The seminar focuses on deeper understanding of selected unsupervised machine learning methods for students who already have basic knowledge of machine learning and probability models. The first half of the semester is devoted to methods of unsupervised learning using Bayesian inference (Dirichlet-Categorical models, Mixture of Categoricals, Mixture of Gaussians, Expectation Maximization, Gibbs sampling) and implementation of these methods on selected tasks. Other lectures will be devoted to clustering methods, componet analysis and unsupervised inspecting deep neural networks.
Students are expected to be familiar with basic probabilistic concepts, roughly in the extent of:
In the second half of the course, it will be an advantage for you if you know the basics of deep-learning methods. I recommend to attend
3. Dirichlet-Categorical probabilistic model, Modeling document collections Dirichlet-Categorical (by C.E.Rasmussen) Posteriors and Predictions Document collections (by C.E.Rasmussen) Categorical Mixture Models (by C.E.Rasmussen) Modeling Document Collections
5. Gibbs Sampling in Latent Dirichlet Allocation, Entropy, Assignment 1 Gibbs Sampling (by C.E.Rasmussen) Gibbs Sampling Latent Dirichlet allocation (by C.E.Rasmussen) Algorithms for LDA and Mixture of Categoricals Latent Dirichlet Allocation
Deadline: Nov 25, 23:59 10 points
Deadline: Dec 09 23:59 10 points
Deadline: Jan 20 23:59 10 points
Define Beta distribution, describe its parameters. Plot (roughly) the following distributions: Beta(1,1), Beta(0.1,0.1), Beta(10, 10).
Derive the posterior distribution from the prior (Beta distribution) and likelihood (Binomial distribution). Derive the predictive distribution for the Beta-Bernoulli posterior.
Explain Dirichlet distribution, describe its parameters. Plot (roughly) the following distributions: Dir(1,1,1), Dir(0.1,0.1,0.1), Dir(10, 10, 10).
Derive the posterior distribution from the prior (Dirichlet distribution) and likelihood (Multinomial distribution). Derive the predictive distribution for the Dirichlet-Categorical posterior.
Explain the "Mixture of Categoricals" model (a topic is assigned to each document) for Modeling document collections. Describe all its parameters and hyperparameters. From what distributions are they drawn? Describe the Expectation-Maximization algorithm for training such model.
Explain the Latent Dirichlet Allocation model (a topic is asigned to each word in each document). Describe all its parameters and hyperparameters. From what distributions are they drawn? What are the latent variables? Describe the learning algorithm.
Explain Collapsed Gibbs sampling. Choose one unsupervised task from the lectures (word alignment, tagging, segmentation) and describe the basic algorithm. What is annealing?
Explain Chinese Restaurant Process. What distributions does it generate? What is exchangeability? Explain its generalization to the Pitman-Yor process.
Explain the K-means and Gaussian Mixture model for clustering. What are the advantages of Gaussian Mixture model? Provide an example of clusters in 2D where K-means fails and where Gaussian Mixture model works well.
Explain Hierarchical Agglomerative clustering methods. What are their advantages over K-means? What linkage criteria do you know? Provide examples of clusters in 2D where these criteria fail.
What is t-SNE? How does it work? What is it used for?
What is Principal Component Analysis? How does it work? What is it used for? Explain it in a 2D example.
Christopher Bishop: Pattern Recognition and Machine Learning, Springer-Verlag New York, 2006 (read here)
Kevin P. Murphy: Machine Learning: A Probabilistic Perspective, The MIT Press, Cambridge, Massachusetts, 2012 (read here)
David Mareček, Jindřich Libovický, Tomáš Musil, Rudolf Rosa, Tomasz Limisiewicz: HIDDEN IN THE LAYERS: Interpretation of Neural Networks for Natural Language Processing. Institute of Formal and Applied Linguistics, 2020 (read_here)