Mixture of linear regressions is a popular learning theoretic model that is used widely to represent heterogeneous data. In the simplest form, this model assumes that the labels are generated from either of two different linear models and mixed together. Recent works of Yin et al. and Krishnamurthy et al., 2019, focus on an experimental design setting of model recovery for this problem. It is assumed that the features can be designed and queried with to obtain their label. When queried, an oracle randomly selects one of the two different sparse linear models and generates a label accordingly. How many such oracle queries are needed to recover both of the models simultaneously? This question can also be thought of as a generalization of the well-known compressed sensing problem (Cand\`es and Tao, 2005, Donoho, 2006). In this work, we address this query complexity problem and provide efficient algorithms that improves on the previously best known results.

中文翻译：

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从混合线性样本中恢复稀疏信号

混合线性回归是一种流行的学习理论模型，广泛用于表示异构数据。在最简单的形式中，该模型假设标签是从两个不同的线性模型中的任何一个生成并混合在一起的。尹等人的近期作品。和 Krishnamurthy 等人，2019 年，专注于针对此问题的模型恢复的实验设计设置。假设可以设计和查询特征以获得它们的标签。查询时，预言机随机选择两个不同的稀疏线性模型之一，并相应地生成标签。同时恢复两个模型需要多少这样的 oracle 查询？这个问题也可以被认为是对著名的压缩感知问题的概括（Cand\`es 和 Tao，2005，Donoho，2006）。在这项工作中，