基于XOR的二元分类：基本极限和有效算法
Binary Classification with XOR Queries: Fundamental Limits and An Efficient Algorithm
摘要：
我们考虑了一个基于查询的数据采集问题，用于未知标签的二进制分类，它在通信，众包，推荐系统和主动学习中有不同的应用。为了确保尽可能少的查询数量的未知标签的可靠恢复，我们考虑了一个有效的查询类型，要求“组属性”的一个选定的子集的对象。特别是，我们考虑的问题，分类$m$二进制标签与XOR查询，询问是否有一个给定的属性在所选择的子集大小$d$的对象的数量是偶数或奇数。子集大小$d$，我们称之为查询度，可以随查询而变化。我们考虑一个一般的噪声模型，其中查询的答案的准确性的变化取决于工人（数据提供者）和查询度$d$。对于这个一般的模型，我们的特征信息理论的最佳数量的查询，可靠地恢复$m$标签的程度$d$查询和噪声参数的组合方面的限制。此外，我们提出了一个有效的推理算法，即使在噪声参数是未知的，达到这一限制。
英文摘要：
We consider a query-based data acquisition problem for binary classification of unknown labels, which has diverse applications in communications, crowdsourcing, recommender systems and active learning. To ensure reliable recovery of unknown labels with as few number of queries as possible, we consider an effective query type that asks "group attribute" of a chosen subset of objects. In particular, we consider the problem of classifying $m$ binary labels with XOR queries that ask whether the number of objects having a given attribute in the chosen subset of size $d$ is even or odd. The subset size $d$, which we call query degree, can be varying over queries. We consider a general noise model where the accuracy of answers on queries changes depending both on the worker (the data provider) and query degree $d$. For this general model, we characterize the information-theoretic limit on the optimal number of queries to reliably recover $m$ labels in terms of a given combination of degree-$d$ queries and noise parameters. Further, we propose an efficient inference algorithm that achieves this limit even when the noise parameters are unknown.
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