Beijing Institute of Mathematical Sciences and Applications

Song Cheng , Da Wei Ding , Jin Peng Liu , Zheng Wei Liu , Ziwen Liu

Xingjian Zhang

Friday, November 22, 2024 4:00 PM - 5:30 PM

Shuangqing-B627

Zoom 230 432 7880 (BIMSA)

Understanding causal relationships is an everlasting theme of scientific research. To interpret correlations between observed variables, a natural thought suggests causal explanations. In classical causal theories, all the variables, including both observed and latent ones, are modelled as random variables. However, as shown by the renowned Bell’s theorem, the classical formulation is incomplete when the latent variables enjoy a quantum nature. In this talk, I will present a new causal model formulated solely from the concept of independence. At a high level, we treat every causal structure as a low-dimensional projection from a high-dimensional Bell-type structure, where valid correlations among observed variables are projected from correlations in the Bell-type structure subjected to the independence conditions. We prove this formulation comprises all the predictions in generalized probabilistic theories. From a mathematical perspective, it reproduces the nested Markov model, an algebraically complete causal model defined by all the equality constraints within a causal structure. Moreover, we show inequality constraints may emerge from the projection of the equality constraints of independence. Nevertheless, we also present causal structures where “physical operations” pose stringently additional inequality constraints. Considering the undebatable role of independence in physics and algebra, we suggest the new model supersets any physically motivated causal theory. If time allows, I will also discuss applications of the new model in causal inference and the discovery of non-classical causal structures.

http://arxiv.org/abs/2411.11614