Publikation
Learning Large DAGs is Harder than you Think: Many Losses are Minimal for the Wrong DAG
Jonas Seng; Matej Zecevic; Devendra Singh Dhami; Kristian Kersting
In: The Twelfth International Conference on Learning Representations, ICLR 2024, Vienna, Austria, May 7-11, 2024. International Conference on Learning Representations (ICLR), OpenReview.net, 2024.
Zusammenfassung
Structure learning is a crucial task in science, especially in fields such as medicine
and biology, where the wrong identification of (in)dependencies among random
variables can have significant implications. The primary objective of structure
learning is to learn a Directed Acyclic Graph (DAG) that represents the underlying
probability distribution of the data. Many prominent DAG learners rely on least
square losses or log-likelihood losses for optimization. It is well-known from
regression models that least square losses are heavily influenced by the scale of
the variables. Recently it has been demonstrated that the scale of data also affects
performance of structure learning algorithms, though with a strong focus on linear
2-node systems and simulated data. Moving beyond these results, we provide
conditions under which square-based losses are minimal for wrong DAGs in d-
dimensional cases. Furthermore, we also show that scale can impair performance
of structure learners if relations among variables are non-linear for both square
based and log-likelihood based losses. We confirm our theoretical findings through
extensive experiments on synthetic and real-world data.