Finite Mixture Models: Parameter Estimation Techniques

Explore parameter estimation techniques for Finite Mixture Models, including MLE, EM algorithm, Bayesian methods, and more.

misc•Nov 1, 2024

Finite Mixture Models: Parameter Estimation Techniques

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Table of Contents

Finite Mixture Models: Parameter Estimation Techniques
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2. Basics of Finite Mixture Models
2.1 Key Parts and Terms
2.2 Where They're Used
3. What You Need to Know First
3.1 Statistics Basics
3.2 Probability Distributions
4. Parameter Estimation Basics
4.1 Why It Matters and What's Difficult
4.2 Main Approaches
5. Maximum Likelihood Estimation (MLE)
5.1 How MLE Works
5.2 MLE in Finite Mixture Models
6. Expectation-Maximization (EM) Algorithm
6.1 What is the EM Algorithm?
6.2 E-step and M-step Explained
7. Method of Moments
7.1 How It Works and When to Use It
7.2 The Good, The Bad, and The MoM-ly
8. Bayesian Methods
8.1 Basics of Bayesian Estimation
8.2 MCMC and Gibbs Sampling
9. Kolmogorov-Smirnov Distance Estimators
9.1 How It Works
9.2 Using It and Comparing to Other Methods
10. Putting It Into Practice
10.1 Useful Tools and Software
10.2 Common Mistakes to Avoid
11. Checking Your Results
11.1 Ways to Measure Accuracy
11.2 Using Cross-validation
12. Advanced Methods
12.1 Maximum Mean Discrepancy Method
12.2 Working with Large Datasets
13. Solving Common Problems
13.1 Dealing with Convergence and Identifiability
14. Real-World Example
14.1 Step-by-Step Case Study
15. Wrap-Up
Key Points and Best Practices
What's Next in This Field
FAQs
What is the expectation maximization algorithm for Gaussian mixture models?

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