Learning Graphs with a Few Hubs
نویسندگان
چکیده
We consider the problem of recovering the graph structure of a “hub-networked” Ising model given i.i.d. samples, under high-dimensional settings, where number of nodes p could be potentially larger than the number of samples n. By a “hub-networked” graph, we mean a graph with a few “hub nodes” with very large degrees. State of the art estimators for Ising models have a sample complexity that scales polynomially with the maximum node-degree, and are thus ill-suited to recovering such graphs with a few hub nodes. Some recent proposals for specifically recovering hub graphical models do not come with theoretical guarantees, and even empirically provide limited improvements over vanilla Ising model estimators. Here, we show that under such low sample settings, instead of estimating “difficult” components such as hub-neighborhoods, we can use quantitative indicators of our inability to do so, and thereby identify hub-nodes. This simple procedure allows us to recover hub-networked graphs with very strong statistical guarantees even under very low sample settings.
منابع مشابه
Application of n-distance balanced graphs in distributing management and finding optimal logistical hubs
Optimization and reduction of costs in management of distribution and transportation of commodity are one of the main goals of many organizations. Using suitable models in supply chain in order to increase efficiency and appropriate location for support centers in logistical networks is highly important for planners and managers. Graph modeling can be used to analyze these problems and many oth...
متن کاملHubness: An Interesting Property of Nearest Neighbor Graphs and its Impact on Classification
The presence of hubs, i.e., a few vertices that appear as neighbors of surprisingly many other vertices, is a recently explored property of nearest neighbor graphs. Several Authors argue that the presence of hubs should be taken into account for various data mining tasks, such as classification, clustering or instance selection. In this paper, we review recent works on hubness-aware instance se...
متن کاملA Scale-Free Network View of the UMLS to Learn Terminology Translations
The UMLS Metathesaurus belongs to the class of scale-free networks with few concept hubs possessing a large number of relationships. The hubs provide useful links between the concepts from disparate terminologies in the UMLS; however, they also exponentially increase the number of possible transitive cross-terminology paths. Towards the goal of using machine learning to rank cross-terminology t...
متن کاملCuckoo Optimization Algorithm for a Reliable Location-Allocation of Hubs among the Clients
Hubs are critical elements of transportation networks. Location of hubs and allocation of demands to them are of high importance in the network design. The most important purpose of these models is to minimize the cost, but path reliability is also another important factor which can influence the location of hubs. In this paper, we propose a P-center hub location model with full interconnection...
متن کامل