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通过随机扰动与矩估计实现 β 模型的边差分隐私估计AI 解读

A standing challenge in data privacy is the trade-off between the level of privacy and the efficiency of statistical inference. Here, we conduct an in-depth study of this trade-off for parameter estimation in the β-model (Ann. Appl. Probab. 21 (2011) 1400–1435) for edge differentially private network data released via jittering (J. R. Stat. Soc. Ser. C. Appl. Stat. 66 (2017) 481–500). Unlike most previous approaches based on maximum likelihood estimation for this network…

《统计学家的共引与合著网络》讨论AI 解读

1. We thank the authors for their new contribution to a high quality dataset and interesting findings from the modeling and analysis of the co-citation and co-authorship networks of statisticians. ...

含噪网络中的子图密度估计AI 解读

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Here we study the problem of estimating the density of an arbitrary subgraph, given a noisy version…

无标签网络的平均：几何刻画与渐近行为AI 解读

It is becoming increasingly common to see large collections of network data objects, that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based analogues of even many of the most basic tools already standard for scalar and vector data. In this paper, our focus is on averages of unlabeled, undirected networks with edge weights. Specifically, we (i) characterize a certain notion of the…

用于非参数函数估计的多尺度广义线性模型AI 解读

We present a method for extracting information about both the scale and trend of local components of an inhomogeneous function in a nonparametric generalised linear model. Our multiscale framework combines recursive partitions, which allow for the incorporation of scale in a natural manner, with systems of piecewise polynomials supported on the partition intervals, which serve to summarise the smooth trend within each interval. Our estimators are formulated as solutions of…

多尺度似然分析与复杂度惩罚估计AI 解读

We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L2 function, a given likelihood function has an alternative representation as a product of conditional densities reflecting information in both the data and the parameter vector localized in position and scale. The framework is developed as a set of sufficient conditions for the existence of such factorizations, formulated in analogy…

泊松过程的贝叶斯多尺度模型AI 解读

I introduce a class of Bayesian multiscale models (BMSM's) for one-dimensional inhomogeneous Poisson processes. The focus is on estimating the (discretized) intensity function underlying the process. Unlike the usual transform-based approach at the heart of most wavelet-based methods for Gaussian data, these BMSM's are constructed using recursive dyadic partitions (RDP's) within an entirely likelihood-based framework. Each RDP may be associated with a binary tree, and a new…

泊松过程的贝叶斯多尺度模型AI 解读

I introduce a class of Bayesian multiscale models (BMSM's) for one-dimensional inhomogeneous Poisson processes. The focus is on estimating the (discretized) intensity function underlying the process. Unlike the usual transform-based approach at the heart of most wavelet-based methods for Gaussian data, these BMSM's are constructed using recursive dyadic partitions (RDP's) within an entirely likelihood-based framework. Each RDP may be associated with a binary tree, and a new…