Clustering and EM
Lecture by Klaus- ̈ller, TU Berlin 2022
Klaus- ̈ller Slides adapted from Haufe & Kindermans Lecture at TUB 2022
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Clustering
Klaus- ̈ller Lecture at TUB 2022
Klaus- ̈ller Lecture at TUB 2022
Density Estimation
Klaus- ̈ller Lecture at TUB 2022
Gaussian Mixture Model (GMM)
Klaus- ̈ller Lecture at TUB 2022
Gaussian Mixture Model (GMM)
Klaus- ̈ller Lecture at TUB 2022
Fitting a GMM using Maximum Likelihood
Klaus- ̈ller Lecture at TUB 2022
Fitting a GMM using EM
Klaus- ̈ller Lecture at TUB 2022
Fitting a GMM using EM: algorithm
Fitting a GMM using EM: algorithm
Klaus- ̈ller Lecture at TUB 2022
Fitting a GMM using EM
Klaus- ̈ller Lecture at TUB 2022
Fitting a GMM: comparison using EM
Fitting a GMM
Klaus- ̈ller Lecture at TUB 2022
Maximum Likelihood for latent variable models
Klaus- ̈ller Lecture at TUB 2022
Example: GMM
Expectation Maximization
Klaus- ̈ller Lecture at TUB 2022
Jensen‘s Inequality
Klaus- ̈ller Lecture at TUB 2022
A lower bound on the log-likelihood
Klaus- ̈ller Lecture at TUB 2022
Expectation Maximization
Klaus- ̈ller Lecture at TUB 2022
Maximization of lower bound
Klaus- ̈ller Lecture at TUB 2022
Expectation: improving q(z)
Klaus- ̈ller Lecture at TUB 2022
Expectation: improving q(z)
Klaus- ̈ller Lecture at TUB 2022
Expectation: improving q(z)
Klaus- ̈ller Lecture at TUB 2022
The Kullback-Leibler divergence
Klaus- ̈ller Lecture at TUB 2022
Expectation: improving q(z)
Maximization of the lower bound
Klaus- ̈ller Lecture at TUB 2022
Maximization: improving
Klaus- ̈ller Lecture at TUB 2022
Maximization: improving
Iterative Optimization
Klaus- ̈ller Lecture at TUB 2022
Iterative Optimization
Klaus- ̈ller Lecture at TUB 2022
Convergence to local maximum
Klaus- ̈ller Lecture at TUB 2022
EM summary
Klaus- ̈ller Lecture at TUB 2022
Why „Expectation“?
Klaus- ̈ller Lecture at TUB 2022
Fitting a GMM using EM: Expectation
Klaus- ̈ller Lecture at TUB 2022
Fitting a GMM using EM: Expectation
Fitting a GMM using EM: Maximization
Klaus- ̈ller Lecture at TUB 2022
Fitting a GMM using EM: Maximization
Klaus- ̈ller Lecture at TUB 2022
Klaus- ̈ller Lecture at TUB 2022
Properties
References
Klaus- ̈ller Lecture at TUB 2022
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