Bayesian Optimization : Theory and Practice Using Python 9781484290637, 9781484290620

Table of contents :
​ 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