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Stochastics and Machine Learning
Last Updated: 2026-06-03 00:14:30
Abstract
This 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.
Objective
Basic 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.
Content
Part 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
Resources
Lecture Notes
Slides will be made available.
Literature
L. Meier. Wahrscheinlichkeitsrechnung und Statistik: Eine Einführung für Verständnis, Intuition und Überblick. Springer, 2020 https://link.springer.com/book/10.1007/978-3-662-61488-4 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 https://www.bishopbook.com/ 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
Learning Materials (Links)
- Main link
- Course Website
General Information
- Language
- English
- Levels
- BSC , DR , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 120 minutes
- Aids
- Ten single-sided A4 pages (or five double-sided A4 pages) of notes. There are no constraints regarding content and layout (text, images, single/double page, margins, font size, etc.). Electronic devices and digital documents are not allowed, with the exception of a non-programmable pocket calculator.
- Digital
- The exam takes place on devices provided by ETH Zurich.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Stochastics and Machine Learning
Unterricht im HG F 7 mit Videoübertragung ins HG F 5.
|
|
2 h weekly |
| lecture with exercise |
Stochastics and Machine Learning
Findet am Freitag Nachmittag im HG F1 mit Videoübertragung ins HG F3 statt.
|
|
1 h weekly |
| exercise | Stochastics and Machine Learning |
|
2 h weekly |