Statistical Methods for AI

Course Objective

After this course, the student should be able to:

• summarize data informatively (graphical and numerical summaries for various kinds of data types), [Knowledge and understanding]
• apply various probabilistic and statistical procedures in different contexts (basic probability rules, law of total probability, Bayes' theorem, estimation of means proportions, and standard deviations, hypothesis tests about those and about categorical and bivariate data, in particular linear regression models) [Applying knowledge and understanding]
• interpret the results of the statistical procedures (conditional probabilities, expected values, outcomes of hypothesis tests, prediction in a linear regression context), [Making Judgements]
• compare different techniques in different situations and when to apply them (1- or 2-sample problems, dependent / independent data, variances known / unknown, test homogeneity between multiple populations or independence of variables within one population, test correlation or linear relationship, checking the assumptions underlying the different tests). [Making Judgements] [Applying knowledge and understanding]
• create informative and scientifically appropriate reports (i.e. a good mixture of figures and written text, completeness of the report, yet conciseness, question-related, and use of adequate language), [Applying knowledge and understanding] [Making judgements]
• communicate with colleagues about statistical topics (solve the assignments in groups of two students, solve theoretical exercises in groups of four to six students, being able to talk about the statistical subjects with other students, the teaching assistants, and the teacher of the course), [Communication]
• lose fear of complex mathematical formulas and develop further interest in statistical aspects in computer science (i.e. apply the formulas and understand what happens; get to know how other fields of science are touched by the course content) [Applying knowledge and understanding] [Lifelong learning skills]
• reflect on difficult content, learn how to use group work and discussions to overcome obstacles (express the problems in your own words, get immediate feedback in conversations with peers and the teacher/teaching assistant). [Making Judgements] [Lifelong learning skills] [Communication]

Course Content

• Summarising data;
• Basics of probability theory;
• Estimating means and fractions;
• Hypothesis testing for one- and two-sample problems about means and proportions;
• Correlation and linear regression;
• Contingency tables.

Additional Information Teaching Methods

• Lectures (10x2 hours; in general, two lectures per week), exercise classes (6x2 hours; in general, once per week), and computer classes
• (6x2 hours; in general, once per week).
• Attendance to all lectures and classes is not mandatory but strongly recommended.

Method of Assessment

Mandatory (group) assignments and exams (midterm and final, both mandatory). You will work on assignments during weekly computer classes.

In the case that one of the exams (midterm or final) is not passed, a resit exam can be taken which covers the whole lecture material. The final grade consists of the following components (with the indicated weights): the exam grade (75%) and the average assignment grade (25%).

The exam grade is either the weighted average of the midterm exam grade (40%) and the final exam grade (60%), or it is the resit exam grade (100%). Both, the exam grade and the overall grade have to be at least 5.5 in order to pass the course.
If the resit exam is written, the homework assignment grades still count towards the final course grade as explained above.
There is no resit possibility for the assignments.