s
5 exercices pour s'entraîner
Practicing partial differentiation20 min
Calculating the Jacobian20 min
Bigger Jacobians!20 min
Calculating Hessians20 min
Assessment: Jacobians and Hessians20 min
3 heures pour terminer

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 vidéos (Total 19 min), 4 quiz
6 vidéos
Simple neural networks5 min
More simple neural networks4 min
See you next module!34s
3 exercices pour s'entraîner
Multivariate chain rule exercise20 min
Simple Artificial Neural Networks20 min
Training Neural Networks25 min
2 heures pour terminer

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 vidéos (Total 41 min), 5 quiz
9 vidéos
Power series derivation9 min
Power series details6 min
Examples5 min
Linearisation5 min
Multivariate Taylor6 min
See you next module!28s
5 exercices pour s'entraîner
Matching functions and approximations20 min
Applying the Taylor series15 min
Taylor series - Special cases10 min
2D Taylor series15 min
Taylor Series Assessment20 min
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Principaux examens pour Mathematics for Machine Learning: Multivariate Calculus

par 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.

par 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

À propos de 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....

À propos de la Spécialisation 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

Foire Aux Questions

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