Machine Learning: Models And Algorithms

Abstract

This textbook introduces the mathematical models and algorithms utilised in machine learning, covering supervised and unsupervised learning as well as reinforcement learning: In supervised learning we present ensemble models, artificial neural networks, deep neural networks, recurrent neural networks and associative reservoir computing, while in unsupervised learning we present radial basis function (RBF), recurrent RBF networks amongst others. In both cases we give examples for chaotic series prediction as well as financial time series. We then introduce the learning theory and formalise supervised learning in the cases of neural networks and recurrent neural networks. We present statistical inference and graph theory in order to introduce probabilistic networks, such as generative models, random graphs, graphical models and complex networks. We discuss the modelling of sequential data and its application to sequence to sequence learning in natural language (NL). We introduce the Transformer model and discuss pre-training techniques in language understanding and language generation. Using stochastic control theory and dynamic programming, we introduce temporal difference (TD) learning and its extensions, discuss Deep BSDE, present reinforcement learning (RL) and deep RL, detailing various algorithms for learning the optimal policy. Then, we introduce constrained optimisation and global search optimisation, and discuss the use of machine learning for solving some continuous and discrete optimisation problems. Finally, we apply supervised and reinforcement learning to the pricing and hedging of option prices.