Influence maximisation beyond organisational boundaries

We consider the problem of choosing influential members within a social network, in order to disseminate a message as widely as possible. While this so-called problem of influence maximisation has been widely studied, little work considers partially-observable networks, where only part of a network is visible to the decision maker. Yet, this is critical in many applications, where an organisation needs to distribute its message far beyond its boundaries and beyond its usual sphere of influence. In this paper, we show that existing algorithms are not sufficient to handle such scenarios. To address this, we propose a set of novel adaptive algorithms that perform well in partially observable settings, achieving an up to 18% improvement on the non-Adaptive state of the art

Indirect influence manipulation with partially observable networks

The propagation of concepts through a population of agents can be modelled as a cascade of influence spread from an initial set of individuals. In real-world environments there may be many concepts spreading and interacting, and we may not be able to directly control the target concept we wish to manipulate, requiring indirect manipulation through a secondary controllable concept. Previous work on influence spread typically assumes that we have full knowledge of a network, which may not be the case. In this paper, we investigate indirect influence manipulation when we can only observe a sample of the full network. We propose a heuristic, known as Target Degree, for selecting seed nodes for a secondary controllable concept that uses the limited information available in a partially observable environment to indirectly manipulate the target concept. Target degree is shown to be effective in synthetic small-world networks and in real-world networks when the controllable concept is introduced after the target concept

Seeding with Costly Network Information

We study the task of selecting $k$ nodes in a social network of size $n$, to seed a diffusion with maximum expected spread size, under the independent cascade model with cascade probability $p$. Most of the previous work on this problem (known as influence maximization) focuses on efficient algorithms to approximate the optimal seed set with provable guarantees, given the knowledge of the entire network. However, in practice, obtaining full knowledge of the network is very costly. To address this gap, we first study the achievable guarantees using $o(n)$ influence samples. We provide an approximation algorithm with a tight (1-1/e){\mbox{OPT}}-\epsilon n guarantee, using $O_{\epsilon}(k^2\log n)$ influence samples and show that this dependence on $k$ is asymptotically optimal. We then propose a probing algorithm that queries ${O}_{\epsilon}(p n^2\log^4 n + \sqrt{k p} n^{1.5}\log^{5.5} n + k n\log^{3.5}{n})$ edges from the graph and use them to find a seed set with the same almost tight approximation guarantee. We also provide a matching (up to logarithmic factors) lower-bound on the required number of edges. To address the dependence of our probing algorithm on the independent cascade probability $p$, we show that it is impossible to maintain the same approximation guarantees by controlling the discrepancy between the probing and seeding cascade probabilities. Instead, we propose to down-sample the probed edges to match the seeding cascade probability, provided that it does not exceed that of probing. Finally, we test our algorithms on real world data to quantify the trade-off between the cost of obtaining more refined network information and the benefit of the added information for guiding improved seeding strategies

Identifying spatial invasion of pandemics on metapopulation networks via anatomizing arrival history

Spatial spread of infectious diseases among populations via the mobility of humans is highly stochastic and heterogeneous. Accurate forecast/mining of the spread process is often hard to be achieved by using statistical or mechanical models. Here we propose a new reverse problem, which aims to identify the stochastically spatial spread process itself from observable information regarding the arrival history of infectious cases in each subpopulation. We solved the problem by developing an efficient optimization algorithm based on dynamical programming, which comprises three procedures: i, anatomizing the whole spread process among all subpopulations into disjoint componential patches; ii, inferring the most probable invasion pathways underlying each patch via maximum likelihood estimation; iii, recovering the whole process by assembling the invasion pathways in each patch iteratively, without burdens in parameter calibrations and computer simulations. Based on the entropy theory, we introduced an identifiability measure to assess the difficulty level that an invasion pathway can be identified. Results on both artificial and empirical metapopulation networks show the robust performance in identifying actual invasion pathways driving pandemic spread.Comment: 14pages, 8 figures; Accepted by IEEE Transactions on Cybernetic