Thematic Statistics seminar:
Speaker: Tom Claassen (Radboud University Nijmegen)
Title: Causal discovery from real-world data: relaxing the faithfulness assumption
Time: 15:00-16:00, 17th of May, 2019
Location: room 412, Snellius building, MI, Leiden University, Niels Bohrweg 1

Abstract:
The so-called causal Markov and causal faithfulness assumptions are well-established pillars behind causal discovery from observational data. The first is closely related to the memorylessness property of dynamical systems, and allows us to predict observable conditional independencies in the data from the underlying causal model. The second is the causal equivalent of Ockham’s razor, and enables us to reason backwards from data to the causal model of interest.
Though theoretically reasonable, in practice with limited data from real-world systems we often encounter violations of faithfulness. Some of these, like weak long-distance interactions, are handled surprisingly well by benchmark constraint-based algorithms such as FCI. Other violations may imply inconsistencies between observed (conditional) independence statements in the data that cannot currently be handled both effectively and efficiently by most constraint based algorithms. A fundamental question is whether our output retains any validity when not all our assumptions are satisfied, or whether it is still possible to reliably rescue parts of the model.
In this talk we introduce a novel approach based on a relaxed form of the faithfulness assumption that is able to handle many of the detectable faithfulness violations efficiently while ensuring the output causal model remains valid. Essentially we obtain a principled and efficient form of error-correction on observed in/dependencies, that can significantly improve both accuracy and reliability of the output causal models in practice. True; it cannot handle all possible violations, but the relaxed faithfulness assumption may be a promising step towards a more realistic, and so more effective, underpinning of the challenging task of causal discovery from real-world systems.

Bayes club:
Speaker: Stefan Franssen (Leiden University)
Title: Uncertainty quantification with species sampling processes
Time: 16:00-17:00, 17th of May, 2019
Location: room 412, Snellius building, MI, Leiden University, Niels Bohrweg 1

Abstract:
In this talk, we will introduce a class of species sampling process priors with independent relative stick-breaking weights which include the Dirichlet process and more generally the Pitman-Yor process. We will see a couple of results that make the latter two classes special. We will study the theoretical performance of the class by means of consistency theorems and prove Bernstein-von Mises theorems in two cases. We will first show the Bernstein-von Mises theorem for the Pitman-Yor prior, and then for a larger class of priors, we will show a Bernstein-von Mises theorem for atomless $P_0$.