Start Date: 07/05/2020
Course Type: Common Course |
Course Link: https://www.coursera.org/learn/multivariate-calculus-machine-learning
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.
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. Typically, 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 off 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.
Mathematics for Machine Learning: Multivariate Calculus Mathematics is for everyone who wants to understand the fundamentals of mathematics, including math majors and non-math majors alike. Designed to help non-mathematicians understand the concepts and notation of mathematics, this course includes a large number of lectures and hands-on exercises. The course is primarily targeted at the non-mathematician who wants to understand the fundamentals of mathematics, and is motivated by a desire to learn more. After completing this course, you will: * Understand the basics of matrix algebra and how to use trigonometric identities * Know the essentials of vector spaces and their applications * Know how to construct vectors and how to use linearization * Know how to construct vectors and how to use linearization * Know how to construct linearized control structures and their associated dependent variables * Know the essentials of linearized control structures and their associated dependent variables * Know the basics of matrix factorization and how to use trigonometric identities * Know how to construct vectors and how to use linearization * Know the essentials of vector spaces and their applications * Know how to construct vectors and how to use linearization * Know the basics of linearized control structures and their associated dependent variables * Know the basics of vector spaces and their applications * Know how to construct control structures and how to use trigonometric identities * Know the basics of linearized control structures and their associated dependent
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Maplets for Calculus | In March 2008, Maplets for Calculus received the 2008 ICTCM Award for Excellence and Innovation in Using Technology to Enhance the Teaching and Learning of Mathematics at the 20th International Conference on Technology in Collegiate Mathematics. |
Matrix calculus | Matrix differential calculus is used in statistics, particularly for the statistical analysis of multivariate distributions, especially the multivariate normal distribution and other elliptical distributions. |
Calculus | Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". "Calculus" (plural "calculi") is also used for naming some methods of calculation or theories of computation, such as propositional calculus, calculus of variations, lambda calculus, and process calculus. |
Machine learning | Rule-based machine learning is a general term for any machine learning method that identifies, learns, or evolves `rules’ to store, manipulate or apply, knowledge. The defining characteristic of a rule-based machine learner is the identification and utilization of a set of relational rules that collectively represent the knowledge captured by the system. This is in contrast to other machine learners that commonly identify a singular model that can be universally applied to any instance in order to make a prediction. Rule-based machine learning approaches include learning classifier systems, association rule learning, and artificial immune systems. |
Tanagra (machine learning) | Tanagra makes a good compromise between the statistical approaches (e.g. parametric and nonparametric statistical tests), the multivariate analysis methods (e.g. factor analysis, correspondence analysis, cluster analysis, regression) and the machine learning techniques (e.g. neural network, support vector machine, decision trees, random forest). |
Multivariable calculus | Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables, rather than just one. |
Investigations in Mathematics Learning | Investigations in Mathematics Learning is the official research journal of the Research Council for Mathematics Learning. Information about submission can be found here. RCML seeks to stimulate, generate, coordinate, and disseminate research efforts designed to understand and/or influence factors that affect mathematics learning. |
British Society for Research into Learning Mathematics | The British Society for Research into Learning Mathematics is a United Kingdom association for people interested in research in mathematics education. |
GRE Mathematics Test | The GRE subject test in mathematics is a standardized test in the United States created by the Educational Testing Service (ETS), and is designed to assess a candidate's potential for graduate or post-graduate study in the field of mathematics. It contains questions from many fields of mathematics. About 50% of the questions come from calculus (including pre-calculus topics, multivariate calculus, and differential equations), 25% from algebra (including linear algebra, abstract algebra, and number theory), and 25% from a broad variety of other topics typically encountered in undergraduate mathematics courses, such as point-set topology, probability and statistics, geometry, and real analysis. |
Multivariable calculus | Multivariable calculus is used in many fields of natural and social science and engineering to model and study high-dimensional systems that exhibit deterministic behavior. In economics, for example, consumer choice over a variety of goods, and producer choice over various inputs to use and outputs to produce, are modeled with multivariate calculus. Quantitative analysts in finance also often use multivariate calculus to predict future trends in the stock market. |
Active learning (machine learning) | Recent developments are dedicated to hybrid active learning and active learning in a single-pass (on-line) context, combining concepts from the field of Machine Learning (e.g., conflict and ignorance) with adaptive, incremental learning policies in the field of Online machine learning. |
Attributional calculus | Michalski, R.S., "ATTRIBUTIONAL CALCULUS: A Logic and Representation Language for Natural Induction," Reports of the Machine Learning and Inference Laboratory, MLI 04-2, George Mason University, Fairfax, VA, April, 2004. |
Machine learning | Some statisticians have adopted methods from machine learning, leading to a combined field that they call "statistical learning". |
Machine learning | Machine learning tasks are typically classified into three broad categories, depending on the nature of the learning "signal" or "feedback" available to a learning system. These are |
Matrix calculus | In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities. This greatly simplifies operations such as finding the maximum or minimum of a multivariate function and solving systems of differential equations. The notation used here is commonly used in statistics and engineering, while the tensor index notation is preferred in physics. |
Machine learning | Another categorization of machine learning tasks arises when one considers the desired "output" of a machine-learned system: |
Relevance vector machine | In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification. |
Machine learning | Machine Learning poses a host of ethical questions. Systems which are trained on datasets collected with biases may exhibit these biases upon use, thus digitizing cultural prejudices. Responsible collection of data thus is a critical part of machine learning. |
Machine learning | Machine learning is closely related to (and often overlaps with) computational statistics, which also focuses on prediction-making through the use of computers. It has strong ties to mathematical optimization, which delivers methods, theory and application domains to the field. Machine learning is sometimes conflated with data mining, where the latter subfield focuses more on exploratory data analysis and is known as unsupervised learning. Machine learning can also be unsupervised and be used to learn and establish baseline behavioral profiles for various entities and then used to find meaningful anomalies. |
Quantum machine learning | The term quantum machine learning is also used for approaches that apply classical methods of machine learning to the study of quantum systems, for instance in the context of quantum information theory or for the development of quantum technologies. For example, when experimentalists have to deal with incomplete information on a quantum system or source, Bayesian methods and concepts of algorithmic learning can be fruitfully applied. This includes the application of machine learning to tackle quantum state classification, Hamiltonian learning, or learning an unknown unitary transformation. |