Binomial Mixture Model With U-shape Constraint

Abstract

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 = Ω(n 2 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.

Towards Robust Off-policy Learning for Runtime Uncertainty

“…The observed response or reward Y may well be contaminated during the collection of large datasets, which is referred to as noisy label learning (Natarajan et al 2013;Northcutt, Jiang, and Chuang 2021;Zheng et al 2020;Ghosh, Kumar, and Sastry 2017). In addition, the field of measurement error concerns the case where there exist some errors in measuring the covariates X, or X is blurred by some systematic noise (Neumayer and Plümper 2017;Blackwell, Honaker, and King 2017;Ye and Bickel 2021). Most studies in this venue focus on recovering the true underlying distribution f 0 (X, Y ) given the noisy observed training distribution f train (X, Y ).…”

Towards Robust Off-Policy Learning for Runtime Uncertainty

“…The observed response or reward Y may well be contaminated during the collection of large datasets, which is referred to as noisy label learning (Natarajan et al 2013;Northcutt, Jiang, and Chuang 2021;Zheng et al 2020;Ghosh, Kumar, and Sastry 2017). In addition, the field of measurement error concerns the case where there exist some errors in measuring the covariates X, or X is blurred by some systematic noise (Neumayer and Plümper 2017;Blackwell, Honaker, and King 2017;Ye and Bickel 2021). Most studies in this venue focus on recovering the true underlying distribution f 0 (X, Y ) given the noisy observed training distribution f train (X, Y ).…”