Jing Luo, Haoyu Wei, Xiaoyu Lei, Jiaxin Guo
arXiv 2 Nov 2021 · Mathematics — Statistics Theory · publishedCommunication in Statistics-Theory and Methods (2024)
arXiv:2111.01301 · PDF · DOI · OpenAlex · Extracted main text
For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, we release the degree sequences of the binary networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish the asymptotic result including both consistency and asymptotically normality of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real data example are provided to illustrate asymptotic results.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Ting Yan and Jinfeng Xu (2013) A central limit theorem in the $$-model for undirected random graphs with a diverging number of vertices | 0.843 | 4 | 3 | 75% |
| 2 | Vishesh Karwa and Aleksandra Slavković (2016) Inference using noisy degrees: Differentially private $ $-model and synthetic graphs | 0.737 | 3 | 2 | 100% |
| 3 | Stéphane Boucheron, Gábor Lugosi, and Pascal Massart (2013) Concentration inequalities: A nonasymptotic theory of independence | 0.644 | 3 | 2 | 67% |
| 4 | Chung Fan and Linyuan Lu (2002) Connected components in random graphs with given expected degree sequences | 0.644 | 2 | 2 | 100% |
| 5 | Christopher Hillar and Andre Wibisono (2013) Maximum entropy distributions on graphs | 0.644 | 2 | 2 | 100% |
| 6 | Philippe Rigollet and Jan-Christian Hütter (2019) High dimensional statistics | 0.511 | 3 | 2 | 33% |
| 7 | Seidu Inusah and Tomasz J. Kozubowski (2006) A discrete analogue of the laplace distribution | 0.511 | 2 | 2 | 50% |
| 8 | Leudo Antonio Cutillo, Refik Molva, and Thorsten Strufe (2010) Privacy preserving social networking through decentralization | 0.405 | 1 | 1 | 100% |
| 9 | Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith (2006) Calibrating noise to sensitivity in private data analysis | 0.405 | 1 | 1 | 100% |
| 10 | Paul Erdos, Alfréd Rényi, et al (1960) On the evolution of random graphs | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 43 scored citations.