Bayesian Statistics: Mixture Models by カリフォルニア大学サンタクルーズ校(University of California, Santa Cruz)
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Week 1 : Basic concepts on Mixture Models
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Introduction
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The R Environment for Statistical Computing
- 動画: 講座 Installing and using R. Duration: 5分
- 学習用教材: An Introduction to R. Duration: 45分
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Definition of mixture models
- 動画: 講座 Basic definitions. Duration: 25分
- 練習問題: Basic definitions 3 個の問題
- 動画: 講座 Mixtures of Gaussians. Duration: 10分
- 学習用教材: Example of a bimodal mixture of Gaussians. Duration: 3分
- 学習用教材: Example of a unimodal and skewed mixture of Gaussians. Duration: 3分
- 学習用教材: Example of a unimodal, symmetric and heavy tailed mixture of Gaussians. Duration: 3分
- 練習問題: Mixtures of Gaussians 2 個の問題
- ディスカッションのプロンプト: When are mixture models helpful? Duration: 15分
- 動画: 講座 Zero-inflated mixtures. Duration: 11分
- 学習用教材: Example of a zero-inflated negative binomial distribution. Duration: 3 分
- 学習用教材: Example of a zero-inflated log Gaussian distribution. Duration: 3分
- 練習問題: Zero-inflated distributions 2 個の問題
- テスト: Definition of Mixture Models 5 個の問題
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Likelihood function for mixture models
- 動画: 講座 Hierarchical representations. Duration: 7分
- 動画: 講座 Sampling from a mixture model. Duration: 5分
- 学習用教材: Sample code for simulating from a Mixture Model. Duration: 10分
- 受講生によるテストの実施: Simulating from a Mixture Model. Duration: 20分
- 動画: 講座 The likelihood function. Duration: 14分
- 練習問題: The likelihood function 2 個の問題
- 動画: 講座 Parameter identifiability. Duration: 10分
- 練習問題: Identifiability 2 個の問題
- テスト: Likelihood function for mixture models 2 個の問題
- 受講生によるテスト: Likelihood function for mixture models. Duration: 20分
- 他の受講生の課題を確認: Likelihood function for mixture models
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Week 2 : Maximum likelihood estimation for Mixture Models
- The EM algorithm for Mixture Models
- 動画: 講座 EM for general mixtures. Duration: 24分
- 動画: 講座 EM for location mixtures of Gaussians. Duration: 22分
- 動画: 講座 EM example 1. Duration: 12 分
- 学習用教材: Sample code for EM example 1. Duration: 10分
- 動画: 講座 EM example 2. Duration: 13分
- 学習用教材: Sample code for EM example 2. Duration: 10分
- ディスカッションのプロンプト: Mixtures of log-Gaussians. Duration: 10分
- 受講生によるテストの実施: The EM algorithm for zero-inflated mixtures. Duration: 1時間
- 受講生によるテスト: The EM algorithm for Mixture Models. Duration: 1 時間
- 他の受講生の課題を確認: The EM algorithm for Mixture Models
- The EM algorithm for Mixture Models
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Week 3 : Bayesian estimation for Mixture Models
- Markov chain Monte Carlo algorithms for Mixture Models
- 動画: 講座 Markov Chain Monte Carlo algorithms part 1. Duration: 12分
- 動画: 講座 Markov Chain Monte Carlo algorithms, part 2. Duration: 13分
- 動画: 講座 MCMC for location mixtures of normals Part 1. Duration: 19分
- 動画: 講座 MCMC for location mixtures of normals Part 2. Duration: 14分
- 動画: 講座 MCMC Example 1. Duration: 11分
- 学習用教材: Sample code for MCMC example 1. Duration: 10分
- 動画: 講座 MCMC Example 2. Duration: 11分
- 学習用教材: Sample code for MCMC example 2. Duration: 10分
- 受講生によるテストの実施: The MCMC algorithm for zero-inflated mixtures. Duration: 1 時間
- 受講生によるテスト: Markov chain Monte Carlo algorithms for Mixture Models. Duration: 1 時間
- 他の受講生の課題を確認: Markov chain Monte Carlo algorithms for Mixture Models
- Markov chain Monte Carlo algorithms for Mixture Models
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Week 4 : Applications of Mixture Models
- Applications of Mixture Models
- 動画: 講座 Density estimation using Mixture Models. Duration: 12分
- 動画: 講座 Density Estimation Example. Duration: 10分
- 学習用教材: Sample code for density estimation problems. Duration: 10分
- 受講生によるテスト: The EM algorithm and density estimation. Duration: 50分
- 受講生によるテスト: MCMC algorithms and density estimation. Duration: 50分
- 他の受講生の課題を確認: MCMC algorithms and density estimation
- Clustering
- Classification
- 動画: 講座 Mixture Models and naive Bayes classifiers. Duration: 21分
- 動画: 講座 Linear and quadratic discriminant analysis in the context of Mixture Models. Duration: 18分
- 動画: 講座 Classification example. Duration: 10分
- 学習用教材: Sample EM algorithm for classification problems. Duration: 10 分
- 受講生によるテスト: Classification. Duration: 45分
- 他の受講生の課題を確認: Classification
- Applications of Mixture Models
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Week 5 : Practical considerations
- Computational considerations for Mixture Models
- 動画: 講座 Numerical stability. Duration: 14分
- 学習用教材: Sample code to illustrate numerical stability issues. Duration: 10分
- 動画: 講座 Computational issues associated with multimodality. Duration: 11分
- 学習用教材: Sample code to illustrate multimodality issues 1. Duration: 10分
- 学習用教材: Sample code to illustrate multimodality issues 2. Duration: 10分
- テスト: Computational considerations for Mixture Models 3 個の問題
- Determining the number of components in a Mixture Model
- 動画: 講座 Bayesian Information Criteria (BIC). Duration: 10分
- 練習問題: Bayesian Information Criteria (BIC) 1 個の問題
- 動画: 講座 Bayesian Information Criteria Example. Duration: 10分
- 学習用教材: Sample code: Bayesian Information Criteria. Duration: 10分
- 受講生によるテスト: BIC for zero-inflated mixtures. Duration: 1 時間
- 他の受講生の課題を確認: BIC for zero-inflated mixtures
- 動画: 講座 Estimating the number of components in Bayesian settings. Duration: 9 分
- テスト: Estimating the number of components in Bayesian settings 4 個の問題
- 動画: 講座 Estimating the full partition structure in Bayesian settings. Duration: 18分
- ディスカッションのプロンプト: Simplifying Binder's expected loss function. Duration: 30分
- 動画: 講座 Example: Bayesian inference for the partition structure. Duration: 15分
- 学習用教材: Sample code for estimating the number of components and the partition structure in Bayesian models. Duration: 10分
- 練習問題: Estimating the partition structure in Bayesian models 4 個の問題
- Computational considerations for Mixture Models
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