Mixture Models and Applications 1st Edition by Nizar Bouguila, Wentao Fan ISBN 303023875X 9783030238766

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ISBN 10: 303023875X 
ISBN 13: 9783030238766
Author: Nizar Bouguila, Wentao Fan

This book focuses on recent advances, approaches, theories and applications related to mixture models. In particular, it presents recent unsupervised and semi-supervised frameworks that consider mixture models as their main tool. The chapters considers mixture models involving several interesting and challenging problems such as parameters estimation, model selection, feature selection, etc. The goal of this book is to summarize the recent advances and modern approaches related to these problems. Each contributor presents novel research, a practical study, or novel applications based on mixture models, or a survey of the literature.

• Reports advances on classic problems in mixture modeling such as parameter estimation, model selection, and feature selection;
• Present theoretical and practical developments in mixture-based modeling and their importance in different applications;
• Discusses perspectives and challenging future works related tomixture modeling.

Mixture Models and Applications 1st Table of contents:

• Chapter 1: Basic Concepts of Mixture Models

  • Definition and Structure of Mixture Models
  • The Concept of Latent Variables
  • Types of Mixture Models (Gaussian, Poisson, etc.)
  • Basic Statistical Properties

• Chapter 2: Theoretical Foundations

  • Probability Distributions and Mixture Components
  • The Expectation-Maximization (EM) Algorithm
  • Maximum Likelihood Estimation (MLE) for Mixture Models
  • Identifiability Issues and Model Complexity

• Chapter 3: Estimation Methods

  • Overview of Estimation Techniques
  • The Expectation-Maximization Algorithm in Detail
  • Bayesian Inference and Markov Chain Monte Carlo (MCMC)
  • Other Estimation Methods (e.g., Maximum A Posteriori, Variational Methods)

• Chapter 4: Model Selection and Diagnostics

  • Criteria for Model Selection (AIC, BIC, Cross-Validation)
  • Diagnostic Tools for Assessing Fit (Residuals, Log-Likelihood, etc.)
  • Overfitting and Underfitting in Mixture Models
  • Model Comparison and Validation Techniques

• Chapter 5: Applications in Clustering and Classification

  • Using Mixture Models for Cluster Analysis
  • Gaussian Mixture Models in Unsupervised Learning
  • Classification and Labeling with Mixture Models
  • Case Studies in Clustering Applications

• Chapter 6: Applications in Image Analysis and Signal Processing

  • Mixture Models for Image Segmentation
  • Pixel Classification in Image Processing
  • Application of Mixture Models in Signal Denoising
  • Examples from Medical Imaging

• Chapter 7: Mixture Models in Finance and Risk Management

  • Financial Time Series Data and Mixture Models
  • Application in Portfolio Management and Asset Pricing
  • Mixture Models for Risk Assessment and Value-at-Risk Estimation
  • Case Studies in Financial Modeling

• Chapter 8: Handling Complex Data with Mixture Models

  • Multivariate Mixture Models
  • Non-Gaussian Mixture Models
  • Dealing with Missing Data in Mixture Models
  • Applications in High-Dimensional Data

• Chapter 9: Advanced Topics in Mixture Models

  • Dirichlet Process Mixture Models
  • Finite Mixture Models vs. Infinite Mixture Models
  • Copula Models and Mixture Models
  • Nonparametric and Semi-Parametric Models

• Chapter 10: Software and Computational Tools

  • Overview of Software Packages for Mixture Models (e.g., R, Python)
  • Implementing the EM Algorithm in Practice
  • Computational Challenges and Solutions
  • Case Studies Using R or Python for Mixture Models

• Chapter 11: Future Directions in Mixture Models

  • Emerging Trends and Research Areas
  • Applications in Big Data and Machine Learning
  • Challenges in Estimation and Scalability
  • New Algorithms and Approaches in Mixture Models

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Nizar Bouguila,Wentao Fan,Mixture Models,Applications