# A Locally Adaptive Algorithm for Multiple Testing with Network Structure

arXiv: https://arxiv.org/abs/2203.11461 · HTML: https://mlsanity.com/paper/2203.11461/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 22 Mar 2022.

## Builds on (most cited first, 10 of 10)

- [Parsimonious Tensor Response Regression](https://mlsanity.com/paper/1501.07815/) (2015)
- [Structured Matrix Completion with Applications to Genomic Data Integration](https://mlsanity.com/paper/1504.01823/) (2015)
- [AdaPT: An interactive procedure for multiple testing with side information](https://mlsanity.com/paper/1609.06035/) (2016)
- [Multiple testing with the structure adaptive Benjamini-Hochberg algorithm](https://mlsanity.com/paper/1606.07926/) (2016)
- [A unified treatment of multiple testing with prior knowledge using the p-filter](https://mlsanity.com/paper/1703.06222/) (2017)
- [Covariate powered cross-weighted multiple testing](https://mlsanity.com/paper/1701.05179/) (2017)
- [Weighted False Discovery Rate Control in Large-Scale Multiple Testing](https://mlsanity.com/paper/1508.01605/) (2015)
- [STAR: A general interactive framework for FDR control under structural constraints](https://mlsanity.com/paper/1710.02776/) (2017)
- [The Control of the False Discovery Rate in Fixed Sequence Multiple Testing](https://mlsanity.com/paper/1611.03146/) (2016)
- [Heterocedasticity-Adjusted Ranking and Thresholding for Large-Scale Multiple Testing](https://mlsanity.com/paper/1910.08107/) (2019)

## Built on by (most cited first, 2 of 2)

- [Integrative conformal p-values for powerful out-of-distribution testing with labeled outliers](https://mlsanity.com/paper/2208.11111/) (2022)
- [Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithm](https://mlsanity.com/paper/2310.08798/) (2023)

## Abstract (arXiv)

Incorporating auxiliary information alongside primary data can significantly enhance the accuracy of simultaneous inference. However, existing multiple testing methods face challenges in efficiently incorporating complex side information, especially when it differs in dimension or structure from the primary data, such as network side information. This paper introduces a locally adaptive structure learning algorithm (LASLA), a flexible framework designed to integrate a broad range of auxiliary information into the inference process. Although LASLA is specifically motivated by the challenges posed by network-structured data, it also proves highly effective with other types of side information, such as spatial locations and multiple auxiliary sequences. LASLA employs a p-value weighting approach, leveraging structural insights to derive data-driven weights that prioritize the importance of different hypotheses. Our theoretical analysis demonstrates that LASLA asymptotically controls the false discovery rate (FDR) under independent or weakly dependent p-values, and achieves enhanced power in scenarios where the auxiliary data provides valuable side information. Simulation studies are conducted to evaluate LASLA's numerical performance, and its efficacy is further illustrated through two real-world applications.