We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.

Causal manipulation theorems proposed by Spirtes et al. and Pearl in the context of directed probabilistic graphs, such as Bayesian networks, oŒer a simple and theoretically sound formalism for predicting the eŒect of manipulation of a system from its causal model. While the theorems are applicable to a wide variety of equilibrium causal models, they do not address the issue of reversible causa...

We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous decisions, while others are very adept at handling and representing uncertainty, but need to rely on undesirable assumptions. Our aim is to combine the inherent ro...

Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning acausal networks are fairly well developed. These methods often employ assumptions to facilitate the construction of priors, including the assumptions of para...

Bayesian networks are limited in differentiating between causal and spurious relationships among decision factors. Decision making without differentiating the two relationships cannot be effective. To overcome this limitation of Bayesian networks, this study proposes linking Bayesian networks to structural equation modeling (SEM), which has an advantage in testing causal relationships between f...

We target the problem of accuracy and robustness in causal inference from finite data sets. Our aim is to combine the inherent robustness of the Bayesian approach with the theoretical strength and clarity of constraint-based methods. We use a Bayesian score to obtain probability estimates on the input statements used in a constraint-based procedure. These are subsequently processed in decreasin...

Artificial intelligence research on reasoning with criminal evidence in terms of arguments, hypothetical scenarios, and probabilities inspired the approach in this paper. That research showed that Bayesian Networks can be used for modeling arguments and structured hypotheses. Also well-known issues with Bayesian Network were encountered: More numbers are needed than are available, and there is ...

In designing a Bayesian network for an actual problem, developers need to bridge the gap between the mathematical abstractions offered by the Bayesian-network formalism and the features of the problem to be modelled. A notion that has been suggested in the literature to facilitate Bayesian-network development is causal independence. It allows exploiting compact representations of probabilistic ...

Knowing the cause and effect is important to researchers who are interested in modeling the effects of actions, and Artificial Intelligence researchers are among them. One commonly used method for modeling cause and effect is graphical model. Bayesian Network is a probabilistic graphical model for representing and reasoning uncertain knowledge. It has been used as a fundamental tool and is beco...

Modeling causal dependencies often demands cycles at a coarse-grained temporal scale. If Bayesian networks are to be used for modeling uncertainties, cycles are eliminated with dynamic Bayesian networks, spreading indirect dependencies over time and enforcing an infinitesimal resolution of time. Without a “causal design,” i.e., without anticipating indirect influences appropriately in time, we ...