The network paradigm is widely accepted as the gold standard in modelling complex systems such as epidemics or neuronal activity in the brain; however, in most cases, the exact nature of the network on which such dynamics unfold is unknown. This has motivated a significant amount of work on network inference. Whilst a large body of work is concerned with inferring network structure based on detailed node-level temporal data, in this work we tackle the more challenging scenario of inferring the family of the underlying network when only population-level temporal incidence data are available . A key obstacle is the forbiddingly high dimensionality of the resulting stochastic epidemicmodel. To tackle this, we approximate the susceptible-infected-susceptible (SIS) model on networks by a Birth-Death process , whose rates encode the structure of the underlying network and disease dynamics. Using systematic simulations , we propose a parsimonious (three-parameter) model of these ratess-R\'enyi } and  show that different wellknown network families map onto distinct regions of the parameter space of this model. This result provides an a priori characterisation of different network families. Then, given populationlevel temporal epidemic data, we employ a Bayesian classifier to derive posterior distributions over diferent network families . We show that the proposed methodology yields excellent results when tested on synthetic and real-world networks . Our framework extends readily to many network families and spreading processes and it could provide a new benchmark in network inference from population-level data .
Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e. the number of infected individuals at a finite set of discrete times of a single realisation of the epidemic), the only information likely to be available in real world settings . To tackle this, epidemics on networks are approximated by a Birth-and-Death process which keeps track of the number of infected nodes at population level. The rates of this surrogate model encode both the structure of the underlying network and disease dynamics. We use extensive simulations over Regular, Erd\H{os-R\'enyi } and Barab\'asi-Albert networks to build network class-specific priors for these rates. \% show that different well-known network classes map onto distinct regions of the parameter space of this model. We then use Bayesian model selection to recover the most likely underlying network class, based only on a single realisation of the epidemic . We show that the proposed methodology yields good results on both synthetic and real-world networks .
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The network paradigm is widely accepted as the gold standard in modelling complex systems such as epidemics or neuronal activity in the brain; however, in most cases, the exact nature of the network on which such dynamics unfold is unknown. This has motivated a significant amount of work on network inference. Whilst a large body of work is concerned with inferring network structure based on detailed node-level temporal data, in this work we tackle the more challenging scenario
Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem
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family
class
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only
epidemic data is only available at
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temporal incidence data are available
(i.e. the number of infected individuals at a finite set of discrete times of a single realisation of the epidemic), the only information likely to be available in real world settings
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A key obstacle is the forbiddingly high dimensionality of the resulting stochastic epidemicmodel.
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we approximate the susceptible-infected-susceptible (SIS) model on networks by a Birth-Death process , whose rates encode
epidemics on networks are approximated by a Birth-and-Death process which keeps track of the number of infected nodes at population level. The rates of this surrogate model encode both
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Using systematic simulations , we propose a parsimonious (three-parameter) model of these rates
We use extensive simulations over Regular, Erd\H{o
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Barab\'asi-Albert networks to build network class-specific priors for these rates. \%
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wellknown network families
well-known network classes
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This result provides an a priori characterisation of different network families. Then, given populationlevel temporal epidemic data, we employ a Bayesian classifier to derive posterior distributions over diferent network families
We then use Bayesian model selection to recover the most likely underlying network class, based only on a single realisation of the epidemic
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excellent results when tested on
good results on both
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. Our framework extends readily to many network families and spreading processes and it could provide a new benchmark in network inference from population-level data