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ویرایش: نویسندگان: Barbu A., Zhu S.-C سری: ISBN (شابک) : 9789811329708, 9789811329715 ناشر: Springer سال نشر: 2020 تعداد صفحات: 433 زبان: English فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 9 مگابایت
در صورت تبدیل فایل کتاب Monte Carlo methods به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
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Preface Contents About the Authors 1 Introduction to Monte Carlo Methods 1.1 Introduction 1.2 Motivation and Objectives 1.3 Tasks in Monte Carlo Computing 1.3.1 Task 1: Sampling and Simulation 1.3.2 Task 2: Estimating Quantities by Monte Carlo Simulation 1.3.3 Task 3: Optimization and Bayesian Inference 1.3.4 Task 4: Learning and Model Estimation 1.3.5 Task 5: Visualizing the Landscape References 2 Sequential Monte Carlo 2.1 Introduction 2.2 Sampling a 1-Dimensional Density 2.3 Importance Sampling and Weighted Samples 2.4 Sequential Importance Sampling (SIS) 2.4.1 Application: The Number of Self-Avoiding Walks 2.4.2 Application: Particle Filtering for Tracking Objectsin a Video 2.4.2.1 Application: Curve Tracking 2.4.3 Summary of the SMC Framework 2.5 Application: Ray Tracing by SMC 2.5.1 Example: Glossy Highlights 2.6 Preserving Sample Diversity in Importance Sampling 2.6.1 Parzen Window Discussion 2.7 Monte Carlo Tree Search 2.7.1 Pure Monte Carlo Tree Search 2.7.2 AlphaGo 2.8 Exercises References 3 Markov Chain Monte Carlo: The Basics 3.1 Introduction 3.2 Markov Chain Basics 3.3 Topology of Transition Matrix: Communication and Period 3.4 The Perron-Frobenius Theorem 3.5 Convergence Measures 3.6 Markov Chains in Continuous or Heterogeneous State Spaces 3.7 Ergodicity Theorem 3.8 MCMC for Optimization by Simulated Annealing 3.8.1 Page Rank Example 3.9 Exercises References 4 Metropolis Methods and Variants 4.1 Introduction 4.2 The Metropolis-Hastings Algorithm 4.2.1 The Original Metropolis-Hastings Algorithm 4.2.2 Another Version of the Metropolis-Hastings Algorithm 4.2.3 Other Acceptance Probability Designs 4.2.4 Key Issues in Metropolis Design 4.3 The Independence Metropolis Sampler 4.3.1 The Eigenstructure of the IMS 4.3.2 General First Hitting Time for Finite Spaces 4.3.3 Hitting Time Analysis for the IMS 4.4 Reversible Jumps and Trans-Dimensional MCMC 4.4.1 Reversible Jumps 4.4.2 Toy Example: 1D Range Image Segmentation 4.4.2.1 Jump-Diffusion 4.5 Application: Counting People 4.5.1 Marked Point Process Model 4.5.2 Inference by MCMC 4.5.3 Results 4.6 Application: Furniture Arrangement 4.7 Application: Scene Synthesis 4.8 Exercises References 5 Gibbs Sampler and Its Variants 5.1 Introduction 5.2 Gibbs Sampler 5.2.1 A Major Problem with the Gibbs Sampler 5.3 Gibbs Sampler Generalizations 5.3.1 Hit-and-Run 5.3.2 Generalized Gibbs Sampler 5.3.3 Generalized Hit-and-Run 5.3.4 Sampling with Auxiliary Variables 5.3.5 Simulated Tempering 5.3.6 Slice Sampling 5.3.7 Data Augmentation 5.3.8 Metropolized Gibbs Sampler 5.4 Data Association and Data Augmentation 5.5 Julesz Ensemble and MCMC Sampling of Texture 5.5.1 The Julesz Ensemble: A Mathematical Definitionof Texture 5.5.2 The Gibbs Ensemble and Ensemble Equivalence 5.5.3 Sampling the Julesz Ensemble 5.5.4 Experiment: Sampling the Julesz Ensemble 5.6 Exercises References 6 Cluster Sampling Methods 6.1 Introduction 6.2 Potts Model and Swendsen-Wang 6.3 Interpretations of the SW Algorithm 6.3.1 Interpretation 1: Metropolis-Hastings Perspective 6.3.2 Interpretation 2: Data Augmentation 6.4 Some Theoretical Results 6.5 Swendsen-Wang Cuts for Arbitrary Probabilities 6.5.1 Step 1: Data-Driven Clustering 6.5.2 Step 2: Color Flipping 6.5.3 Step 3: Accepting the Flip 6.5.4 Complexity Analysis 6.6 Variants of the Cluster Sampling Method 6.6.1 Cluster Gibbs Sampling: The ``Hit-and-Run\'\' Perspective 6.6.2 The Multiple Flipping Scheme 6.7 Application: Image Segmentation 6.8 Multigrid and Multi-level SW-cut 6.8.1 SW-Cuts at Multigrid 6.8.2 SW-cuts at Multi-level 6.9 Subspace Clustering 6.9.1 Subspace Clustering by Swendsen-Wang Cuts 6.9.2 Application: Sparse Motion Segmentation 6.10 C4: Clustering Cooperative and Competitive Constraints 6.10.1 Overview of the C4 Algorithm 6.10.2 Graphs, Coupling, and Clustering 6.10.3 C4 Algorithm on Flat Graphs 6.10.4 Experiments on Flat Graphs 6.10.5 Checkerboard Ising Model 6.10.6 C4 on Hierarchical Graphs 6.10.7 Experiments on Hierarchical C4 6.11 Exercises References 7 Convergence Analysis of MCMC 7.1 Introduction 7.2 Key Convergence Topics 7.3 Practical Methods for Monitoring 7.4 Coupling Methods for Card Shuffling 7.4.1 Shuffling to the Top 7.4.2 Riffle Shuffling 7.5 Geometric Bounds, Bottleneck and Conductance 7.5.1 Geometric Convergence 7.6 Peskun\'s Ordering and Ergodicity Theorem 7.7 Path Coupling and Exact Sampling 7.7.1 Coupling From the Past 7.7.2 Application: Sampling the Ising Model 7.8 Exercises References 8 Data Driven Markov Chain Monte Carlo 8.1 Introduction 8.2 Issues with Segmentation and Introduction to DDMCMC 8.3 Simple Illustration of the DDMCMC 8.3.1 Designing MCMC: The Basic Issues 8.3.2 Computing Proposal Probabilities in the Atomic Spaces: Atomic Particles 8.3.3 Computing Proposal Probabilities in Object Spaces: Object Particles 8.3.4 Computing Multiple, Distinct Solutions: Scene Particles 8.3.5 The Ψ-World Experiment 8.4 Problem Formulation and Image Models 8.4.1 Bayesian Formulation for Segmentation 8.4.2 The Prior Probability 8.4.3 The Likelihood for Grey Level Images 8.4.4 Model Calibration 8.4.5 Image Models for Color 8.5 Anatomy of Solution Space 8.6 Exploring the Solution Space by Ergodic Markov Chains 8.6.1 Five Markov Chain Dynamics 8.6.2 The Bottlenecks 8.7 Data-Driven Methods 8.7.1 Method I: Clustering in Atomic Spaces 8.7.2 Method II: Edge Detection 8.8 Computing Importance Proposal Probabilities 8.9 Computing Multiple Distinct Solutions 8.9.1 Motivation and a Mathematical Principle 8.9.2 A K-Adventurers Algorithm for Multiple Solutions 8.10 Image Segmentation Experiments 8.11 Application: Image Parsing 8.11.1 Bottom-Up and Top-Down Processing 8.11.2 Generative and Discriminative Methods 8.11.3 Markov Chain Kernels and Sub-Kernels 8.11.4 DDMCMC and Proposal Probabilities 8.11.4.1 Generative Models and Bayesian Formulation 8.11.4.2 Shape Models 8.11.4.3 Generative Intensity Models 8.11.4.4 Overview of the Algorithm 8.11.4.5 Discriminative Methods 8.11.4.6 Control Structure of the Algorithm 8.11.5 The Markov Chain Kernels 8.11.5.1 Boundary Evolution 8.11.5.2 Markov Chain Sub-Kernels 8.11.5.3 AdaBoost for Discriminative Probabilities for Face and Text 8.11.6 Image Parsing Experiments 8.12 Exercises References 9 Hamiltonian and Langevin Monte Carlo 9.1 Introduction 9.2 Hamiltonian Mechanics 9.2.1 Hamilton\'s Equations 9.2.2 A Simple Model of HMC 9.3 Properties of Hamiltonian Mechanics 9.3.1 Conservation of Energy 9.3.2 Reversibility 9.3.3 Symplectic Structure and Volume Preservation 9.4 The Leapfrog Discretization of Hamilton\'s Equations 9.4.1 Euler\'s Method 9.4.2 Modified Euler\'s Method 9.4.3 The Leapfrog Integrator 9.4.4 Properties of the Leapfrog Integrator 9.5 Hamiltonian Monte Carlo and Langevin Monte Carlo 9.5.1 Formulation of HMC 9.5.2 The HMC Algorithm 9.5.3 The LMC Algorithm 9.5.4 Tuning HMC 9.5.5 Proof of Detailed Balance for HMC 9.6 Riemann Manifold HMC 9.6.1 Linear Transformations in HMC 9.6.2 RMHMC Dynamics 9.6.3 RMHMC Algorithm and Variants 9.6.4 Covariance Functions in RMHMC 9.7 HMC in Practice 9.7.1 Simulated Experiments on Constrained NormalDistributions 9.7.2 Sampling Logistic Regression Coefficients with RMHMC 9.7.3 Sampling Image Densities with LMC: FRAME, GRADE and DeepFRAME 9.8 Exercises References 10 Learning with Stochastic Gradient 10.1 Introduction 10.2 Stochastic Gradient: Motivation and Properties 10.2.1 Motivating Cases 10.2.2 Robbins-Monro Theorem 10.2.3 Stochastic Gradient Descent and the Langevin Equation 10.3 Parameter Estimation for Markov Random Field (MRF) Models 10.3.1 Learning a FRAME Model with Stochastic Gradient 10.3.2 Alternate Methods of Learning for FRAME 10.3.3 Four Variants of the FRAME Algorithm 10.3.4 Experiments 10.4 Learning Image Models with Neural Networks 10.4.1 Contrastive Divergence and Persistent ContrastiveDivergence 10.4.2 Learning a Potential Energy for Images with Deep Networks: DeepFRAME 10.4.3 Generator Networks and Alternating Backward Propagation 10.4.4 Cooperative Energy and Generator Models 10.5 Exercises References 11 Mapping the Energy Landscape 11.1 Introduction 11.2 Landscape Examples, Structures, and Tasks 11.2.1 Energy-Based Partitions of the State Space 11.2.2 Constructing a Disconnectivity Graph 11.2.3 ELM Example in 2D 11.2.4 Characterizing the Difficulty (or Complexity) of Learning Tasks 11.3 Generalized Wang-Landau Algorithm 11.3.1 Barrier Estimation for GWL Mapping 11.3.2 Volume Estimation with GWL 11.3.3 GWL Convergence Analysis 11.4 GWL Experiments 11.4.1 GWL Mappings of Gaussian Mixture Models 11.4.1.1 GMM Energy and Gradient Computations 11.4.1.2 Experiments on Synthetic GMM Data 11.4.1.3 Experiments on GMMs of Real Data 11.4.2 GWL Mapping of Grammar Models 11.4.2.1 Learning Dependency Grammars 11.4.2.2 Energy Function of Dependency Grammar 11.4.2.3 Discretization of the Dependency Grammar Hypothesis Space 11.4.2.4 GWL Dependency Grammar Experiments and Curriculum Learning 11.5 Mapping the Landscape with Attraction-Diffusion 11.5.1 Metastability and a Macroscopic Partition 11.5.2 Introduction to Attraction-Diffusion 11.5.3 Attraction-Diffusion and the Ising Model 11.5.4 Attraction-Diffusion ELM Algorithm 11.5.5 Tuning ADELM 11.5.6 Barrier Estimation with AD 11.6 Mapping the SK Spin Glass Model with GWL and ADELM 11.7 Mapping Image Spaces with Attraction-Diffusion 11.7.1 Structure of Image Galaxies 11.7.2 Experiments 11.7.2.1 Digits 0–9 ELM in Latent Space 11.7.2.2 Ivy Texton ELM in Latent Space 11.7.2.3 Multiscale Ivy ELM in Latent Space 11.7.2.4 Cat Faces ELM in Latent Space 11.8 Exercises References Index