252-0870-00L  Stochastics and Machine Learning

SemesterFrühjahrssemester 2024
DozierendeP. Cheridito, C. Cotrini Jimenez, A. Streich
Periodizitätjährlich wiederkehrende Veranstaltung

KurzbeschreibungThis is an introduction to probability, statistics, and machine learning for students of mechanical engineering. We cover the fundamental concepts from probability theory, statistics and machine learning, with a focus on applications for mechanical engineering.
LernzielBasic notions of probability theory and statistics such as probability space, probability measure, random variables, expected value, variance, covariance, standard deviation, correlation, quantiles, conditional distributions, parameter estimation, statistical tests, linear regression

Learn the fundamentals of machine learning: training, testing, validation, model selection.

Learn essential Python libraries for machine learning: scikit-learn, pytorch, gym.

Understand the mathematical foundations of diverse ML algorithms: empirical risk minimization, bias-variance tradeoff, stochastic gradient descent, back propagation, Bellman equations.

Learn how to preprocess data for machine learning.

Acquire an overview of the trending applications of machine learning for mechanical engineering.
InhaltPart I: Stochastics

Probability space, probability measure, independence, conditional probabilities, Bayes’ theorem, random variables, probability mass functions, densities, distributions, expected value, variance, covariance, standard deviation, correlation, random vectors, multivariate distributions, law of large numbers, central limit theorem, descriptive statistics, histograms, box plots, empirical distributions, parameter estimation, statistical tests

Part II: Machine learning

Linear and logistic regression. Basic regression and classification with machine learning
Regularization and bias-variance tradeoff
Ensembles and unsupervised learning
Deep learning, neural networks, convolutional neural networks, and transformers
Autoencoders, GANs
Reinforcement learning, Markov decision processes, Q learning
SkriptSlides will be made available.
LiteraturL. Meier. Wahrscheinlichkeitsrechnung und Statistik: Eine Einführung für Verständnis, Intuition und Überblick. Springer, 2020

J.A. Rice Mathematical Statistics and Data Analysis, Third Edition. Thomson, 2007.

C. Bishop. Pattern Recognition and Machine Learning. Springer 2007.

C. Bishop. Deep Learning - Foundations and Concepts. Springer 2024

T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical
Learning: Data Mining, Inference, and Prediction; Second Edition. Springer, 2009.

Peter Norvig, Stuart Russell: Artificial Intelligence: A Modern Approach, Global 4th Edition. Pearson 2021
Voraussetzungen / BesonderesLinear algebra I & II
Analysis I & II
Informatik I & II
Fachspezifische KompetenzenKonzepte und Theoriengeprüft
Verfahren und Technologiengefördert
Methodenspezifische KompetenzenAnalytische Kompetenzengeprüft
Medien und digitale Technologiengefördert
Soziale KompetenzenKommunikationgefördert
Kooperation und Teamarbeitgefördert
Menschenführung und Verantwortunggefördert
Sensibilität für Vielfalt gefördert
Persönliche KompetenzenAnpassung und Flexibilitätgefördert
Kreatives Denkengefördert
Kritisches Denkengeprüft
Integrität und Arbeitsethikgefördert
Selbstbewusstsein und Selbstreflexion gefördert
Selbststeuerung und Selbstmanagement gefördert