Machine Learning for Risk Calculations : A Practitioner's View

Cover -- Title Page -- Copyright Page -- Contents -- Acknowledgements -- Foreword -- Motivation and aim of this book -- Part One Fundamental Approximation Methods -- Chapter 1 Machine Learning -- 1.1 Introduction to Machine Learning -- 1.1.1 A brief history of Machine Learning Methods -- 1.1.2 Main sub‐categories in Machine Learning -- 1.1.3 Applications of interest -- 1.2 The Linear Model -- 1.2.1 General concepts -- 1.2.2 The standard linear model -- 1.3 Training and predicting -- 1.3.1 The frequentist approach -- 1.3.2 The Bayesian approach -- 1.3.3 Testing - in search of consistent accurate predictions -- 1.3.4 Underfitting and overfitting -- 1.3.5 K‐fold cross‐validation -- 1.4 Model complexity -- 1.4.1 Regularisation -- 1.4.2 Cross‐validation for regularisation -- 1.4.3 Hyper‐parameter optimisation -- Chapter 2 Deep Neural Nets -- 2.1 A brief history of Deep Neural Nets -- 2.2 The basic Deep Neural Net model -- 2.2.1 Single neuron -- 2.2.2 Artificial Neural Net -- 2.2.3 Deep Neural Net -- 2.3 Universal Approximation Theorems -- 2.4 Training of Deep Neural Nets -- 2.4.1 Backpropagation -- 2.4.2 Backpropagation example -- 2.4.3 Optimisation of cost function -- 2.4.4 Stochastic gradient descent -- 2.4.5 Extensions of stochastic gradient descent -- 2.5 More sophisticated DNNs -- 2.5.1 Convolution Neural Nets -- 2.5.2 Other famous architectures -- 2.6 Summary of chapter -- Chapter 3 Chebyshev Tensors -- 3.1 Approximating functions with polynomials -- 3.2 Chebyshev Series -- 3.2.1 Lipschitz continuity and Chebyshev projections -- 3.2.2 Smooth functions and Chebyshev projections -- 3.2.3 Analytic functions and Chebyshev projections -- 3.3 Chebyshev Tensors and interpolants -- 3.3.1 Tensors and polynomial interpolants -- 3.3.2 Misconception over polynomial interpolation -- 3.3.3 Chebyshev points -- 3.3.4 Chebyshev interpolants.