DGP-LVM: Derivative Gaussian process latent variable models

Fuente: arXiv
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Autores principales: Mukherjee, Soham, Claassen, Manfred, Bürkner, Paul-Christian
Formato: Preprint
Publicado: 2024
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author Mukherjee, Soham
Claassen, Manfred
Bürkner, Paul-Christian
author_facet Mukherjee, Soham
Claassen, Manfred
Bürkner, Paul-Christian
contents We develop a framework for derivative Gaussian process latent variable models (DGP-LVMs) that can handle multi-dimensional output data using modified derivative covariance functions. The modifications account for complexities in the underlying data generating process such as scaled derivatives, varying information across multiple output dimensions as well as interactions between outputs. Further, our framework provides uncertainty estimates for each latent variable samples using Bayesian inference. Through extensive simulations, we demonstrate that latent variable estimation accuracy can be drastically increased by including derivative information due to our proposed covariance function modifications. The developments are motivated by a concrete biological research problem involving the estimation of the unobserved cellular ordering from single-cell RNA (scRNA) sequencing data for gene expression and its corresponding derivative information known as RNA velocity. Since the RNA velocity is only an estimate of the exact derivative information, the derivative covariance functions need to account for potential scale differences. In a real-world case study, we illustrate the application of DGP-LVMs to such scRNA sequencing data. While motivated by this biological problem, our framework is generally applicable to all kinds of latent variable estimation problems involving derivative information irrespective of the field of study.
format Preprint
id arxiv_https___arxiv_org_abs_2404_04074
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle DGP-LVM: Derivative Gaussian process latent variable models
Mukherjee, Soham
Claassen, Manfred
Bürkner, Paul-Christian
Methodology
We develop a framework for derivative Gaussian process latent variable models (DGP-LVMs) that can handle multi-dimensional output data using modified derivative covariance functions. The modifications account for complexities in the underlying data generating process such as scaled derivatives, varying information across multiple output dimensions as well as interactions between outputs. Further, our framework provides uncertainty estimates for each latent variable samples using Bayesian inference. Through extensive simulations, we demonstrate that latent variable estimation accuracy can be drastically increased by including derivative information due to our proposed covariance function modifications. The developments are motivated by a concrete biological research problem involving the estimation of the unobserved cellular ordering from single-cell RNA (scRNA) sequencing data for gene expression and its corresponding derivative information known as RNA velocity. Since the RNA velocity is only an estimate of the exact derivative information, the derivative covariance functions need to account for potential scale differences. In a real-world case study, we illustrate the application of DGP-LVMs to such scRNA sequencing data. While motivated by this biological problem, our framework is generally applicable to all kinds of latent variable estimation problems involving derivative information irrespective of the field of study.
title DGP-LVM: Derivative Gaussian process latent variable models
topic Methodology
url https://arxiv.org/abs/2404.04074