**Project Heads**

*Carlos Enrique Améndola Cerón*

**Project Members**

Kamillo Hugh Ferry

**Project Duration**

01.04.2023 – 31.03.2026

**Located at**

TU Berlin

Above connection between our models and tropical geometry manifests itself in a tropical polytope that we can associate to the model parameters. The immediate goal is then to study the combinatorics of these tropical polytopes, e.g. to see if all possible combinatorial types arise from a max-linear Bayesian network or which actually do appear.

Above question is interesting in its own right, but it also serves as an intermediate step to the next goal. It is known that whether certain inequalities between the model parameters hold or not can lead to radically different conditional independence (CI) behavior on the same network. Thus, we aim to determine whether the combinatorics of the tropical polytope of a max-linear Bayesian network can reveal CI statements between subsets of variables, and viceversa.

Since max-linear Bayesian networks are a type of graphical model, one can also derive CI statements from the underlying graph structure. For other types of graphical models, like Gaussian networks, there exist separation but also algebraic criteria for conditional independence. Thus, we aim to find similar criteria in the max-linear Bayesian case.

**Project Webpages**

**Selected Publications
**

**Selected Pictures
**

These are *graphical models* with recursive structural equations in the *max-times semiring*. One example is given right above.

yield conditional independence statements. This means we can reason about the conditional independence of variables in our model by turning to reachability in the underlying graph. In above case, we can conclude that 1 is independent from 3 given 4 and 5, which means that knowing 1 and then finding out about 4 and 5 does not give any information about 3, at least in a max-linear Bayesian network.

Please insert any kind of pictures (photos, diagramms, simulations, graphics) related to the project in the above right field (Image with Text), by choosing the green plus image on top of the text editor. (You will be directed to the media library where you can add new files.)

(We need pictures for a lot of purposes in different contexts, like posters, scientific reports, flyers, website,…

Please upload pictures that might be just nice to look at, illustrate, explain or summarize your work.)

As Title in the above form please add a copyright.

And please give a short description of the picture and the context in the above textbox.

Don’t forget to press the “Save changes” button at the bottom of the box.

If you want to add more pictures, please use the “clone”-button at the right top of the above grey box.