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作者：Gao, Chao; Zhou, Harrison H.
作者单位：Yale University
摘要：A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rate-optimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian sequence model, Gaussian regression and spectral density estimation.
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作者：Karwa, Vishesh; Slavkovic, Aleksandra
作者单位：Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The beta-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the beta-model, and show that the MLE never exists for the degree partition beta-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the parameters of beta-model, a...
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作者：Lei, Jing
作者单位：Carnegie Mellon University
摘要：The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix obtained by subtracting the estimated block mean effect from the adjacency matrix. Asymptotic null distribution is obtained using recent advances in random matrix theory. The test is proved to have full power against alternative models with finer structures...
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作者：Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly
作者单位：Ruhr University Bochum; Cardiff University
摘要：This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. We then demonstrate that we can design the experiments, such that asymptotically the new estimat...
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作者：El Karoui, Noureddine; Wu, Hau-Tieng
作者单位：University of California System; University of California Berkeley; University of Toronto
摘要：Recently, several data analytic techniques based on graph connection Laplacian (GCL) ideas have appeared in the literature. At this point, the properties of these methods are starting to be understood in the setting where the data is observed without noise. We study the impact of additive noise on these methods and show that they are remarkably robust. As a by-product of our analysis, we propose modifications of the standard algorithms that increase their robustness to noise. We illustrate our...
