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M4ML - Multivariate Calculus - 4.8 Multivariate Taylor

Welcome to the “Mathematics for Machine Learning: Multivariate Calculus” course, offered by Imperial College London. This video is part of an online specialisation in Mathematics for Machine Learning (m4ml) hosted by Coursera. For more information on the course and to access the full experience, please visit: https://www.coursera.org/specializati... Week 4, Video 8 - Multivariate Taylor Full Playlist -    • Mathematics for Machine Learning - Mu...   Your course instructors are Dr Sam Cooper (@camsooper,   / camsooper  ) Dr David Dye (@DavidDye9,   / daviddye9  ) If you have any questions about the course, please contact the instructors via Twitter. This course offers an introduction to the multivariate calculus required for 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 build up some tools for making calculus easier, as well as generalising the concepts to multidimensional systems. Next, we learn how to calculate vectors that point downhill on surfaces and show how this is used for training neural networks 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 finish the course by bringing all of these concepts together by showing you how to use code to fit a function to some data in a process known as non-linear regression. This course was designed to help you quickly build an intuitive understanding of calculus, as well as the language necessary to look concepts up yourselves when you get stuck; it is not intended cover all the details. We hope you enjoy it and that it gives you the confidence to dive into one of the many other wonderful machine learning courses available online!