
On the Intersection Property of Conditional Independence and its Application to Causal Discovery
This work investigates the intersection property of conditional independ...
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Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions
We show that the only parameter prior for complete Gaussian DAG models t...
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On Testing Whether an Embedded Bayesian Network Represents a Probability Model
Testing the validity of probabilistic models containing unmeasured (hidd...
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Determining full conditional independence by loworder conditioning
A concentration graph associated with a random vector is an undirected g...
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Multivariate binary probability distribution in the Grassmann formalism
We propose a probability distribution for multivariate binary random var...
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Diagonal Nonlinear Transformations Preserve Structure in Covariance and Precision Matrices
For a multivariate normal distribution, the sparsity of the covariance a...
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Safe Probability
We formalize the idea of probability distributions that lead to reliable...
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Perfect TreeLike Markovian Distributions
We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations enclosed in the distribution. The same result is shown to hold also for multivariate strictly positive normal distributions. Our proof uses a new property of conditional independence that holds for these two classes of probability distributions.
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