Latent variable models are frequently used to identify structure in dichotomous network data, in part because they give rise to a Bernoulli product likelihood that is both well understood and consistent with the notion of exchangeable random graphs. In this article we propose conservative confidence sets that hold with respect to these underlying Bernoulli parameters as a function of any given partition of network nodes, enabling us to assess estimates of \emph{residual} network structure, that is, structure that cannot be explained by known covariates and thus cannot be easily verified by manual inspection. We demonstrate the proposed methodology by analyzing student friendship networks from the National Longitudinal Survey of Adolescent Health that include race, gender, and school year as covariates. We employ a stochastic expectation-maximization algorithm to fit a logistic regression model that includes these explanatory variables as well as a latent stochastic blockmodel component and additional node-specific effects. Although maximum-likelihood estimates do not appear consistent in this context, we are able to evaluate confidence sets as a function of different blockmodel partitions, which enables us to qualitatively assess the significance of estimated residual network structure relative to a baseline, which models covariates but lacks block structure.

At low bit rates, the linear subband coders are susceptible to the ringing effect, which causes rippling and blurring around the edges in the images. On the other hand, the nonlinear coders are affected by the smearing effect wherein the detail regions are removed. In this paper, we introduce fuzzy subband coding system. This system uses fuzzy median filters in the analysis and synthesis stage of the coder. The motivation for this study is to determine if this novel system can reduce both ringing and smearing effect. Experimental results show that this new subband coder does out-perform linear and median filter subband coders, both in PSNR and visually.