When using differential privacy to publish high-dimensional data, the huge dimensionality leads to greater noise. Especially for high-dimensional binary data, it is easy to be covered by excessive noise. Most existing methods cannot address real high-dimensional data problems appropriately because they suffer from high time complexity. Therefore, in response to the problems above, we propose the differential privacy adaptive Bayesian network algorithm PrivABN to publish high-dimensional binary data. This algorithm uses a new greedy algorithm to accelerate the construction of Bayesian networks, which reduces the time complexity of the GreedyBayes algorithm from to . In addition, it uses an adaptive algorithm to adjust the structure and uses a differential privacy Exponential mechanism to preserve the privacy, so as to generate a high-quality protected Bayesian network. Moreover, we use the Bayesian network to calculate the conditional distribution with noise and generate a synthetic dataset for publication. This synthetic dataset satisfies -differential privacy. Lastly, we carry out experiments against three real-life high-dimensional binary datasets to evaluate the functional performance.

中文翻译：

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等式第1章第1节通过自适应贝叶斯网络发布差分私有高维二进制数据

当使用差分隐私发布高维数据时，巨大的维数会导致更大的噪声。特别是对于高维二进制数据，很容易被过多的噪声所覆盖。大多数现有方法由于时间复杂度高而无法适当地解决真正的高维数据问题。因此，针对上述问题，我们提出差分隐私自适应贝叶斯网络算法PrivABN来发布高维二进制数据。该算法使用了一种新的贪心算法来加速贝叶斯网络的构建，将贪心贝叶斯算法的时间复杂度从 降低到。此外，它使用自适应算法调整结构，并使用差分隐私指数机制来保护隐私，从而生成高质量的受保护贝叶斯网络。此外，我们使用贝叶斯网络来计算带有噪声的条件分布并生成用于发布的合成数据集。这个合成数据集满足-差分隐私。最后，我们针对三个现实生活中的高维二进制数据集进行实验以评估功能性能。