ADVANCED STATISTICAL INFERENCE
This course focuses on the principles of learning from data and quantification of uncertainty, by complementing and enriching the Machine Learning and Intelligent Systems course. In particular, the course is divided into two main parts that correspond to the supervised and unsupervised learning paradigms.
The presentation of the material follows a common thread based on the probabilistic data modeling approach, so that many classical algorithms, such as least squares and k-means, can be seen as special cases of inference problems for more general probabilistic models. Taking a probabilistic view also allows the course to derive inference algorithms for a class of nonparametric models that have close connections with neural networks and support vector machines. The focus is not on the algorithmic background of the methods, but rather on their mathematical and statistical foundations.
This advanced course is complemented by lab sessions to guide students through the design and validation of the methods developed during the lectures.
Sillabus
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Introduction
- Recap on linear algebra and calculus
- Overview of probability theory
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Supervised learning
- Linear regression
- Linear classification
- Bayesian classification
- Kernel methods for nonlinear regression and classification
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Unsupervised learning
- K-means and Kernel K_means
- Gaussian mixture models
- Principal component analysis (PCA) and Kernel PCA
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Advanced topics
- Gaussian Processes
- Variational inference
- Markov chain Monte Carlo