# Binomial Mixture Model With U-shape Constraint

arXiv: https://arxiv.org/abs/2107.13756 · HTML: https://mlsanity.com/paper/2107.13756/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2021.

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

- [Towards Robust Off-policy Learning for Runtime Uncertainty](https://mlsanity.com/paper/2202.13337/) (2022)

## Abstract (arXiv)

In this article, we study the binomial mixture model under the regime that the binomial size m can be relatively large compared to the sample size n. This project is motivated by the GeneFishing method (Liu et al., 2019), whose output is a combination of the parameter of interest and the subsampling noise. To tackle the noise in the output, we utilize the observation that the density of the output has a U shape and model the output with the binomial mixture model under a U shape constraint. We first analyze the estimation of the underlying distribution F in the binomial mixture model under various conditions for F. Equipped with these theoretical understandings, we propose a simple method Ucut to identify the cutoffs of the U shape and recover the underlying distribution based on the Grenander estimator (Grenander, 1956). It has been shown that when m = Omega(n2/3), the identified cutoffs converge at the rate O(n-1/3). The L1 distance between the recovered distribution and the true one decreases at the same rate. To demonstrate the performance, we apply our method to varieties of simulation studies, a GTEX dataset used in (Liu et al., 2019) and a single cell dataset from Tabula Muris.