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Mathematics for Machine Learning: Multivariate Calculus · LearnSpace
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Mathematics for Machine Learning: Multivariate Calculus

Курс от Imperial College London
Начальный≈ 17.8 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. We start at the very beginning with a refresher on the “rise over run” formulation of a slope, before converting this to the formal definition of the gradient of a function. We then start to build up a set of tools for making calculus easier and faster. Next, we learn how to calculate vectors that point up hill on multidimensional surfaces and even put this into action using an interactive game. We take a look at how we can use calculus to build approximations to functions, as well as helping us to quantify how accurate we should expect those approximations to be. We also spend some time talking about where calculus comes up in the training of neural networks, before finally showing you how it is applied in linear regression models. This course is intended to offer an intuitive understanding of calculus, as well as the language necessary to look concepts up yourselves when you get stuck. Hopefully, without going into too much detail, you’ll still come away with the confidence to dive into some more focused machine learning courses in future.

Навыки, которые вы освоите

CalculusModel OptimizationRegression AnalysisLinear AlgebraDerivativesArtificial Neural NetworksMathematical SoftwareNumerical AnalysisMachine Learning MethodsMathematical Theory & AnalysisApplied MathematicsDeep LearningApplied Machine Learning

Программа курса

6 модулей · 85 учебных материалов

01What is calculus?22 материалов

Welcome to this course

Welcome to Multivariate CalculusВидеоAbout Imperial College & the teamЧтениеHow to be successful in this courseЧтениеGrading PolicyЧтение

Учитесь у экспертов

Samuel J. Cooper

Associate Professor

David Dye

Professor of Metallurgy

A. Freddie Page

Strategic Teaching Fellow

Mathematics for Machine Learning: Multivariate Calculus
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≈ 17.8 ч

6 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Вьетнамский, Нидерландский, Корейский, Немецкий, Пушту, Урду, Русский, Тайский, Индонезийский, Шведский, Турецкий, Азербайджанский, Испанский, Дари, Хинди, Японский, Казахский, Венгерский, Польский

Часть программы вашего университета
Additional Readings & Helpful ReferencesЧтение
Nice to meet you!Обсуждение
Pre-course SurveyPLUGIN

Back to basics: functions

Welcome to Module 1!ВидеоFunctionsВидеоMatching functions visuallyЗадание

Gradients and derivatives

Rise Over RunВидеоMatching the graph of a function to the graph of its derivativeЗаданиеDefinition of a derivativeВидеоDifferentiation examples & special casesВидеоLet's differentiate some functionsЗадание

Time saving rules

Product ruleВидеоPracticing the product ruleЗаданиеChain ruleВидеоTaming a beastВидеоPracticing the chain ruleЗадание

Assessment

Unleashing the toolboxЗаданиеSee you next module!Видео
02Multivariate calculus16 материалов

Moving to multivariate

Welcome to Module 2!ВидеоVariables, constants & contextВидеоDifferentiate with respect to anythingВидеоPracticing partial differentiationЗадание

Jacobians - vectors of derivatives

The JacobianВидеоCalculating the JacobianЗаданиеJacobian appliedВидеоBigger Jacobians!Задание

The sandpit game

The SandpitВидеоThe SandpitЛабораторнаяThe Sandpit - Part 2ЛабораторнаяThe HessianВидеоCalculating HessiansЗаданиеReality is hardВидеоAssessment: Jacobians and HessiansЗадание
03Multivariate chain rule and its applications12 материалов

Chain rule intro.

Welcome to Module 3!ВидеоMultivariate chain ruleВидеоMore multivariate chain ruleВидеоMultivariate chain rule exerciseЗадание

Neural Networks

Simple neural networksВидеоSimple Artificial Neural NetworksЗаданиеMore simple neural networksВидеоTraining Neural NetworksЗаданиеBackpropagationЛабораторнаяBackpropagationПрограммированиеI ❤️ backpropagationОбсуждениеSee you next module!Видео
04Taylor series and linearisation15 материалов

Taylor series for approximations

Welcome to Module 4!ВидеоBuilding approximate functionsВидеоPower seriesВидеоMatching functions and approximationsЗаданиеVisualising Taylor SeriesPLUGINPower series derivationВидеоPower series detailsВидеоApplying the Taylor seriesЗаданиеExamplesВидео

Multivariable Taylor Series

LinearisationВидеоTaylor series - Special casesЗаданиеMultivariate TaylorВидео2D Taylor seriesЗаданиеTaylor Series AssessmentЗаданиеSee you next module!Видео
05Intro to optimisation10 материалов

Fitting as minimisation problem

Welcome to Module 5!ВидеоNewton-Raphson in one dimension ЗаданиеGradient DescentВидеоGradient descent in a sandpitЛабораторнаяSteepest strategiesОбсуждениеChecking Newton-RaphsonЗадание

Lagrange multipliers

Constrained optimisationВидеоLagrange multipliersЗадание

Assessment

Optimisation scenariosЗаданиеSee you next module!Видео
06Regression10 материалов

Into to linear regression

Simple linear regressionВидеоLinear regressionЗадание

Non-linear regression

General non linear least squaresВидеоFitting a non-linear functionЗаданиеDoing least squares regression analysis in practiceВидеоFitting the distribution of heights dataЛабораторнаяFitting the distribution of height dataПрограммированиеWrap up of this courseВидеоDid you like the course? Let us know!ЧтениеPost-course SurveyPLUGIN
See you next module!Видео