Fast sequential Monte Carlo methods for counting and optimization 1st Edition by Reuven Rubinstein, Ad Ridder, Radislav Vaisman 1118612353 9781118612378

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Product details:

ISBN 10: 1118612353 

ISBN 13: 9781118612378

Author: Reuven Y. Rubinstein; Ad Ridder; Radislav Vaisman

A comprehensive account of the theory and application of Monte Carlo methods Based on years of research in efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization, Fast Sequential Monte Carlo Methods for Counting and Optimization is a complete illustration of fast sequential Monte Carlo techniques. The book provides an accessible overview of current work in the field of Monte Carlo methods, specifically sequential Monte Carlo techniques, for solving abstract counting and optimization problems. Written by authorities in the field, the book places emphasis on cross-entropy, minimum cross-entropy, splitting, and stochastic enumeration. Focusing on the concepts and application of Monte Carlo techniques, Fast Sequential Monte Carlo Methods for Counting and Optimization includes: Detailed algorithms needed to practice solving real-world problems Numerous examples with Monte Carlo method produced solutions within the 1-2% limit of relative error A new generic sequential importance sampling algorithm alongside extensive numerical results An appendix focused on review material to provide additional background information Fast Sequential Monte Carlo Methods for Counting and Optimization is an excellent resource for engineers, computer scientists, mathematicians, statisticians, and readers interested in efficient simulation techniques. The book is also useful for upper-undergraduate and graduate-level courses on Monte Carlo methods.

Table of contents:

Chapter 1 Introduction to Monte Carlo Methods
Chapter 2 Cross-Entropy Method
2.1. Introduction
2.2. Estimation of Rare-Event Probabilities
2.3. Cross-Entrophy Method for Optimization
2.3.1. The Multidimensional 0/1 Knapsack Problem
2.3.2. Mastermind Game
2.3.3. Markov Decision Process and Reinforcement Learning
2.4. Continuous Optimization
2.5. Noisy Optimization
2.5.1. Stopping Criterion

Chapter 3 Minimum Cross-Entropy Method
3.1. Introduction
3.2. Classic MinxEnt Method
3.3. Rare Events and MinxEnt
3.4. Indicator MinxEnt Method
3.4.1. Connection between CE and IME
3.5. IME Method for Combinatorial Optimization
3.5.1. Unconstrained Combinatorial Optimization
3.5.2. Constrained Combinatorial Optimization: The Penalty Function Approach

Chapter 4 Splitting Method for Counting and Optimization
4.1. Background
4.2. Quick Glance at the Splitting Method
4.3. Splitting Algorithm with Fixed Levels
4.4. Adaptive Splitting Algorithm
4.5. Sampling Uniformly on Discrete Regions
4.6. Splitting Algorithm for Combinatorial Optimization
4.7. Enhanced Splitting Method for Counting
4.7.1. Counting with the Direct Estimator
4.7.2. Counting with the Capture-Recapture Method
4.8. Application of Splitting to Reliability Models
4.8.1. Introduction
4.8.2. Static Graph Reliability Problem
4.8.3. BMC Algorithm for Computing S(Y)
4.8.4. Gibbs Sampler
4.9. Numerical Results with the Splitting Algorithms
4.9.1. Counting
4.9.2. Combinatorial Optimization
4.9.3. Reliability Models
4.10. Appendix: Gibbs Sampler

Chapter 5 Stochastic Enumeration Method
5.1. Introduction
5.2. OSLA Method and Its Extensions
5.2.1. Extension of OSLA: nSLA Method
5.2.2. Extension of OSLA for SAW: Multiple Trajectories
5.3. SE Method
5.3.1. SE Algorithm
5.4. Applications of SE
5.4.1. Counting the Number of Trajectories in a Network
5.4.2. SE for Probabilities Estimation
5.4.3. Counting the Number of Perfect Matchings in a Graph
5.4.4. Counting SAT
5.5. Numerical Results
5.5.1. Counting SAW
5.5.2. Counting the Number of Trajectories in a Network
5.5.3. Counting the Number of Perfect Matchings in a Graph
5.5.4. Counting SAT
5.5.5. Comparison of SE with Splitting and SampleSearch

Appendix A Additional Topics
A.1. Combinatorial Problems
A.1.1. Counting
A.1.2. Combinatorial Optimization
A.2. Information
A.2.1. Shannon Entropy
A.2.2. Kullback-Leibler Cross-Entropy
A.3. Efficiency of Estimators
A.3.1. Complexity
A.3.2. Complexity of Randomized Algorithms

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Tags: Reuven Rubinstein, Ad Ridder, Radislav Vaisman, sequential