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The core idea of Monte Carlo (MC) methods is to perform computer simulations of a real-world system based on pseudo-random numbers. MC is applied in a large variety of research areas: physical sciences, computer sciences, engineering, statistics, finance, etc. Moreover, ideas that have originally been developed in the context of MC are meanwhile also in use for sampling problems in the area of machine learning. Although, being a simple and very direct approach to analyze a system, MC methods come with a lot of challenges, in particular, when sampling rare events or when systems have multiple time scales. In this seminar, we take a computer science perspective on Monte Carlo and cover different MC algorithms to tackle these challenges.
|7. 12.||Variance Reduction|
|14. 12.||Random Process Generation|
|4. 1.||Probabilistic Programming|
|11. 1.||Markov Chain Monte Carlo|
|18. 1.||Stochastic Gradient Descent|
|25. 1.||Rare Event Simulation and Cross-Entropy Method|
|1. 2.||Evolutionary Algorithms|
The final grade consists of: your presentation (50%), reports (40%), and participation during the seminar discussions (10%).
You should have successfully passed MfI3, the Statistics Lab, or a comparable course covering probability theory/statistics.