Full Citation

Title: Modeling Trends In Distributions

Citation Type: Miscellaneous

Publication Year: 2015

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Abstract: We present a nonparametric framework to model an evolving sequence of probability distributions that vary both due to underlying effects of sequential progression and confounding noise. To distinguish between these two types of variation and estimate the sequential-progression effects, our approach leverages an assumption that these effects follow a persistent trend. This work is motivated by the recent rise of single-cell RNAsequencing time course experiments, which aim to identify genes relevant to the progression of a particular biological process across diverse cell populations. While classical statistical tools focus on scalar-response regression or order-agnostic differences between distributions, it is desirable in this setting to consider both the full distributions as well as the structure imposed by their ordering. We introduce a new regression model for ordinal covariates where responses are univariate distributions and the underlying relationship reflects coherent changes in the distributions over increasing levels of the covariate, a concept we formalize as trends in distributions. Implemented via a fast alternating projections algorithm, our method exhibits numerous strengths in simulations and application to single-cell gene-expression data. Additionally, we characterize theoretical properties of the proposed estimators and the generality of our trends-assumption.

Url: http://arxiv.org/pdf/1511.04486.pdf

User Submitted?: No

Authors: Mueller, Jonas; Jaakola, Tommi; Gifford, David

Publisher: MIT Computer Science and Artificial Intelligence Laboratory

Data Collections: IPUMS USA

Topics: Other

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