# 252-0526-00L Statistical Learning Theory

Semester | Spring Semester 2019 |

Lecturers | J. M. Buhmann |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | The course covers advanced methods of statistical learning : Statistical learning theory;variational methods and optimization, e.g., maximum entropy techniques, information bottleneck, deterministic and simulated annealing; clustering for vectorial, histogram and relational data; model selection; graphical models. |

Learning objective | The course surveys recent methods of statistical learning. The fundamentals of machine learning as presented in the course "Introduction to Machine Learning" are expanded and in particular, the theory of statistical learning is discussed. |

Content | # Theory of estimators: How can we measure the quality of a statistical estimator? We already discussed bias and variance of estimators very briefly, but the interesting part is yet to come. # Variational methods and optimization: We consider optimization approaches for problems where the optimizer is a probability distribution. Concepts we will discuss in this context include: * Maximum Entropy * Information Bottleneck * Deterministic Annealing # Clustering: The problem of sorting data into groups without using training samples. This requires a definition of ``similarity'' between data points and adequate optimization procedures. # Model selection: We have already discussed how to fit a model to a data set in ML I, which usually involved adjusting model parameters for a given type of model. Model selection refers to the question of how complex the chosen model should be. As we already know, simple and complex models both have advantages and drawbacks alike. # Statistical physics models: approaches for large systems approximate optimization, which originate in the statistical physics (free energy minimization applied to spin glasses and other models); sampling methods based on these models |

Lecture notes | A draft of a script will be provided; transparencies of the lectures will be made available. |

Literature | Hastie, Tibshirani, Friedman: The Elements of Statistical Learning, Springer, 2001. L. Devroye, L. Gyorfi, and G. Lugosi: A probabilistic theory of pattern recognition. Springer, New York, 1996 |

Prerequisites / Notice | Requirements: knowledge of the Machine Learning course basic knowledge of statistics, interest in statistical methods. It is recommended that Introduction to Machine Learning (ML I) is taken first; but with a little extra effort Statistical Learning Theory can be followed without the introductory course. |