Bayesian optimization : theory and practice using Python

This book covers the essential theory and implementation of popular Bayesian optimization techniques in an intuitive and well-illustrated manner. The techniques covered in this book will enable you to better tune the hyperparemeters of your machine learning models and learn sample-efficient approaches to global optimization. The book begins by introducing different Bayesian Optimization (BO) techniques, covering both commonly used tools and advanced topics. It follows a “develop from scratch” method using Python, and gradually builds up to more advanced libraries such as BoTorch, an open-source project introduced by Facebook recently. Along the way, you’ll see practical implementations of this important discipline along with thorough coverage and straightforward explanations of essential theories. This book intends to bridge the gap between researchers and practitioners, providing both with a comprehensive, easy-to-digest, and useful reference guide. After completing this book, you will have a firm grasp of Bayesian optimization techniques, which you’ll be able to put into practice in your own machine learning models. What You Will Learn Apply Bayesian Optimization to build better machine learning models Understand and research existing and new Bayesian Optimization techniques Leverage high-performance libraries such as BoTorch, which offer you the ability to dig into and edit the inner working Dig into the inner workings of common optimization algorithms used to guide the search process in Bayesian optimization Who This Book Is For Beginner to intermediate level professionals in machine learning, analytics or other roles relevant in data science. Table of Contents About the Author About the Technical Reviewer Acknowledgments Introduction Chapter 1: Bayesian Optimization Overview Global Optimization The Objective Function The Observation Model Bayesian Statistics Bayesian Inference Frequentist vs. Bayesian Approach Joint, Conditional, and Marginal Probabilities Independence Prior and Posterior Predictive Distributions Bayesian Inference: An Example Bayesian Optimization Workflow Gaussian Process Acquisition Function The Full Bayesian Optimization Loop Summary Chapter 2: Gaussian Processes Reviewing the Gaussian Basics Understanding the Covariance Matrix Marginal and Conditional Distribution of Multivariate Gaussian Sampling from a Gaussian Distribution Gaussian Process Regression The Kernel Function Extending to Other Variables Learning from Noisy Observations Gaussian Process in Practice Drawing from GP Prior Obtaining GP Posterior with Noise-Free Observations Working with Noisy Observations Experimenting with Different Kernel Parameters Hyperparameter Tuning Summary Chapter 3: Bayesian Decision Theory and Expected Improvement Optimization via the Sequential Decision-Making Seeking the Optimal Policy Utility-Driven Optimization Multi-step Lookahead Policy Bellman’s Principle of Optimality Expected Improvement Deriving the Closed-Form Expression Implementing the Expected Improvement Using Bayesian Optimization Libraries Summary Chapter 4: Gaussian Process Regression with GPyTorch Introducing GPyTorch The Basics of PyTorch Revisiting GP Regression Building a GP Regression Model Fine-Tuning the Length Scale of the Kernel Function Fine-Tuning the Noise Variance Delving into Kernel Functions Combining Kernel Functions Predicting Airline Passenger Counts Summary Chapter 5: Monte Carlo Acquisition Function with Sobol Sequences and Random Restart Analytic Expected Improvement Using BoTorch Introducing Hartmann Function GP Surrogate with Optimized Hyperparameters Introducing the Analytic EI Optimization Using Analytic EI Grokking the Inner Optimization Routine Using MC Acquisition Function Using Monte Carlo Expected Improvement Summary Chapter 6: Knowledge Gradient: Nested Optimization vs. One-Shot Learning Introducing Knowledge Gradient Monte Carlo Estimation Optimizing Using Knowledge Gradient One-Shot Knowledge Gradient Sample Average Approximation One-Shot Formulation of KG Using SAA One-Shot KG in Practice Optimizing the OKG Acquisition Function Summary Chapter 7: Case Study: Tuning CNN Learning Rate with BoTorch Seeking Global Optimum of Hartmann Generating Initial Conditions Updating GP Posterior Creating a Monte Carlo Acquisition Function The Full BO Loop Hyperparameter Optimization for Convolutional Neural Network Using MNIST Defining CNN Architecture Training CNN Optimizing the Learning Rate Entering the Full BO Loop Summary Index