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A digital twin (DT) leverages a virtual representation of the physical world, along with communication (e.g., 6G), computing (e.g., edge computing), and artificial intelligence (AI) technologies to enable many connected intelligence services. In order to handle the large amounts of network data based on digital twins (DTs), wireless systems can exploit the paradigm of semantic communication (SC) for facilitating informed decision-making under strict communication constraints by utilizing AI techniques such as causal reasoning.

In the past decade, the emergence of beyond fifth generation (B5G) wireless networks has necessitated the timely updating of system states in Internet of Things (IoT) and cyber-physical systems, where Age of Information (AoI) has been a well-concentrated metric. However, the content-agnostic nature of AoI reflects its limitation of characterizing the significance of status update messages, which induces various variants for AoI including Age of Incorrect Information (AoII).

We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone Variational Inequality (VI) formulation, we cast the causal discovery problem as a general convex optimization. Furthermore, we develop a non-asymptotic recovery guarantee and quantifiable uncertainty by solving a linear program to establish confidence intervals for a wide range of non-linear monotone link functions.