The structure of real-world social networks in large part determines the evolution of social phenomena, including opinion formation, diffusion of information and influence, and the spread of disease. Globally, network structure is characterized by features such as degree distribution, degree assortativity, and clustering coefficient. However, information about global structure is usually not available to each vertex. Instead, each vertex's knowledge is generally limited to the locally observable portion of the network consisting of the subgraph over its immediate neighbors. Such subgraphs, known as ego networks, have properties that can differ substantially from those of the global network. In this paper, we study the structural properties of ego networks and show how they relate to the global properties of networks from which they are derived. Through empirical comparisons and mathematical derivations, we show that structural features, similar to static attributes, suffer from paradoxes. We quantify the differences between global information about network structure and local estimates. This knowledge allows us to better identify and correct the biases arising from incomplete local information.
With traditional independent data, the global statistics of a population remain unbiased estimates for subsets. In networks, however, the complex dependencies can skew localized statistics, leading to inhomogeneity at different scales and positions. Numerous efforts have been made to develop generative models which can reproduce realistic structure with simple local algorithms @cite_8 @cite_21 @cite_26 @cite_5 . Unfortunately, structural features are so intertwined that preserving one often biases another. The same difficulty is also observed in graph sampling, where different sampling techniques can lead to different biases @cite_6 @cite_10 .
@cite_26 @cite_8 @cite_21 @cite_6 @cite_5 @cite_10
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Many statistical learning problems in NLP call for local model search methods. But accuracy tends to suffer with current techniques, which often explore either too narrowly or too broadly: hill-climbers can get stuck in local optima, whereas samplers may be inefficient. We propose to arrange individual local optimizers into organized networks. Our building blocks are operators of two types: (i) transform, which suggests new places to search, via non-random restarts from already-found local optima; and (ii) join, which merges candidate solutions to find better optima. Experiments on grammar induction show that pursuing different transforms (e.g., discarding parts of a learned model or ignoring portions of training data) results in improvements. Groups of locally-optimal solutions can be further perturbed jointly, by constructing mixtures. Using these tools, we designed several modular dependency grammar induction networks of increasing complexity. Our complete system achieves 48.6 accuracy (directed dependency macro-average over all 19 languages in the 2006 7 CoNLL data) — more than 5 higher than the previous state-of-the-art. Inspired by the tremendous success of deep generative models on generating continuous data like image and audio, in the most recent year, few deep graph generative models have been proposed to generate discrete data such as graphs. They are typically unconditioned generative models which has no control on modes of the graphs being generated. Differently, in this paper, we are interested in a new problem named : given an input graph, we want to infer a target graph based on their underlying (both global and local) translation mapping. Graph translation could be highly desirable in many applications such as disaster management and rare event forecasting, where the rare and abnormal graph patterns (e.g., traffic congestions and terrorism events) will be inferred prior to their occurrence even without historical data on the abnormal patterns for this graph (e.g., a road network or human contact network). To achieve this, we propose a novel Graph-Translation-Generative Adversarial Networks (GT-GAN) which will generate a graph translator from input to target graphs. GT-GAN consists of a graph translator where we propose new graph convolution and deconvolution layers to learn the global and local translation mapping. A new conditional graph discriminator has also been proposed to classify target graphs by conditioning on input graphs. Extensive experiments on multiple synthetic and real-world datasets demonstrate the effectiveness and scalability of the proposed GT-GAN. short-lived or high degree peers due to the dynamics of peer participation or the heterogeneity of peer degrees, respectively. This paper presents Respondent-Driven Sampling (RDS) as a promising technique for sampling unstructured P2P overlays. This allows one to accurately estimate the distribution of a desired peer property without capturing the entire overlay structure. RDS is a variant of snowball sampling that has been proposed and used in the social sciences to characterize hidden population in a society [9], [13]. We apply the RDS technique to unstructured P2P network and evaluate its performance over a wide range of static and dynamic graphs as well as a widely deployed P2P system. Throughout our evaluation, we compare and contrast the performance of the RDS technique with another sampling technique, namely Metropolized Random Walk (MRW), that we developed in our earlier work [16]. Our main findings can be summarized as follows: First, RDS outperforms MRW across all scenarios. In particular, RDS exhibits a significantly better performance than MRW when the overlay structure exhibits a combination of highly skewed node degrees and highly skewed (local) clustering coefficients. Second, our simulation and empirical evaluations reveal that both the RDS and MRW techniques can accurately estimate key peer properties over dynamic unstructured overlays. Third, our empirical evaluations suggest that the efficiency of the two sampling techniques in practice is lower than in our simulations involving synthetic graphs. We attribute this to our inability to capture accurate reference snapshots. The rest of the paper is organized as follows: Section II presents an overview of both the RDS and MRW techniques, and sketches our evaluation methodology. We examine both techniques over variety of static and dynamic graphs in Section III and IV, respectively. Section V presents the empirical evaluation of the two sampling techniques over Gnutella network. Various paradigms, based on differential privacy, have been proposed to release a privacy-preserving dataset with statistical approximation. Nonetheless, most existing schemes are limited when facing highly correlated attributes, and cannot prevent privacy threats from untrusted servers. In this paper, we propose a novel Copula- based scheme to efficiently synthesize and release multi-dimensional crowdsourced data with local differential privacy. In our scheme, each participant's (or user's) data is locally transformed into bit strings based on a randomized response technique, which guarantees a participant's privacy on the participant (user) side. Then, Copula theory is leveraged to synthesize multi-dimensional crowdsourced data based on univariate marginal distribution and attribute dependence. Univariate marginal distribution is estimated by the Lasso-based regression algorithm from the aggregated privacy- preserving bit strings. Dependencies among attributes are modeled as multivariate Gaussian Copula, of which parameter is estimated by Pearson correlation coefficients. We conduct experiments to validate the effectiveness of our scheme. Our experimental results demonstrate that our scheme is effective for the release of multi-dimensional data with local differential privacy guaranteed to distributed participants.