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We address the problems of causal structure inference from conditional independence facts when latent confounders are admitted. The conditions that allow one to identify latent confounders and fully or partially recognize causal links are described. The updated implicative rules for orienting edges under confounding are suggested. We propose several new rules that are able to reveal bows and confounded causal edges. The rules rely on facts of absence of certain authentic edges (edge absence may be implied by Verma constraint or given in input as a priori requirement). [ABSTRACT FROM AUTHOR]

The problems of causal inference of models from empirical data (by independence-based methods) and some error mechanisms are examined. We demonstrate that the known rules for orienting edges of model can produce misleading results under presence of latent confounders. We propose corrections to the orientation rules aiming to successfully extend them for inference of models beyond the ancestral model class. The necessary assumptions justifying the inference of adequate causal relationships from data are suggested. [ABSTRACT FROM AUTHOR]

This paper proposes a novel algorithm for optimizing decision variables with respect to an outcome variable of interest in complex problems, such as those arising from big data. The proposed algorithm builds on the notion of Markov blankets in Bayesian networks to alleviate the computational challenges associated with optimization tasks in complex datasets. Through a case study, we apply the algorithm to optimize medication prescriptions for diabetic patients, who have different characteristics, suffer from multiple comorbidities, and take multiple medications concurrently. In particular, we demonstrate how the optimal combination of diabetic medications can be found by examining the comparative effectiveness of the medications among similar patients. The case study is based on 5 years of data for 19,223 diabetic patients. Our results indicate that certain patient characteristics (e.g., clinical and demographic features) influence optimal treatment decisions. Among patients examined, monotherapy with metformin was the most common optimal medication decision. The results are consistent with the relevant clinical guidelines and reports in the medical literature. The proposed algorithm obviates the need for knowledge of the whole Bayesian network model, which can be very complex in big data problems. The procedure can be applied to any complex Bayesian network with numerous features, multiple decision variables, and a target variable. [ABSTRACT FROM AUTHOR]

The aim of the paper is to relate Bell's notion of local causality to the Causal Markov Condition. To this end, first a framework, called local physical theory, will be introduced integrating spatiotemporal and probabilistic entities and the notions of local causality and Markovity will be defined. Then, illustrated in a simple stochastic model, it will be shown how a discrete local physical theory transforms into a Bayesian network and how the Causal Markov Condition arises as a special case of Bell's local causality and Markovity. [ABSTRACT FROM AUTHOR]

This paper considers the problem of estimating the bounds on the average controlled direct effects (ACDEs) of a treatment variable on an unobserved response variable in the presence of unobserved confounders between an intermediate variable and the response variable. When the response variable is observed, Cai, et al.(2008) derived the formulas for the sharp bounds on the ACDEs. When the response variable is unobserved, the authors propose a graphical criterion for selecting variables affected by the response variable to derive the formulas for the bounds on the ACDEs, which is an extension of the result of Kuroki(2005) to ACDEs. The results enable us not only to judge from the graph structure whether the bounds on the ACDEs can be expressed through observed variables when the response variable is unobserved, but also to provide their formulas when the answer is affirmative. [ABSTRACT FROM AUTHOR]

Consider a family $${(X_i)_{i \in I}}$$ of random variables endowed with the structure of a Bayesian network, and a subset S of I. This paper examines the problem of computing the probability distribution of the subfamily $${(X_{a})_{a \in S}}$$ (respectively the probability distribution of $${ (X_{b})_{b \in {\bar{S}}}}$$ , where $${{\bar{S}} = I - S}$$ , conditional on $${(X_{a})_{a \in S}}$$). This paper presents some theoretical results that makes it possible to compute joint and conditional probabilities over a subset of variables by computing over separate components. In other words, it is demonstrated that it is possible to decompose this task into several parallel computations, each related to a subset of S (respectively of $${{\bar{S}}}$$); these partial results are then put together as a final product. In computing the probability distribution over $${(X_a)_{a \in S}}$$ , this procedure results in the production of a structure of level two Bayesian network structure for S. [ABSTRACT FROM AUTHOR]

Active networks are network architectures with processors that are capable of executing code carried by the packets passing through them. A critical network management concern is the optimization of such networks and tight bounds on their performance serve as useful design benchmarks. A new bound on communication rates is developed that applies to network coding, which is a promising active network application that has processors transmit packets that are general functions, for example a bit-wise XOR, of selected received packets. The bound generalizes an edge-cut bound on routing rates by progressively removing edges from the network graph and checking whether certain strengthened d-separation conditions are satisfied. The bound improves on the cut-set bound and its efficacy is demonstrated by showing that routing is rate-optimal for some commonly cited examples in the networking literature. [ABSTRACT FROM AUTHOR]

Consider a case where cause-effect relationships between variables can be described as a causal diagram and the corresponding Gaussian linear structural equation model. In order to identify total effects in studies with an unobserved response variable, this paper proposes graphical criteria for selecting both covariates and variables caused by the response variable. The results enable us not only to judge from the graph structure whether a total effect can be expressed through the observed covariances, but also to provide its closed-form expression in case where its answer is affirmative. The graphical criteria of this paper are helpful to infer total effects when it is difficult to observe a response variable. [ABSTRACT FROM AUTHOR]