**Instructors:** Nathan Ratliff and Marc Toussaint

Machine Learning & Robotics Lab, IPVS, University of Stuttgart.

*Co-listed with Theoretical and Methodological Foundations of Autonomous Systems*

*If you’re attending the course but aren’t yet on the course mailing list, please email Nathan Ratliff to be added.* Important information regarding lectures, notes, homework, solutions, etc. is broadcast via the mailing list.

### Time:

**Lessons:**Thurs 15:45-17:15 at room 0.463**Tutorial:**Tue 17:30-19:00 at room 0.108**Office hours:**Nathan – Thurs 14:00-15:00 at room 2.228

*Zielgruppe:* Master-Studiengang Informatik (Vertiefungslinien und Katalog MINF), Diplom-Studiengang Informatik (Hauptstudium), Master-Studiengang Softwaretechnik (Vertiefungslinien), Diplom-Studiengang Softwaretechnik (Hauptstudium), International Master in Computer Science – Studienprofil AUT

### Description

This course prepares students for further study of autonomous robotic and learning systems. Methodologies in autonomous systems are highly mathematical and require on a concrete understanding of core areas such as linear algebra, functional analysis, differential geometry, optimization, probability, statistics, and decision theory. The course especially emphasizes geometric intuition behind more abstract ideas with concrete examples taken from robotics and machine learning. The first half of the course covers topics from higher mathematics that form the backbone and description language for many of the advanced tools and modeling techniques used in machine learning and robotics, and second half builds the theoretical foundations of decision theory exploring important tools from probability and statistics along the way. Specific topics include, coordinate free linear algebra, numerical linear algebra, multidimensional quadratic functions and Gaussians, algorithmic covariance, the method of lagrange multipliers and KKT conditions in optimization, probabilistic graphical models, Monte Carlo sampling, maximum likelihood and maximum entropy, statistical bounds, Markov decision processes, hidden Markov models, spectral algorithms, and more.

### Topics:

- Coordinate free Linear Algebra
- Review of Vector Calculus and some Differential Geometry
- Optimization
- Probability
- Statistics
- Decision theory

**Reference material.** (Books, links, etc.)

### Homework policy

Homework shapes your understanding of the material and gives you an opportunity to think critically about the concepts and their application. We’ll have **weekly homework assignments**, and we’ll discuss the solutions during the Tutorial sections. The homework, itself, doesn’t affect your final grade, but **you need to have done at least 50% of the problems in order to take the final exam**. (That’s 50% total, not on a per-week basis.)

Note again, though, that doing the homework is a very important part of the learning process, especially for this material. Please try your hand at each of the problems. During the tutorial section, if you have a solution that makes sense to you, mark down that you’ve done the problem. Even if the solution ends up begin “wrong”, it’s more important that it makes sense to you, and that though the discussion you revise your understanding so that you ultimately find the mistake and the correct solution makes sense. These problems are meant to be difficult, and in some cases more difficult than what I’d expect you to answer on the fly during a test. But doing them will force you to come to terms with what you do and do not understand, which itself is sometimes unclear initially with complicated topics.

### Schedule, slides & exercises

Date | Lecture | Notes & References | Homework |
---|---|---|---|

16.10.14 | Introduction to the course and coordinate free linear algebra | Lecture 1 notes | Homework 1 |

23.10.14 | Linear algebra II: SVD, Eigenvectors, fundamental spaces | Lecture 2 notes | Homework 2 |

30.10.14 | Linear algebra III: Computation in coordinates | Lecture 3 notes | Homework 3 |

06.11.14 | Linear algebra IV: Eigen-algorithms | Same as previous notes. | Homework 4 |

20.11.14 | Multi-dimensional calculus | Lecture 5 notes | Homework 5 |

27.11.2014 | Smooth Mappings and Linear Algebra | Lecture 6 notes | Homework 6 Software (manipulator Jacobian) |

04.12.14 | Optimization I: Analytical optimization | Lecture 7 notes | Homework 7 |

11.12.14 | Optimization II: Numeric methods | Lecture 8 notes (preliminary) | Homework 8 Links to software and data |

18.12.14 | None! Canceled. Christmas! | ||

08.01.15 | Probability I: The multi-dimensional basics | Lecture 9 notes | Homework 9 |

15.01.15 | Review | Review homework | |

22.01.15 | Probability II: Maximum Likelihood and Structured in Probability and Optimization | Lecture 11 notes | Homework 11 |

29.01.15 | Statistical Bounds and Information Theory | Lecture 12 notes I - Information Geometry and Natural Gradients Lecture 12 notes II - Statistical bounds | Homework 12 |

05.02.15 | Decision theory | Lecture 13 notes | Homework 13 |

12.02.15 | Review and interesting applications |