Large-scale inference with block structure
具有块结构的大规模统计推断AI 解读 ↓
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具有块结构的大规模统计推断
- 研究问题
- 大量数据中的微弱稀疏信号若聚集于多个小块，能否利用这种结构改善检测能力，并适应未知的块结构？
- 方法与思路
- 作者允许块数和块长随样本量按多项式增长，推导单变量、多变量及网络簇检测的边界，并构造自适应方法。
- 材料陈述的贡献
- 摘要称该框架涵盖无结构稀疏检测与单区间扫描，并可在存在结构时达到最优自适应检测、无结构时不付出显著代价。
- 阅读关注点
- 应核对信号与噪声模型、块的位置及重叠限制、检测边界和自适应最优性的定义，并查验信号强度的原始表达。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，不能推断刊本变化。速率文字可能丢失数学格式，需查原PDF，不能外推具体增益。
原文摘要
The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale multiple testing that is inherent in these problems. Here, we show that fundamentally more powerful statistical inference is possible when there is some structure in the signal that can be exploited, for example, if the signal is clustered in many small blocks, as is the case in some relevant applications. We derive the detection boundary in such a situation where we allow both the number of blocks and the block length to grow polynomially with sample size. We derive these results both for the univariate and the multivariate settings as well as for the problem of detecting clusters in a network. These results recover as special cases the sparse signal detection problem (Ann. Statist. 32 (2004) 962–994) where there is no structure in the signal, as well as the scan problem (Statist. Sinica 23 (2013) 409–428) where the signal comprises a single interval. We develop methodology that allows optimal adaptive detection in the general setting, thus exploiting the structure if it is present without incurring a relevant penalty in the case where there is no structure. The advantage of this methodology can be considerable, as in the case of no structure the means need to increase at the rate logn to ensure detection, while the presence of structure allows detection even if the means decrease at a polynomial rate.