# Fisher-Pitman permutation tests based on nonparametric Poisson mixtures with application to single cell genomics

arXiv: https://arxiv.org/abs/2106.03022 · HTML: https://mlsanity.com/paper/2106.03022/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 103 references that are in the map.
- First posted on arXiv 6 Jun 2021.

## Builds on (most cited first, 9 of 9)

- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation](https://mlsanity.com/paper/1909.08733/) (2019)
- [On the nonparametric maximum likelihood estimator for Gaussian location mixture densities with application to Gaussian denoising](https://mlsanity.com/paper/1712.02009/) (2017)
- [Self-regularizing Property of Nonparametric Maximum Likelihood Estimator in Mixture Models](https://mlsanity.com/paper/2008.08244/) (2020)
- [Maximum Likelihood Estimation for Learning Populations of Parameters](https://mlsanity.com/paper/1902.04553/) (2019)
- [A Multivariate Poisson-Log Normal Mixture Model for Clustering Transcriptome Sequencing Data](https://mlsanity.com/paper/1711.11190/) (2017)
- [BNP-Seq: Bayesian Nonparametric Differential Expression Analysis of Sequencing Count Data](https://mlsanity.com/paper/1608.03991/) (2016)
- [On the Competitive Analysis and High Accuracy Optimality of Profile Maximum Likelihood](https://mlsanity.com/paper/2004.03166/) (2020)

## Built on by (most cited first, 1 of 1)

- [Nonparametric mixture MLEs under Gaussian-smoothed optimal transport distance](https://mlsanity.com/paper/2112.02421/) (2021)

## Abstract (arXiv)

This paper investigates the theoretical and empirical performance of Fisher-Pitman-type permutation tests for assessing the equality of unknown Poisson mixture distributions. Building on nonparametric maximum likelihood estimators (NPMLEs) of the mixing distribution, these tests are theoretically shown to be able to adapt to complicated unspecified structures of count data and also consistent against their corresponding ANOVA-type alternatives; the latter is a result in parallel to classic claims made by Robinson (Robinson, 1973). The studied methods are then applied to a single-cell RNA-seq data obtained from different cell types from brain samples of autism subjects and healthy controls; empirically, they unveil genes that are differentially expressed between autism and control subjects yet are missed using common tests. For justifying their use, rate optimality of NPMLEs is also established in settings similar to nonparametric Gaussian (Wu and Yang, 2020a) and binomial mixtures (Tian et al., 2017; Vinayak et al., 2019).