The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

'The field of machine learning has grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This comprehensive text covers the key mathematical concepts that underpin modern machine learning, with a focus on linear algebra, calculus, and probability theory. It will prove valuable both as a tutorial for newcomers to the field, and as a reference text for machine learning researchers and engineers.' Christopher Bishop, Microsoft Research Cambridge

Auteur

Marc Peter Deisenroth is DeepMind Chair in Artificial Intelligence at the Department of Computer Science, University College London. Prior to this, he was a faculty member in the Department of Computing, Imperial College London. His research areas include data-efficient learning, probabilistic modeling, and autonomous decision making. Deisenroth was Program Chair of the European Workshop on Reinforcement Learning (EWRL) 2012 and Workshops Chair of Robotics Science and Systems (RSS) 2013. His research received Best Paper Awards at the International Conference on Robotics and Automation (ICRA) 2014 and the International Conference on Control, Automation and Systems (ICCAS) 2016. In 2018, he was awarded the President's Award for Outstanding Early Career Researcher at Imperial College London. He is a recipient of a Google Faculty Research Award and a Microsoft P.hD. grant.

Résumé
This self-contained textbook introduces all the relevant mathematical concepts needed to understand and use machine learning methods, with a minimum of prerequisites. Topics include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics.

Contenu

Introduction and motivation; 2. Linear algebra; 3. Analytic geometry; 4. Matrix decompositions; 5. Vector calculus; 6. Probability and distribution; 7. Optimization; 8. When models meet data; 9. Linear regression; 10. Dimensionality reduction with principal component analysis; 11. Density estimation with Gaussian mixture models; 12. Classification with support vector machines.