Probabilistic graphical models (PGMs) represent the world in a simple way that humans can understand better.
They are graphical representations to understand the complex relationships between a set of random variables of interest (nodes). The edges that connect these nodes show the statistical dependencies between them.
PGMs have numerous applications in social and behavioral sciences, life sciences, economics, computer science, and many more fields.
In this introductory course, two types of graphical models are briefly introduced: undirected (Markov random fields) and directed (Bayesian networks). I will discuss how we can apply these models to estimate the dependencies between variables of interest in the form of a network. We will review excellent real-world examples and exercises (using R) to reinforce learning.
This course will open a new door for you and enable you to see the dependencies from a network point of view, which is much more comprehensive.
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In this one-day course, first of all, probabilistic graphical models (PGMs) will be introduced in general along with some applications of PGMs in real life. We will clarify what we mean by edges and nodes in PGMs. Then, the concept of (conditional) dependency and independency will be looked into, including how edges and lack of edges can be interpreted based on these concepts. Then some terminologies used in PGMs will be introduced. After that various types of PGMs, namely Markov random fields (MRFs) and Bayesian networks (BNs) will be presented. In MRFs, we will elaborate on how network structure can be estimated from continuous data (Graphical lasso approach) as well as from discrete data (Ising model). In BNs, the concept of (conditional) (in)dependency and their relations to the edge and lack of edges will be discussed, after which we will go through the concepts of the path, blocked path, and d-separation, which simplifies the understanding of conditional (in)dependencies between variables. Afterward, different types of BNs used for estimating the network structure will be discussed. Conditional independence test and network score, two well-known approaches for network inference, will be explained. Lastly, we will briefly compare MRFs and BNs, then discuss when we should use which method. There is a practical exercise after each lecture. You will work on these exercises in R to get experience with the material from the lectures and to practice how the network structure can be estimated from some real data sets. As a prerequisite, participants should be familiar with basic statistics including probability theory, and basic R programming. Please note that R and RStudio should be installed on your own laptop in advance. The software is available online.
In case you have trouble installing, watch the following:
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Lecturers
Mahdi Shafiee Kamalabad
Target audience
Researchers, students, engineers, and analysts.
A maximum of 20 participants will be accepted to this course.
For an overview of all our summer school courses offered by the Department of Methodology and Statistics please click here.
Aim of the course
The aim of this course is to provide fundamental knowledge of graphical models for network inference for, for example, medical scientists, psychologists, biologists, economists, and other researchers who wish to learn the network structure in order to discover the relationships between variables of interest.
Study load
One day (10.00 – 17.00). Lectures and computer lab exercises will be alternated during this informal one-day workshop.
Please note that there are no graded activities included in this course. Therefore, we are not able to provide students with a transcript of grades. You will obtain a certificate upon completion of this course.
Costs
- Tuition fee for PhD students from the Faculty of Social and Behavioural Sciences from Utrecht University will be funded by the Graduate School of Social and Behavioural Sciences.
- The tuition fee for staff off the Faculty of Social and Behavioural Sciences from Utrecht University will be funded by FSBS
Utrecht Summer School does not offer scholarships for this course.
Contact details
Irma Reyersen | E: ms.summerschool@uu.nl