Humans' trust in AI constitutes a pivotal element in fostering a synergistic relationship between humans and AI. This is particularly significant in the context of systems that leverage AI technology, such as autonomous driving systems and human-robot interaction. Trust facilitates appropriate utilization of these systems, thereby optimizing their potential benefits. If humans over-trust or under-trust an AI, serious problems such as misuse and accidents occur. To prevent over/under-trust, it is necessary to predict trust dynamics. However, trust is an internal state of humans and hard to directly observe. Therefore, we propose a prediction model for trust dynamics using dynamic structure equation modeling, which extends SEM that can handle time-series data. A path diagram, which shows causalities between variables, is developed in an exploratory way and the resultant path diagram is optimized for effective path structures. Over/under-trust was predicted with 90\% accuracy in a drone simulator task,, and it was predicted with 99\% accuracy in an autonomous driving task. These results show that our proposed method outperformed the conventional method including an auto regression family.

We extend the classical path analysis by showing that, for a singly-connected path diagram, the partial covariance of two random variables factorizes over the nodes and edges in the path between the variables. This result allows us to give an alternative explanation to some causal phenomena previously discussed by Pearl (2013), and to show that Simpson's paradox cannot occur in singly-connected path diagrams.

We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also prove some necessary and some sufficient conditions for distributional equivalence of BAPs which are used in an algorithmic ap- proach to compute (nearly) equivalent model structures. This allows us to infer lower bounds of causal effects. We also present applications to real and simulated datasets using our publicly available R-package.

DAG models with hidden variables present many difficulties that are absent when all nodes are observed. In particular, fully observed DAG models are identified and correspond to well-defined sets of distributions, whereas this is not true if nodes are unobserved. In this paper we characterize exactly the set of distributions given by a class of Gaussian models with one-dimensional latent variables. These models relate two blocks of observed variables, modeling only the crosscovariance matrix. We describe the relation of this model to the singular value decomposition of the cross-covariance matrix. We show that, although the model is underidentified, useful information may be extracted. We further consider an alternative parameterization in which one latent variable is associated with each block. Our analysis leads to some novel covariance equivalence results for Gaussian hidden variable models.