We are analyzing https://link.springer.com/article/10.1007/s11222-025-10644-4.

Title:
DGP-LVM: Derivative Gaussian process latent variable models | Statistics and Computing
Description:
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.
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Keywords {🔍}

left, full, fracdelta, latent, mathbb, eleft, hyperparameters, delta, article, effects, derivative, varying, outputs, scenario, data, gaussian, inputs, fig, size, image, correlated, alpha, derivatives, scaled, information, model, xjrho, including, google, scholar, version, recovery, main, process, models, nature, matern, quad, variable, exp, interaction, assuming, singlecell, plots, covariance, systems, text, fracsqrtxi, research, statistics,

Topics {✒️}

single-cell rna-seq data cohort-wide differential expression frac{\delta }{\delta x_j}\left frac{\delta }{\delta x_i}y_i frac{\delta }{\delta x_i}\left single-cell rna-sequencing hierarchical bayesian modelling single-cell pseudotime inference stochastic gene expression stochastic variational inference frac{\delta }{\delta single-cell rna month download article/chapter $$\begin{aligned} \text {cov} gaussian process models gaussian process model single-cell data single-cell proteogenomics related subjects sparse gaussian processes real-world case study k_{10}&= \frac{\delta k_{01}&= \frac{\delta scaling gaussian processes bayesian multilevel models supporting soham mukherjee latent variable samples simulation-based inference full article pdf privacy choices/manage cookies cell fate decisions generalizing rna velocity rna velocity fields holds exclusive rights transient cell states high dimensional data latent inputs fig model evaluation plots exact derivative information derivative covariance functions check access inducing variables instant access scrna sequencing data gaussian processes specific derivative forms } \end{aligned}$$ fig tail ess plots multiple output dimensions machine learning research

Schema {🗺️}

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            Statistical Theory and Methods
            Probability and Statistics in Computer Science
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