Nonparametric Bayes Modeling of Populations of Networks

Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network-valued data. Available models for a single network are not designed specifically for inference on the entire probability mass function of a network-valued random variable and therefore lack flexibility in characterizing the distribution of relevant topological structures. We propose a flexible Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges is defined via a mixture model which reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations. The formulation leads to an efficient Gibbs sampler and provides simple and coherent strategies for inference and goodness-of-fit assessments. We provide theoretical results on the flexibility of our model and illustrate improved performance --- compared to state-of-the-art models --- in simulations and application to human brain networks

Matrix powers algorithms for trust evaluation in PKI architectures

This paper deals with the evaluation of trust in public-key infrastructures. Different trust models have been proposed to interconnect the various PKI components in order to propagate the trust between them. In this paper we provide a new polynomial algorithm using linear algebra to assess trust relationships in a network using different trust evaluation schemes. The advantages are twofold: first the use of matrix computations instead of graph algorithms provides an optimized computational solution; second, our algorithm can be used for generic graphs, even in the presence of cycles. Our algorithm is designed to evaluate the trust using all existing (finite) trust paths between entities as a preliminary to any exchanges between PKIs. This can give a precise evaluation of trust, and accelerate for instance cross-certificate validation