2,361 research outputs found
Uncertainty Reduction for Stochastic Processes on Complex Networks
Many real-world systems are characterized by stochastic dynamical rules where
a complex network of interactions among individual elements probabilistically
determines their state. Even with full knowledge of the network structure and
of the stochastic rules, the ability to predict system configurations is
generally characterized by a large uncertainty. Selecting a fraction of the
nodes and observing their state may help to reduce the uncertainty about the
unobserved nodes. However, choosing these points of observation in an optimal
way is a highly nontrivial task, depending on the nature of the stochastic
process and on the structure of the underlying interaction pattern. In this
paper, we introduce a computationally efficient algorithm to determine
quasioptimal solutions to the problem. The method leverages network sparsity to
reduce computational complexity from exponential to almost quadratic, thus
allowing the straightforward application of the method to mid-to-large-size
systems. Although the method is exact only for equilibrium stochastic processes
defined on trees, it turns out to be effective also for out-of-equilibrium
processes on sparse loopy networks.Comment: 5 pages, 2 figures + Supplemental Material. A python implementation
of the algorithm is available at
https://github.com/filrad/Maximum-Entropy-Samplin
Exponential-family Random Network Models
Random graphs, where the connections between nodes are considered random
variables, have wide applicability in the social sciences. Exponential-family
Random Graph Models (ERGM) have shown themselves to be a useful class of models
for representing com- plex social phenomena. We generalize ERGM by also
modeling nodal attributes as random variates, thus creating a random model of
the full network, which we call Exponential-family Random Network Models
(ERNM). We demonstrate how this framework allows a new formu- lation for
logistic regression in network data. We develop likelihood-based inference for
the model and an MCMC algorithm to implement it. This new model formulation is
used to analyze a peer social network from the National Lon- gitudinal Study of
Adolescent Health. We model the relationship between substance use and
friendship relations, and show how the results differ from the standard use of
logistic regression on network data
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