具有相关观测值的自适应数据分析
Adaptive Data Analysis with Correlated Observations
摘要：
自适应数据分析的绝大多数工作都集中在数据集中样本独立的情况下。有几种方法和工具已经成功地应用于此，例如差分隐私、最大信息、压缩参数等。如果没有独立性假设，这种情况就不那么容易理解。我们着手系统地研究相关观测的自适应数据分析的可能性。首先，我们表明，在某些情况下，差分隐私保证泛化，即使有样本内的依赖关系，我们量化使用的概念，我们称之为吉布斯依赖。我们用一个严格的反例来补充这个结果。其次，我们表明，转录压缩和自适应数据分析之间的连接可以扩展到非iid设置。
英文摘要：
The vast majority of the work on adaptive data analysis focuses on the case where the samples in the dataset are independent. Several approaches and tools have been successfully applied in this context, such as differential privacy, max-information, compression arguments, and more. The situation is far less well-understood without the independence assumption. We embark on a systematic study of the possibilities of adaptive data analysis with correlated observations. First, we show that, in some cases, differential privacy guarantees generalization even when there are dependencies within the sample, which we quantify using a notion we call Gibbs-dependence. We complement this result with a tight negative example. Second, we show that the connection between transcript-compression and adaptive data analysis can be extended to the non-iid setting.
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