Lattice Conditional Independence models are a class of models developed first for the Gaussian case in which a distributive lattice classifies all the conditional independence statements. The main result is that these models can equivalently be described via a transitive directed acyclic graph (TDAG) in which, as is normal for causal models, the conditional independence is in terms of conditioning on ancestors in the graph. We demonstrate that a parallel stream of research in algebra, the theory of Hibi ideals, not only maps directly to the LCI models but gives a vehicle to generalise the theory from the linear Gaussian case. Given a distributive lattice (i) each conditional independence statement is associated with a Hibi relation defined ...
AbstractIn this paper we study the problem of representing probabilistic independence models, in par...
We explore the conditional probabilistic independences of systems of random variables (I ; J jK), to...
AbstractIn this paper, we deal with conditional independence models closed with respect to graphoid ...
Lattice conditional independence models [Andersson and Perlman, Lattice models for conditional indep...
AbstractDifferent conditional independence models have been proposed in literature; in this paper we...
In this paper we study conditional independence structures arising from conditional probabilities an...
summary:The simultaneous occurrence of conditional independences among subvectors of a regular Gauss...
AbstractConditional independence models in the Gaussian case are algebraic varieties in the cone of ...
In this paper we consider conditional independence models closed under graphoid properties. We inves...
summary:In this paper, we characterise and classify a list of full conditional independences via the...
We consider the problem of estimating the marginal independence structure of a Bayesian network from...
In this paper, we deal with conditional independence models closed with respect to graphoid properti...
AbstractGraphs provide an excellent framework for interrogating symmetric models of measurement rand...
Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs spec...
It follows from the known relationships among the dierent classes of graphical Markov models for c...
AbstractIn this paper we study the problem of representing probabilistic independence models, in par...
We explore the conditional probabilistic independences of systems of random variables (I ; J jK), to...
AbstractIn this paper, we deal with conditional independence models closed with respect to graphoid ...
Lattice conditional independence models [Andersson and Perlman, Lattice models for conditional indep...
AbstractDifferent conditional independence models have been proposed in literature; in this paper we...
In this paper we study conditional independence structures arising from conditional probabilities an...
summary:The simultaneous occurrence of conditional independences among subvectors of a regular Gauss...
AbstractConditional independence models in the Gaussian case are algebraic varieties in the cone of ...
In this paper we consider conditional independence models closed under graphoid properties. We inves...
summary:In this paper, we characterise and classify a list of full conditional independences via the...
We consider the problem of estimating the marginal independence structure of a Bayesian network from...
In this paper, we deal with conditional independence models closed with respect to graphoid properti...
AbstractGraphs provide an excellent framework for interrogating symmetric models of measurement rand...
Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs spec...
It follows from the known relationships among the dierent classes of graphical Markov models for c...
AbstractIn this paper we study the problem of representing probabilistic independence models, in par...
We explore the conditional probabilistic independences of systems of random variables (I ; J jK), to...
AbstractIn this paper, we deal with conditional independence models closed with respect to graphoid ...