Über diesen Kurs
129,814 recent views

100 % online

Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.

Flexible Fristen

Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.

Stufe „Anfänger“

Ca. 21 Stunden zum Abschließen

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

Englisch

Untertitel: Englisch, Griechisch, Spanisch

Kompetenzen, die Sie erwerben

Linear RegressionVector CalculusMultivariable CalculusGradient Descent

100 % online

Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.

Flexible Fristen

Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.

Stufe „Anfänger“

Ca. 21 Stunden zum Abschließen

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

Englisch

Untertitel: Englisch, Griechisch, Spanisch

Lehrplan - Was Sie in diesem Kurs lernen werden

Woche
1
4 Stunden zum Abschließen

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 Videos (Gesamt 46 min), 4 Lektüren, 6 Quiz
10 Videos
Rise Over Run4m
Definition of a derivative10m
Differentiation examples & special cases7m
Product rule4m
Chain rule5m
Taming a beast5m
See you next module!39
4 Lektüren
About Imperial College & the team5m
How to be successful in this course5m
Grading Policy5m
Additional Readings & Helpful References5m
6 praktische Übungen
Matching functions visually20m
Matching the graph of a function to the graph of its derivative20m
Let's differentiate some functions20m
Practicing the product rule20m
Practicing the chain rule20m
Unleashing the toolbox20m
Woche
2
3 Stunden zum Abschließen

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 Videos (Gesamt 41 min), 5 Quiz
9 Videos
The Jacobian5m
Jacobian applied6m
The Sandpit4m
The Hessian5m
Reality is hard4m
See you next module!23
5 praktische Übungen
Practicing partial differentiation20m
Calculating the Jacobian20m
Bigger Jacobians!20m
Calculating Hessians20m
Assessment: Jacobians and Hessians20m
Woche
3
3 Stunden zum Abschließen

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 Videos (Gesamt 19 min), 4 Quiz
6 Videos
Simple neural networks5m
More simple neural networks4m
See you next module!34
3 praktische Übungen
Multivariate chain rule exercise20m
Simple Artificial Neural Networks20m
Training Neural Networks25m
Woche
4
2 Stunden zum Abschließen

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 Videos (Gesamt 41 min), 5 Quiz
9 Videos
Power series derivation9m
Power series details6m
Examples5m
Linearisation5m
Multivariate Taylor6m
See you next module!28
5 praktische Übungen
Matching functions and approximations20m
Applying the Taylor series15m
Taylor series - Special cases10m
2D Taylor series15m
Taylor Series Assessment20m
4.7
243 BewertungenChevron Right

29%

nahm einen neuen Beruf nach Abschluss dieser Kurse auf

23%

ziehen Sie für Ihren Beruf greifbaren Nutzen aus diesem Kurs

Top reviews from Mathematics for Machine Learning: Multivariate Calculus

von 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.

von 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.

Dozenten

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

Über 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....

Über die Spezialisierung 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

Häufig gestellte Fragen

  • Sobald Sie sich für ein Zertifikat angemeldet haben, haben Sie Zugriff auf alle Videos, Quizspiele und Programmieraufgaben (falls zutreffend). Aufgaben, die von anderen Kursteilnehmern bewertet werden, können erst dann eingereicht und überprüft werden, wenn Ihr Unterricht begonnen hat. Wenn Sie sich den Kurs anschauen möchten, ohne ihn zu kaufen, können Sie womöglich auf bestimmte Aufgaben nicht zugreifen.

  • Wenn Sie sich für den Kurs anmelden, erhalten Sie Zugriff auf alle Kurse der Spezialisierung und Sie erhalten nach Abschluss aller Arbeiten ein Zertifikat. Ihr elektronisches Zertifikat wird zu Ihrer Seite „Errungenschaften“ hinzugefügt – von dort können Sie Ihr Zertifikat ausdrucken oder es zu Ihrem LinkedIn Profil hinzufügen. Wenn Sie nur lesen und den Inhalt des Kurses anzeigen möchten, können Sie kostenlos als Gast an dem Kurs teilnehmen.

Haben Sie weitere Fragen? Besuchen Sie das Hilfe-Center für Teiln..