Sampling Online Social Networks via Heterogeneous Statistics

Most sampling techniques for online social networks (OSNs) are based on a particular sampling method on a single graph, which is referred to as a statistics. However, various realizing methods on different graphs could possibly be used in the same OSN, and they may lead to different sampling efficiencies, i.e., asymptotic variances. To utilize multiple statistics for accurate measurements, we formulate a mixture sampling problem, through which we construct a mixture unbiased estimator which minimizes asymptotic variance. Given fixed sampling budgets for different statistics, we derive the optimal weights to combine the individual estimators; given fixed total budget, we show that a greedy allocation towards the most efficient statistics is optimal. In practice, the sampling efficiencies of statistics can be quite different for various targets and are unknown before sampling. To solve this problem, we design a two-stage framework which adaptively spends a partial budget to test different statistics and allocates the remaining budget to the inferred best statistics. We show that our two-stage framework is a generalization of 1) randomly choosing a statistics and 2) evenly allocating the total budget among all available statistics, and our adaptive algorithm achieves higher efficiency than these benchmark strategies in theory and experiment

Weighted Random Walk Sampling for Multi-Relational Recommendation

In the information overloaded web, personalized recommender systems are essential tools to help users find most relevant information. The most heavily-used recommendation frameworks assume user interactions that are characterized by a single relation. However, for many tasks, such as recommendation in social networks, user-item interactions must be modeled as a complex network of multiple relations, not only a single relation. Recently research on multi-relational factorization and hybrid recommender models has shown that using extended meta-paths to capture additional information about both users and items in the network can enhance the accuracy of recommendations in such networks. Most of this work is focused on unweighted heterogeneous networks, and to apply these techniques, weighted relations must be simplified into binary ones. However, information associated with weighted edges, such as user ratings, which may be crucial for recommendation, are lost in such binarization. In this paper, we explore a random walk sampling method in which the frequency of edge sampling is a function of edge weight, and apply this generate extended meta-paths in weighted heterogeneous networks. With this sampling technique, we demonstrate improved performance on multiple data sets both in terms of recommendation accuracy and model generation efficiency

Uniform sampling of steady states in metabolic networks: heterogeneous scales and rounding

The uniform sampling of convex polytopes is an interesting computational problem with many applications in inference from linear constraints, but the performances of sampling algorithms can be affected by ill-conditioning. This is the case of inferring the feasible steady states in models of metabolic networks, since they can show heterogeneous time scales . In this work we focus on rounding procedures based on building an ellipsoid that closely matches the sampling space, that can be used to define an efficient hit-and-run (HR) Markov Chain Monte Carlo. In this way the uniformity of the sampling of the convex space of interest is rigorously guaranteed, at odds with non markovian methods. We analyze and compare three rounding methods in order to sample the feasible steady states of metabolic networks of three models of growing size up to genomic scale. The first is based on principal component analysis (PCA), the second on linear programming (LP) and finally we employ the lovasz ellipsoid method (LEM). Our results show that a rounding procedure is mandatory for the application of the HR in these inference problem and suggest that a combination of LEM or LP with a subsequent PCA perform the best. We finally compare the distributions of the HR with that of two heuristics based on the Artificially Centered hit-and-run (ACHR), gpSampler and optGpSampler. They show a good agreement with the results of the HR for the small network, while on genome scale models present inconsistencies.Comment: Replacement with major revision

Unbiased sampling of network ensembles

Sampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. An important requirement is that the sampling process is unbiased and efficient. The main approaches are microcanonical, i.e. they sample graphs that match the enforced constraints exactly. Unfortunately, when applied to strongly heterogeneous networks (like most real-world examples), the majority of these approaches become biased and/or time-consuming. Moreover, the algorithms defined in the simplest cases, such as binary graphs with given degrees, are not easily generalizable to more complicated ensembles. Here we propose a solution to the problem via the introduction of a "Maximize and Sample" ("Max & Sam" for short) method to correctly sample ensembles of networks where the constraints are `soft', i.e. realized as ensemble averages. Our method is based on exact maximum-entropy distributions and is therefore unbiased by construction, even for strongly heterogeneous networks. It is also more computationally efficient than most microcanonical alternatives. Finally, it works for both binary and weighted networks with a variety of constraints, including combined degree-strength sequences and full reciprocity structure, for which no alternative method exists. Our canonical approach can in principle be turned into an unbiased microcanonical one, via a restriction to the relevant subset. Importantly, the analysis of the fluctuations of the constraints suggests that the microcanonical and canonical versions of all the ensembles considered here are not equivalent. We show various real-world applications and provide a code implementing all our algorithms.Comment: MatLab code available at http://www.mathworks.it/matlabcentral/fileexchange/46912-max-sam-package-zi

Exact Simulation for Fork-Join Networks with Heterogeneous Service

This paper considers a fork-join network with a group of heterogeneous servers in each service station, e.g. servers having different service rate. The main research interests are the properties of such fork-join networks in equilibrium, such as distributions of response times, maximum queue lengths and load carried by servers. This paper uses exact Monte-Carlo simulation methods to estimate the characteristics of heterogeneous fork-join networks in equilibrium, for which no explicit formulas are available. The algorithm developed is based on coupling from the past. The efficiency of the sampling algorithm is shown theoretically and via simulation

Study of Heterogeneous Academic Networks

Academic networks are derived from scholarly data. They are heterogeneous in the sense that different types of nodes are involved, such as papers and authors. This dissertation studies such heterogeneous networks for measuring the academic influence and learning vector representations of authors. Academic influence has been traditionally measured by the citation count and metrics derived from it. PageRank based algorithms have been used to give higher weight to citations from more influential papers. A better metric is to add authors into the citation network so that the importance of authors and papers are evaluated recursively within the same framework. Based on such heterogeneous academic networks, we propose a new algorithm for ranking authors. Tested on two large networks, we find that our method outperforms the other 10 methods in terms of the number of award winners among top-ranked authors. We further improve the method by finding and dealing with the long reference issue. Moreover, we find the mutual citation in paper networks and the self citation issue in author networks. Our new method can reduce the impact of the above three issues and identify more rising stars. To learn efficient author representations from heterogeneous academic networks, we propose a new embedding method called Stratified Embedding for Heterogeneous Networks (SEHN) based on Skip-Gram Negative Sampling (SGNS). We conduct Random Walks to generate the traces that represent the structure of the network, then separate the traces into different layers so that each layer contains the nodes of one type only. Such stratification improves embeddings that are derived from the mixed traces by a large margin. SEHN improves the state-of-the-art Metapath2vec by up to 24% at a certain point. The efficacy of stratification is also demonstrated on two classic network embedding algorithms DeepWalk and Node2vec. The results are validated in two heterogeneous networks. We also demonstrate that SEHN outperforms the embedding of homogeneous author networks that are induced from their corresponding heterogeneous networks